32S12-4,8,8-g9

graph data
Name 32S12-4,8,8-g9
Type Hyperbolic
Degree 32
Genus 9
Galois orbit size for 32S12-4,8,8-g9-path1 1
Galois orbit size for 32S12-4,8,8-g9-path10 1
Galois orbit size for 32S12-4,8,8-g9-path11 1
Galois orbit size for 32S12-4,8,8-g9-path12 1
Galois orbit size for 32S12-4,8,8-g9-path13 1
Galois orbit size for 32S12-4,8,8-g9-path14 1
Galois orbit size for 32S12-4,8,8-g9-path15 1
Galois orbit size for 32S12-4,8,8-g9-path16 1
Galois orbit size for 32S12-4,8,8-g9-path17 1
Galois orbit size for 32S12-4,8,8-g9-path18 1
Galois orbit size for 32S12-4,8,8-g9-path19 1
Galois orbit size for 32S12-4,8,8-g9-path2 1
Galois orbit size for 32S12-4,8,8-g9-path20 1
Galois orbit size for 32S12-4,8,8-g9-path21 1
Galois orbit size for 32S12-4,8,8-g9-path22 1
Galois orbit size for 32S12-4,8,8-g9-path23 1
Galois orbit size for 32S12-4,8,8-g9-path24 1
Galois orbit size for 32S12-4,8,8-g9-path25 1
Galois orbit size for 32S12-4,8,8-g9-path26 1
Galois orbit size for 32S12-4,8,8-g9-path27 1
Galois orbit size for 32S12-4,8,8-g9-path28 1
Galois orbit size for 32S12-4,8,8-g9-path29 1
Galois orbit size for 32S12-4,8,8-g9-path3 1
Galois orbit size for 32S12-4,8,8-g9-path30 1
Galois orbit size for 32S12-4,8,8-g9-path31 1
Galois orbit size for 32S12-4,8,8-g9-path32 1
Galois orbit size for 32S12-4,8,8-g9-path33 1
Galois orbit size for 32S12-4,8,8-g9-path34 1
Galois orbit size for 32S12-4,8,8-g9-path35 1
Galois orbit size for 32S12-4,8,8-g9-path36 1
Galois orbit size for 32S12-4,8,8-g9-path37 1
Galois orbit size for 32S12-4,8,8-g9-path38 1
Galois orbit size for 32S12-4,8,8-g9-path39 1
Galois orbit size for 32S12-4,8,8-g9-path4 1
Galois orbit size for 32S12-4,8,8-g9-path40 1
Galois orbit size for 32S12-4,8,8-g9-path41 1
Galois orbit size for 32S12-4,8,8-g9-path42 1
Galois orbit size for 32S12-4,8,8-g9-path43 1
Galois orbit size for 32S12-4,8,8-g9-path44 1
Galois orbit size for 32S12-4,8,8-g9-path45 1
Galois orbit size for 32S12-4,8,8-g9-path46 1
Galois orbit size for 32S12-4,8,8-g9-path5 1
Galois orbit size for 32S12-4,8,8-g9-path6 1
Galois orbit size for 32S12-4,8,8-g9-path7 1
Galois orbit size for 32S12-4,8,8-g9-path8 1
Galois orbit size for 32S12-4,8,8-g9-path9 1
Passport size 2
Pointed size 2

Above

64S17-4,8,8-g17 64S45-8,16,16-g25 64S45-4,16,16-g21 64S44-8,16,16-g25 64S15-8,8,8-g21 64S16-8,8,8-g21 64S44-4,16,16-g21

Below

16T6-4,8,8-g5 16T5-2,8,8-g3 16T6-2,8,8-g3 16T8-4,4,4-g3 16T5-4,8,8-g5

Belyi Curve 1: 32S12-4,8,8-g9-path1

\(1/281487861809153(4278190080\nu^{6} + 4278190080\nu^{2)}x_{1}^{3}x_{2} + 1/18447869999386460161(-551963259305984\nu^{6} + 551963259305984\nu^{2} + 558560496844800)x_{1}^{2}x_{2} + 1/79235416345888816038194577409(21054569610382291398295552\nu^{6} - 21054569610382291398295552\nu^{2} - 7192974947147434285858816)x_{1}^{2}x_{3}^{2} + 1/1209018056149790439571457(-15925501238519529472\nu^{6} - 144119709302029025280\nu^{4} - 15925501238519529472\nu^{2)}x_{1}x_{2} + 1/79235416345888816038194577409(7767832056147431315734528\nu^{6} + 19402720077142142425759744\nu^{4} + 7767832056147431315734528\nu^{2)}x_{1}x_{3}^{2} + x_{2}^{2}x_{3}^{6} - 256/65537x_{2}^{2}x_{3}^{2} + 1/1209018056149790439571457(5486369061334765535232\nu^{6} - 5486369061334765535232\nu^{2} - 52668503024568429969408)x_{2}x_{3}^{4} + 1/1209018056149790439571457(83926972417448083456\nu^{6} - 83926972417448083456\nu^{2} + 64133220239679684608)x_{2} + 1/79235416345888816038194577409(-5978036496363717444763648\nu^{6} + 5978036496363717444763648\nu^{2} + 9809224498993725739892736)x_{3}^{2}\)
\(1/1095250084095(18119655424\nu^{6} + 18119655424\nu^{2)}x_{1}^{2}x_{3}^{2} + x_{1}x_{2}x_{3}^{4} - 256/65537x_{1}x_{2} + 1/1095250084095(-3760193536\nu^{6} + 3760193536\nu^{2)}x_{1}x_{3}^{2} + 1/16711935(8323200\nu^{6} + 32895494\nu^{4} + 8323200\nu^{2)}x_{2}x_{3}^{4} + 1/1095250084095(2130739200\nu^{6} - 8421246464\nu^{4} + 2130739200\nu^{2)}x_{2} + 1/1095250084095(-3225419776\nu^{6} - 3225419776\nu^{2)}x_{3}^{2}\)
\(x_{1}^{3}x_{3}^{2} - 502/255\nu^{4}x_{1}^{2}x_{3}^{2} + 32/255x_{1}x_{3}^{2} + 1/33423360(-4295098369\nu^{6} - 4295098369\nu^{2)}x_{2}x_{3}^{4} + 1/130560(65537\nu^{6} + 65537\nu^{2)}x_{2} - 32/255\nu^{4}x_{3}^{2}\)
\(x_{1}^{4} + 1/65537(-32640\nu^{6} - 16\nu^{4} - 32640\nu^{2)}x_{1}^{3} + 1/65537(64256\nu^{6} - 64256\nu^{2} - 16480)x_{1}^{2} + 1/65537(-4096\nu^{6} + 65792\nu^{4} - 4096\nu^{2)}x_{1} - 65537/256x_{2}x_{3}^{2} + 1/65537(4096\nu^{6} - 4096\nu^{2} + 65792)\)

Belyi Curve 1 Base Field: \(\nu^{8}+1\), discriminant [ <2, 24> ]

Belyi Curve 1 Degree: 20

Belyi Curve 1 Naive Measure: 237709876110283053358479637000

Belyi Map 1 Numerator:

\(4295098369/16777216x_{2}^{2}\)

Belyi Map 1 Denominator:

\(1/1209018056149790439571457(-228847940090384734027776\nu^{6} + 1082241703329537856692224\nu^{4} - 228847940090384734027776\nu^{2)}x_{1}^{3} + 1/1209018056149790439571457(306666382115591569145856\nu^{6} - 306666382115591569145856\nu^{2} + 2036916306678810331889664)x_{1}^{2} + 1/3180448086123866908892017358667073536000000(-12655914695072498634309241394104002379952725964379944\nu^{6} - 16232529504732635368081004723628699208313889265813745\nu^{4} - 12655914695072498634309241394104002379952725964379944\nu^{2)}x_{1}x_{3}^{16} + 1/6211812668210677556429721403646628000000(147562705769716251268536189788093793338589259800\nu^{6} + 332117618009110481901893960169425237457142333907\nu^{4} + 147562705769716251268536189788093793338589259800\nu^{2)}x_{1}x_{3}^{12} + 1/48529786470395918409607198465989281250(1410690109973914056958542149409668140689176\nu^{6} + 587602658043992839169961833981594638900495\nu^{4} + 1410690109973914056958542149409668140689176\nu^{2)}x_{1}x_{3}^{8} + 1/1348774395969140454661121(4136703697140133734121472\nu^{6} - 69454784907410297117474816\nu^{4} + 4136703697140133734121472\nu^{2)}x_{1}x_{3}^{4} + 1/1209018056149790439571457(-70826201928862388977664\nu^{6} - 2011323254710205744545792\nu^{4} - 70826201928862388977664\nu^{2)}x_{1} + 1/122557010170133000345700573455085104761121862198658717408296960000000(86770716176767415711459494690009536269718366877910766210774546117514906129952341784\nu^{6} - 86770716176767415711459494690009536269718366877910766210774546117514906129952341784\nu^{2} - 181311022671795421034347118706785250318387142155132120444728875367669666166499783921)x_{2}^{3}x_{3}^{22} + 1/478738320977082032600392865058926190473132274213510614876160000000(-4225810306369154924659475668809323054030754906216289511045138357245656076966760\nu^{6} + 4225810306369154924659475668809323054030754906216289511045138357245656076966760\nu^{2} + 8412962934469287414319157415221534105127995055614147613293736656991123953382099)x_{2}^{3}x_{3}^{18} + 1/935035783158363344922642314568215215767836473073262919680000000(27948202555635934502043680751719129866437602465034509275253745521385192280\nu^{6} - 27948202555635934502043680751719129866437602465034509275253745521385192280\nu^{2} - 45671966847018276840945070682925052630758760892982048961593610882001722609)x_{2}^{3}x_{3}^{14} + 1/3652483527962356816104071541282090686593111222942433280000000(130969667342613182822449638279399748461805858284955205946885943551160\nu^{6} - 130969667342613182822449638279399748461805858284955205946885943551160\nu^{2} - 564959249705885792174536159157246942346786849651176994428882591267057)x_{2}^{3}x_{3}^{10} + 1/28535027562205912625813058916266333489008681429237760000000(-10503815479179684144578306546243661246474316438147386221024609480\nu^{6} + 10503815479179684144578306546243661246474316438147386221024609480\nu^{2} + 27874433891217719666720448797316483149427374715421895458191068883)x_{2}^{3}x_{3}^{6} + 1/111464951414866846194582261391665365191440161832960000000(58010659395697986480458525394156899495149546109442099978488\nu^{6} - 58010659395697986480458525394156899495149546109442099978488\nu^{2} - 143822284511295000583544490480199931829838696939889924595953)x_{2}^{3}x_{3}^{2} + 1/1826241763981178408052035770641045343296555611471216640000000(-9903256814401738964000793674913847024430833252190575013880739106566652152\nu^{6} + 9903256814401738964000793674913847024430833252190575013880739106566652152\nu^{2} + 28670861395827862405330805524187027464617292026450292463513326933028095729)x_{2}^{2}x_{3}^{20} + 1/1783439222637869539113316182266645843063042589327360000000(-957655902713867308769823535618084792991051889513853956709498320939152\nu^{6} + 957655902713867308769823535618084792991051889513853956709498320939152\nu^{2} + 1289375434278265981267587044903376936309293886872877588913239388584945)x_{2}^{2}x_{3}^{16} + 1/13933118926858355774322782673958170648930020229120000000(17655446617567536749586320785456671743702482358200649284254863400\nu^{6} - 17655446617567536749586320785456671743702482358200649284254863400\nu^{2} - 40648579842730365060710908645333284209376158320099169812676313781)x_{2}^{2}x_{3}^{12} + 1/27213122904020226121724184910074552048691445760000000(83664675904468459738030791658959001923996047383677690439808\nu^{6} - 83664675904468459738030791658959001923996047383677690439808\nu^{2} + 9264234431482751201463766788149464413902942027259044805105)x_{2}^{2}x_{3}^{8} + 1/425205045375316033151940389219914875760803840000000(-1144764751468946475750316788931939447127417170403942168\nu^{6} + 1144764751468946475750316788931939447127417170403942168\nu^{2} + 3287479982624268875481457892970170838119630886218178289)x_{2}^{2}x_{3}^{4} + 1/10495818331107268362240(1258264614492595126352\nu^{6} - 1258264614492595126352\nu^{2} + 2649508534780624160495353)x_{2}^{2} + 1/54426245808040452243448369820149104097382891520000000(26161887348041510032966868885744758644997120846341300487929310776\nu^{6} - 26161887348041510032966868885744758644997120846341300487929310776\nu^{2} - 40951865853513469522717868068731761465712196535823622222418164465)x_{2}x_{3}^{18} + 1/212602522687658016575970194609957437880401920000000(-396716315680079833966720281017498256116311833865568881101912\nu^{6} + 396716315680079833966720281017498256116311833865568881101912\nu^{2} - 20284076641888507600100262021140136112797280365385279114391)x_{2}x_{3}^{14} + 1/830478604248664127249883572695146241720320000000(14110034811813116012985917351453838322375839251318680776\nu^{6} - 14110034811813116012985917351453838322375839251318680776\nu^{2} - 18805615198613214502485526529935948252746437638004155543)x_{2}x_{3}^{10} + 1/3244057047846344247069857705840415006720000000(20105543072979772264568440696443204316154345026008\nu^{6} - 20105543072979772264568440696443204316154345026008\nu^{2} - 68510619720609857169108437402554289146129579262705)x_{2}x_{3}^{6} + 1/1325919413829443369656888304655(-24500450883869293821053168476928\nu^{6} + 24500450883869293821053168476928\nu^{2} - 79871470653247553154859425680568)x_{2}x_{3}^{2} + 1/202753565490396515441866106615025937920000000(264353172068071612909482648555841759810103683236704956\nu^{6} - 264353172068071612909482648555841759810103683236704956\nu^{2} - 223903699467109290607680545627886746411111207194941263)x_{3}^{16} + 1/264002038398953796148263159654981690000000(-4223037064063896855514373731007615356124631760200\nu^{6} + 4223037064063896855514373731007615356124631760200\nu^{2} + 9514132750912655330822291586399034043920830970393)x_{3}^{12} + 1/6187547774975479597224917804413633359375(-145917415033503788660000871706878418120586648\nu^{6} + 145917415033503788660000871706878418120586648\nu^{2} + 169222010161050536222595323359130230150261346)x_{3}^{8} + 1/343937470972130815938585855(-859704087821715946111762432\nu^{6} + 859704087821715946111762432\nu^{2} - 8348624898698737768665448448)x_{3}^{4} + 1/1209018056149790439571457(61972007972672030900224\nu^{6} - 61972007972672030900224\nu^{2} - 869427853338698299146240)\)

Belyi Curve 2: 32S12-4,8,8-g9-path15

\(1/68769820673(-16640\nu^{3} + 16640\nu )x_{1}^{3}x_{2} + 1/281749955297281(84168768\nu^{3} + 84168768\nu - 34611200)x_{1}^{2}x_{2} + 1/4729288235396578172929(-1362245842944\nu^{3} - 1362245842944\nu - 1686592651264)x_{1}^{2}x_{3}^{2} + 1/1154329566852960257(119508246528\nu^{3} - 66607124480\nu^{2} - 119508246528\nu )x_{1}x_{2} + 1/4729288235396578172929(-1828902797312\nu^{3} - 1152525565952\nu^{2} + 1828902797312\nu )x_{1}x_{3}^{2} + x_{2}^{2}x_{3}^{6} - 4/4097x_{2}^{2}x_{3}^{2} + 1/1154329566852960257(-3552920630784\nu^{3} - 3552920630784\nu + 16839143284928)x_{2}x_{3}^{4} + 1/67901739226644721(-1119529984\nu^{3} - 1119529984\nu - 521236736)x_{2} + 1/4729288235396578172929(529115807744\nu^{3} + 529115807744\nu + 186075580416)x_{3}^{2}\)
\(1/1091051585(-12804\nu^{3} + 12804\nu )x_{1}^{2}x_{3}^{2} + x_{1}x_{2}x_{3}^{4} - 4/4097x_{1}x_{2} + 1/1091051585(14592\nu^{3} + 14592\nu )x_{1}x_{3}^{2} + 1/1065220(-135200\nu^{3} + 814783\nu^{2} + 135200\nu )x_{2}x_{3}^{4} + 1/1091051585(-135200\nu^{3} - 814783\nu^{2} + 135200\nu )x_{2} + 1/1091051585(3904\nu^{3} - 3904\nu )x_{3}^{2}\)
\(x_{1}^{3}x_{3}^{2} + 321/260\nu^{2}x_{1}^{2}x_{3}^{2} - 32/65x_{1}x_{3}^{2} + 1/8320(-16785409\nu^{3} + 16785409\nu )x_{2}x_{3}^{4} + 1/2080(4097\nu^{3} - 4097\nu )x_{2} - 4/65\nu^{2}x_{3}^{2}\)
\(x_{1}^{4} + 1/4097(520\nu^{3} + 8192\nu^{2} - 520\nu )x_{1}^{3} + 1/4097(-642\nu^{3} - 642\nu - 6080)x_{1}^{2} + 1/4097(-256\nu^{3} - 2016\nu^{2} + 256\nu )x_{1} - 4097/4x_{2}x_{3}^{2} + 1/4097(32\nu^{3} + 32\nu + 252)\)

Belyi Curve 2 Base Field: \(\nu^{4}+1\), discriminant [ <2, 8> ]

Belyi Curve 2 Degree: 20

Belyi Curve 2 Naive Measure: 14190241548885774298254

Belyi Map 2 Numerator:

\(16785409/16384x_{2}^{2}\)

Belyi Map 2 Denominator:

\(1/4617318267411841028(895598240249916\nu^{3} + 1753053109826887\nu^{2} - 895598240249916\nu )x_{1}^{3} + 1/18469273069647364112(-4584073964370548\nu^{3} - 4584073964370548\nu - 8337310365585351)x_{1}^{2} + 1/196502809010845952212046592000000(753153088295857593693032320843690556772\nu^{3} + 3673394681351911662111761204708789282645\nu^{2} - 753153088295857593693032320843690556772\nu )x_{1}x_{3}^{16} + 1/24562851126355744026505824000000(-813782292101417926026076602346727100\nu^{3} - 38456045259122508477342692413816127\nu^{2} + 813782292101417926026076602346727100\nu )x_{1}x_{3}^{12} + 1/4093808521059290671084304000000(35997345318962045079662325917164\nu^{3} - 88284145478233057738587786292665\nu^{2} - 35997345318962045079662325917164\nu )x_{1}x_{3}^{8} + 1/781538754050033921(-412448600557728\nu^{3} + 7296997155394588\nu^{2} + 412448600557728\nu )x_{1}x_{3}^{4} + 1/18469273069647364112(-1963111456116736\nu^{3} - 3524983341394561\nu^{2} + 1963111456116736\nu )x_{1} + 1/13393128414988192337135432871444480000000(-183206516611713397247265149008786084132216466531426035041411268\nu^{3} - 183206516611713397247265149008786084132216466531426035041411268\nu - 96480026267667567665319740614807705548912496283125471478063019)x_{2}^{3}x_{3}^{22} + 1/3348282103747048084283858217861120000000(139345300827662139310892697335710631126939224628460275361020\nu^{3} + 139345300827662139310892697335710631126939224628460275361020\nu + 112513409761008349202484250721085860149506572045922318202881)x_{2}^{3}x_{3}^{18} + 1/139511754322793670178494092410880000000(-4483314683669540676213271834779887118887157172209771020\nu^{3} - 4483314683669540676213271834779887118887157172209771020\nu - 8728508357930878638674761064496333498546155372773661497)x_{2}^{3}x_{3}^{14} + 1/104633815742095252633870569308160000000(-1735820632889999308817440736365223270428211014768820\nu^{3} - 1735820632889999308817440736365223270428211014768820\nu + 6079731670145690789745946957048410909245942075501397)x_{2}^{3}x_{3}^{10} + 1/52316907871047626316935284654080000000(1648649628788269404998706012949478969177946904460\nu^{3} + 1648649628788269404998706012949478969177946904460\nu - 1407877295774035319315365277817518685110549480703)x_{2}^{3}x_{3}^{6} + 1/4359742322587302193077940387840000000(-46759716232914273723255542293678227334291292\nu^{3} - 46759716232914273723255542293678227334291292\nu + 21671261794203742137885573235613292459539911)x_{2}^{3}x_{3}^{2} + 1/209267631484190505267741138616320000000(-16548857768869795286768833805972831042820643293506630164\nu^{3} - 16548857768869795286768833805972831042820643293506630164\nu - 13734118174866456343037221866665249454617057268132259371)x_{2}^{2}x_{3}^{20} + 1/13079226967761906579233821163520000000(715479629828655835105658553443535422827315423204456\nu^{3} + 715479629828655835105658553443535422827315423204456\nu - 9647538204787821738613752374798842978194161068085355)x_{2}^{2}x_{3}^{16} + 1/6539613483880953289616910581760000000(3499715262960023963716698309770545222773040956700\nu^{3} + 3499715262960023963716698309770545222773040956700\nu + 635427166005260261235485303128979796522040190679)x_{2}^{2}x_{3}^{12} + 1/817451685485119161202113822720000000(-64165662813927275969379868198544512902065984\nu^{3} - 64165662813927275969379868198544512902065984\nu + 598690514748355704166495733938926173629469205)x_{2}^{2}x_{3}^{8} + 1/272483895161706387067371274240000000(-6409383925540723827560436922123985174252\nu^{3} - 6409383925540723827560436922123985174252\nu - 22998098628136177156840317226768000435897)x_{2}^{2}x_{3}^{4} + 1/1549536846840320(-14135994799968296\nu^{3} - 14135994799968296\nu + 1657319184211565113)x_{2}^{2} + 1/6539613483880953289616910581760000000(6302231771146007814146428993056083123620838546188\nu^{3} + 6302231771146007814146428993056083123620838546188\nu - 164770850806069950851136755257550508698751694635)x_{2}x_{3}^{18} + 1/1634903370970238322404227645440000000(-3878707189608154571098765654956766786581930076\nu^{3} - 3878707189608154571098765654956766786581930076\nu + 6131325985184726121021618242925545639341072851)x_{2}x_{3}^{14} + 1/408725842742559580601056911360000000(-878755817720954195612469168328339134097292\nu^{3} - 878755817720954195612469168328339134097292\nu - 1771494066618603264548749537781761241091117)x_{2}x_{3}^{10} + 1/34060486895213298383421409280000000(57973380007520018428074064888449236148\nu^{3} + 57973380007520018428074064888449236148\nu + 24863416109290448170565096729624369735)x_{2}x_{3}^{6} + 1/1665021423178354266655240(-1148329773315364086631216\nu^{3} - 1148329773315364086631216\nu - 1110320583517213436858553)x_{2}x_{3}^{2} + 1/12772682585704986893783028480000000(-23188888296404562964621037496449672415229\nu^{3} - 23188888296404562964621037496449672415229\nu - 102090381292454291278465072958544404095864)x_{3}^{16} + 1/6386341292852493446891514240000000(87703142132361040352001805295007607700\nu^{3} + 87703142132361040352001805295007607700\nu + 4195024913832685504942968265673542549)x_{3}^{12} + 1/266097553868853893620479760000000(-1030808425351791752294139159039873\nu^{3} - 1030808425351791752294139159039873\nu + 2451888257098113431803714309625768)x_{3}^{8} + 1/203200076053008819460(49861378728497224\nu^{3} + 49861378728497224\nu - 804180718572343367)x_{3}^{4} + 1/295508369114357825792(4418202712824832\nu^{3} + 4418202712824832\nu + 8320922350612865)\)

Belyi Curve 3: 32S12-4,8,8-g9-path17

\(-536870912/281487861809153x_{1}^{3}x_{2} + 1/18447869999386460161(211109453758464\nu - 4398046511104)x_{1}^{2}x_{2} + 1/79235416345888816038194577409(377783554022048582860800\nu + 16922526508327728459022336)x_{1}^{2}x_{3}^{2} + 1/1209018056149790439571457(3458746921634496512\nu + 36876599657406398464)x_{1}x_{2} + 1/79235416345888816038194577409(-58018699478645680252125184\nu + 1435575199440775401177088)x_{1}x_{3}^{2} + x_{2}^{2}x_{3}^{6} - 256/65537x_{2}^{2}x_{3}^{2} + 1/1209018056149790439571457(-132154493251801401262080\nu + 5754983331970573926400)x_{2}x_{3}^{4} + 1/1209018056149790439571457(479650248684711444480\nu - 2882488479470583808)x_{2} + 1/79235416345888816038194577409(-1662243026010995337199616\nu - 62852484301350030691794944)x_{3}^{2}\)
\(-41943040/4295098369x_{1}^{2}x_{3}^{2} + x_{1}x_{2}x_{3}^{4} - 256/65537x_{1}x_{2} + 167772160/4295098369\nu x_{1}x_{3}^{2} + 1/65537(393206\nu - 4096)x_{2}x_{3}^{4} + 1/4295098369(-100660736\nu - 1048576)x_{2} + 201326592/4295098369x_{3}^{2}\)
\(x_{1}^{3}x_{3}^{2} - 6\nu x_{1}^{2}x_{3}^{2} - 16x_{1}x_{3}^{2} - 4295098369/2097152x_{2}x_{3}^{4} + 65537/8192x_{2} + 16\nu x_{3}^{2}\)
\(x_{1}^{4} + 1/65537(-16\nu + 4096)x_{1}^{3} + 1/65537(-24576\nu - 96)x_{1}^{2} + 1/65537(256\nu - 65536)x_{1} - 65537/256x_{2}x_{3}^{2} + 1/65537(65536\nu + 256)\)

Belyi Curve 3 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 3 Degree: 20

Belyi Curve 3 Naive Measure: 237709876110283048994627125301

Belyi Map 3 Numerator:

\(4295098369/16777216x_{2}^{2}\)

Belyi Map 3 Denominator:

\(1/1209018056149790439571457(1056860127415873522688000\nu + 54298819971388413050880)x_{1}^{3} + 1/1209018056149790439571457(-198294717427640019451904\nu + 2111267008161106289541120)x_{1}^{2} + 1/1356079728538140278784(356037924580009071364953315830261419\nu - 11874168658730337214828848073048896)x_{1}x_{3}^{16} + 1/152218001137991680(-312252481958038637753759491841\nu + 5226732209515135007176691200)x_{1}x_{3}^{12} + 1/103460672648478720(414570349037226788675027287\nu - 54167170619845447250880)x_{1}x_{3}^{8} + 1/904080742081957724209(33427299738872446976\nu + 13430515443734709534720)x_{1}x_{3}^{4} + 1/1209018056149790439571457(-2407891072964571755839488\nu - 396567818254366011293696)x_{1} + 1/1639399797285755073653007869521289393926569984(-197482611966494330768294649625274746961969171620312022454567816877\nu + 6172617363878532786160292292146310573643066963113162124554835968)x_{2}^{3}x_{3}^{22} + 1/368040543571694296348107010937789465231360(865920442583905508529959236658868949890291201046060381967651\nu - 22036951283004348535936727387236703575824642525661185121280)x_{2}^{3}x_{3}^{18} + 1/62538139239721491762275995999194694287360(-1149544051519665671054737851834021766068150608768160706277\nu + 22579593116601149165889554363218817401250056407197429760)x_{2}^{3}x_{3}^{14} + 1/244289606405162077196390609371854274560(17540985568074396511155261878932526568441310221053669\nu - 242691258032046414148917054969306119972291138411520)x_{2}^{3}x_{3}^{10} + 1/636170850013442909365600545239203840(-89219771940308869888922051499055373661588710647\nu + 716391884084716021263074335875046634894120960)x_{2}^{3}x_{3}^{6} + 1/7455127148595034094128131389521920(816847023595502565510924858430362323257697\nu - 1816479533650177461823415645833906529280)x_{2}^{3}x_{3}^{2} + 1/48857921281032415439278121874370854912(-30709988209134828897102862825030741260119224026009126400\nu - 215637065812307947120065582624421275339201178246700450805)x_{2}^{2}x_{3}^{20} + 1/15904271250336072734140013630980096(87362552423932670036632877359495921872633214415360\nu + 1101014463932569976145619276164676545364986460477095)x_{2}^{2}x_{3}^{16} + 1/1863781787148758523532032847380480(-12674581671005217319514080427058076613315426816\nu - 757455111358754474938518896935872870789092244315)x_{2}^{2}x_{3}^{12} + 1/1213399601008306330424500551680(-58749885517197262808034766326165427496448\nu + 1284194469230200783043745068381713550405955)x_{2}^{2}x_{3}^{8} + 1/11375621259452871847729692672(1272210855499482693226635193285835264\nu - 11734471490664975150668588747615224821)x_{2}^{2}x_{3}^{4} + 1/13794756353130496(-53205329113448637\nu + 3531775394959016192)x_{2}^{2} + 1/50209638662412675741703471104(4062935103583010058643451942206340427780573691\nu - 72558896888116648557463685636324185804529664)x_{2}x_{3}^{18} + 1/28439053148632179619324231680(-26953337927588843554586522746423746920265089\nu + 461246047146572816271991765802462060221440)x_{2}x_{3}^{14} + 1/111090051361844451637985280(411231126824765732009288886803536295297\nu - 6730369329116678091699973058003404800)x_{2}x_{3}^{10} + 1/433945513132204889210880(-2092320589272918681982307334252331\nu + 32670607025043696381131980231680)x_{2}x_{3}^{6} + 1/59250739593825263371485233(75379452938771231481419776\nu - 4501865546715175861656220020)x_{2}x_{3}^{2} + 1/43394551313220488921088(571166458128825752376802594155950592\nu + 18159238658958685673091168429042819439)x_{3}^{16} + 1/423774915168168837120(-23190888648645007323448398436864\nu - 1385429217060224081234707607217963)x_{3}^{12} + 1/3310741524751319040(42839587725964666419902976\nu + 21143264877212490389049665323)x_{3}^{8} + 1/904080742081957724209(-24794792886138333822976\nu + 53019541425683955712)x_{3}^{4} + 1/1209018056149790439571457(330459731585146757840896\nu - 1199887584923845056987136)\)

Belyi Curve 4: 32S12-4,8,8-g9-path18

\(x_{1}^{4}x_{2} + 3x_{1}^{4} + x_{2}^{2} - 1\)
\(x_{1}^{2}x_{3}^{2} - x_{1}^{2} + 1/132(-\nu^{6} - 6\nu^{5} - 35\nu^{4} - 100\nu^{3} - 241\nu^{2} - 298\nu - 375)x_{3}^{2} + 1/132(-\nu^{6} - 6\nu^{5} - 35\nu^{4} - 100\nu^{3} - 241\nu^{2} - 298\nu - 375)\)
\(1/66(\nu^{6} + 6\nu^{5} + 35\nu^{4} + 100\nu^{3} + 241\nu^{2} + 298\nu + 375)x_{1}^{2}x_{2} + 1/22(\nu^{6} + 6\nu^{5} + 35\nu^{4} + 100\nu^{3} + 241\nu^{2} + 298\nu + 375)x_{1}^{2} + x_{2}^{2}x_{3}^{2} - x_{2}^{2} + 2x_{2}x_{3}^{2} + 2x_{2} + 5x_{3}^{2} + 7\)

Belyi Curve 4 Base Field: \(\nu^{8}+8\nu^{7}+44\nu^{6}+152\nu^{5}+402\nu^{4}+744\nu^{3}+1172\nu^{2}+1176\nu^{1}+657\), discriminant [ <2, 60>, <3, 4>, <7, 2>, <11, 4> ]

Belyi Curve 4 Degree: 14

Belyi Curve 4 Naive Measure: 1526

Belyi Map 4 Numerator:

\(-4x_{2}x_{3}^{8} - 4x_{2}x_{3}^{4} - 4x_{3}^{8} - 16x_{3}^{6} - 4x_{3}^{4}\)

Belyi Map 4 Denominator:

\(x_{3}^{12} + 2x_{3}^{10} - x_{3}^{8} - 4x_{3}^{6} - x_{3}^{4} + 2x_{3}^{2} + 1\)

Belyi Curve 5: 32S12-4,8,8-g9-path25

\(x_{2}x_{3}^{4} - \nu^{2}x_{2} - 2\nu^{2}x_{3}^{2}\)
\(x_{1}^{4} + \nu^{2}x_{2}x_{3}^{2} + 1\)

Belyi Curve 5 Base Field: \(\nu^{4}+1\), discriminant [ <2, 8> ]

Belyi Curve 5 Degree: 20

Belyi Curve 5 Naive Measure: 7

Belyi Map 5 Numerator:

\(4\nu^{2}x_{2}x_{3}^{2} + 4\)

Belyi Map 5 Denominator:

\(-\nu^{2}x_{2}^{2} + 2\nu^{2}x_{2}x_{3}^{2} + 4\)

Belyi Curve 6: 32S12-4,8,8-g9-path26

\(x_{2}x_{3}^{4} - \nu^{2}x_{2} - 2\nu^{2}x_{3}^{2}\)
\(x_{1}^{4} + \nu^{2}x_{2}x_{3}^{2} + 1\)

Belyi Curve 6 Base Field: \(\nu^{4}+1\), discriminant [ <2, 8> ]

Belyi Curve 6 Degree: 20

Belyi Curve 6 Naive Measure: 7

Belyi Map 6 Numerator:

\(4\nu^{2}x_{2}x_{3}^{2} + 4\)

Belyi Map 6 Denominator:

\(-\nu^{2}x_{2}^{2} + 2\nu^{2}x_{2}x_{3}^{2} + 4\)

Belyi Curve 7: 32S12-4,8,8-g9-path29

\(536870912/281462092005375\nu x_{1}^{3}x_{2} + 215501057818624/18445618199572250625x_{1}^{2}x_{2} - 52401070514315984896/239885264685437119378125x_{1}^{2}x_{3}^{2} - 157078438757269504/4703632640890923909375\nu x_{1}x_{2} + 180089941899291394048/239885264685437119378125\nu x_{1}x_{3}^{2} + x_{2}^{2}x_{3}^{6} + 256/65535x_{2}^{2}x_{3}^{2} + 31645788798976/277098404709375x_{2}x_{3}^{4} + 1877286233206423552/4703632640890923909375x_{2} + 36189800705642463232/44423197163969836921875x_{3}^{2}\)
\(-8388608/858967245\nu x_{1}^{2}x_{3}^{2} + x_{1}x_{2}x_{3}^{4} + 256/65535x_{1}x_{2} - 33554432/858967245x_{1}x_{3}^{2} + 1546/255\nu x_{2}x_{3}^{4} + 390656/16842495\nu x_{2} + 67108864/1431612075\nu x_{3}^{2}\)
\(x_{1}^{3}x_{3}^{2} - 6\nu x_{1}^{2}x_{3}^{2} - 16x_{1}x_{3}^{2} + 4294836225/2097152\nu x_{2}x_{3}^{4} + 65535/8192\nu x_{2} + 16\nu x_{3}^{2}\)
\(x_{1}^{4} - 16/257\nu x_{1}^{3} - 96/257x_{1}^{2} + 256/257\nu x_{1} + 65535/256x_{2}x_{3}^{2} + 256/257\)

Belyi Curve 7 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 7 Degree: 20

Belyi Curve 7 Naive Measure: 533619437993393453952291

Belyi Map 7 Numerator:

\(-319229886726144/95298165909845\nu x_{1}^{3} - 155732211323109376/24301032307010475x_{1}^{2} + 206842649490594874221386675/188885016576\nu x_{1}x_{3}^{16} + 158366007427330836593047/18814718448\nu x_{1}x_{3}^{12} + 621370562173022888/38428755\nu x_{1}x_{3}^{8} - 38867598602928128/647236113943725\nu x_{1}x_{3}^{4} + 54867038975295488/8100344102336825\nu x_{1} + 748155095279074544632061172796795133116683761179078125/1492470414882768742460583357448192x_{2}^{3}x_{3}^{22} + 56757597840747395171075292062747456911483522209375/5829962558135815400236653740032x_{2}^{3}x_{3}^{18} + 861137114161178139432437302467880137106910625/11386645621359014453587214336x_{2}^{3}x_{3}^{14} + 13064908828358926204301134945306929057375/44479084458433650209325056x_{2}^{3}x_{3}^{10} + 5357033306186489530763362698885325/9391698576527375466496x_{2}^{3}x_{3}^{6} + 601396916968120783660082925075/1357393934888722235392x_{2}^{3}x_{3}^{2} + 2740130601308450740519362185296150775527634335/133437253375300950627975168x_{2}^{2}x_{3}^{20} + 13130229179927805291822140520894407616715/43436605916439111532544x_{2}^{2}x_{3}^{16} + 1695673905168933207373239724005802205/1018045451166541676544x_{2}^{2}x_{3}^{12} + 2698129303541582307435425319115/662790007269883904x_{2}^{2}x_{3}^{8} + 115661183175627798200989087/31068281590775808x_{2}^{2}x_{3}^{4} - 9652497235/19289728x_{2}^{2} + 22445203605195785512233589955142851677/67604580741528158208x_{2}x_{3}^{18} + 60427677880153177284139628626265/15534140795387904x_{2}x_{3}^{14} + 234977350211958477337993073753/15473460557905920x_{2}x_{3}^{10} + 1560649479991815979729/79010725888x_{2}x_{3}^{6} - 65522676639203328/217437491873905x_{2}x_{3}^{2} + 2684866068406259863475564774377/1541301735260160x_{3}^{16} + 40384339012524969958431767/3010354951680x_{3}^{12} + 3036065512903273239437/117591990300x_{3}^{8} - 71730489328664576/647236113943725x_{3}^{4} + 215727978120740864/72903096921031425\)

Belyi Map 7 Denominator:

\(-319229886726144/95298165909845\nu x_{1}^{3} - 155732211323109376/24301032307010475x_{1}^{2} + 206842649490594874221386675/188885016576\nu x_{1}x_{3}^{16} + 158366007427330836593047/18814718448\nu x_{1}x_{3}^{12} + 621370562173022888/38428755\nu x_{1}x_{3}^{8} - 38867598602928128/647236113943725\nu x_{1}x_{3}^{4} + 54867038975295488/8100344102336825\nu x_{1} + 748155095279074544632061172796795133116683761179078125/1492470414882768742460583357448192x_{2}^{3}x_{3}^{22} + 56757597840747395171075292062747456911483522209375/5829962558135815400236653740032x_{2}^{3}x_{3}^{18} + 861137114161178139432437302467880137106910625/11386645621359014453587214336x_{2}^{3}x_{3}^{14} + 13064908828358926204301134945306929057375/44479084458433650209325056x_{2}^{3}x_{3}^{10} + 5357033306186489530763362698885325/9391698576527375466496x_{2}^{3}x_{3}^{6} + 601396916968120783660082925075/1357393934888722235392x_{2}^{3}x_{3}^{2} + 2740130601308450740519362185296150775527634335/133437253375300950627975168x_{2}^{2}x_{3}^{20} + 13130229179927805291822140520894407616715/43436605916439111532544x_{2}^{2}x_{3}^{16} + 1695673905168933207373239724005802205/1018045451166541676544x_{2}^{2}x_{3}^{12} + 2698129303541582307435425319115/662790007269883904x_{2}^{2}x_{3}^{8} + 115663251267346085747635615/31068281590775808x_{2}^{2}x_{3}^{4} - 9652497235/19289728x_{2}^{2} + 22445203605195785512233589955142851677/67604580741528158208x_{2}x_{3}^{18} + 60427677880153177284139628626265/15534140795387904x_{2}x_{3}^{14} + 234977350211958477337993073753/15473460557905920x_{2}x_{3}^{10} + 1560649479991815979729/79010725888x_{2}x_{3}^{6} - 65522676639203328/217437491873905x_{2}x_{3}^{2} + 2684866068406259863475564774377/1541301735260160x_{3}^{16} + 40384339012524969958431767/3010354951680x_{3}^{12} + 3036065512903273239437/117591990300x_{3}^{8} - 71730489328664576/647236113943725x_{3}^{4} + 215727978120740864/72903096921031425\)

Belyi Curve 8: 32S12-4,8,8-g9-path3

\(1/68769820673(-16640\nu^{3} + 16640\nu )x_{1}^{3}x_{2} + 1/281749955297281(84168768\nu^{3} + 84168768\nu - 34611200)x_{1}^{2}x_{2} + 1/4729288235396578172929(-1362245842944\nu^{3} - 1362245842944\nu - 1686592651264)x_{1}^{2}x_{3}^{2} + 1/1154329566852960257(119508246528\nu^{3} - 66607124480\nu^{2} - 119508246528\nu )x_{1}x_{2} + 1/4729288235396578172929(-1828902797312\nu^{3} - 1152525565952\nu^{2} + 1828902797312\nu )x_{1}x_{3}^{2} + x_{2}^{2}x_{3}^{6} - 4/4097x_{2}^{2}x_{3}^{2} + 1/1154329566852960257(-3552920630784\nu^{3} - 3552920630784\nu + 16839143284928)x_{2}x_{3}^{4} + 1/67901739226644721(-1119529984\nu^{3} - 1119529984\nu - 521236736)x_{2} + 1/4729288235396578172929(529115807744\nu^{3} + 529115807744\nu + 186075580416)x_{3}^{2}\)
\(1/1091051585(-12804\nu^{3} + 12804\nu )x_{1}^{2}x_{3}^{2} + x_{1}x_{2}x_{3}^{4} - 4/4097x_{1}x_{2} + 1/1091051585(14592\nu^{3} + 14592\nu )x_{1}x_{3}^{2} + 1/1065220(-135200\nu^{3} + 814783\nu^{2} + 135200\nu )x_{2}x_{3}^{4} + 1/1091051585(-135200\nu^{3} - 814783\nu^{2} + 135200\nu )x_{2} + 1/1091051585(3904\nu^{3} - 3904\nu )x_{3}^{2}\)
\(x_{1}^{3}x_{3}^{2} + 321/260\nu^{2}x_{1}^{2}x_{3}^{2} - 32/65x_{1}x_{3}^{2} + 1/8320(-16785409\nu^{3} + 16785409\nu )x_{2}x_{3}^{4} + 1/2080(4097\nu^{3} - 4097\nu )x_{2} - 4/65\nu^{2}x_{3}^{2}\)
\(x_{1}^{4} + 1/4097(520\nu^{3} + 8192\nu^{2} - 520\nu )x_{1}^{3} + 1/4097(-642\nu^{3} - 642\nu - 6080)x_{1}^{2} + 1/4097(-256\nu^{3} - 2016\nu^{2} + 256\nu )x_{1} - 4097/4x_{2}x_{3}^{2} + 1/4097(32\nu^{3} + 32\nu + 252)\)

Belyi Curve 8 Base Field: \(\nu^{4}+1\), discriminant [ <2, 8> ]

Belyi Curve 8 Degree: 20

Belyi Curve 8 Naive Measure: 14190241548885774298254

Belyi Map 8 Numerator:

\(16785409/16384x_{2}^{2}\)

Belyi Map 8 Denominator:

\(1/4617318267411841028(895598240249916\nu^{3} + 1753053109826887\nu^{2} - 895598240249916\nu )x_{1}^{3} + 1/18469273069647364112(-4584073964370548\nu^{3} - 4584073964370548\nu - 8337310365585351)x_{1}^{2} + 1/196502809010845952212046592000000(753153088295857593693032320843690556772\nu^{3} + 3673394681351911662111761204708789282645\nu^{2} - 753153088295857593693032320843690556772\nu )x_{1}x_{3}^{16} + 1/24562851126355744026505824000000(-813782292101417926026076602346727100\nu^{3} - 38456045259122508477342692413816127\nu^{2} + 813782292101417926026076602346727100\nu )x_{1}x_{3}^{12} + 1/4093808521059290671084304000000(35997345318962045079662325917164\nu^{3} - 88284145478233057738587786292665\nu^{2} - 35997345318962045079662325917164\nu )x_{1}x_{3}^{8} + 1/781538754050033921(-412448600557728\nu^{3} + 7296997155394588\nu^{2} + 412448600557728\nu )x_{1}x_{3}^{4} + 1/18469273069647364112(-1963111456116736\nu^{3} - 3524983341394561\nu^{2} + 1963111456116736\nu )x_{1} + 1/13393128414988192337135432871444480000000(-183206516611713397247265149008786084132216466531426035041411268\nu^{3} - 183206516611713397247265149008786084132216466531426035041411268\nu - 96480026267667567665319740614807705548912496283125471478063019)x_{2}^{3}x_{3}^{22} + 1/3348282103747048084283858217861120000000(139345300827662139310892697335710631126939224628460275361020\nu^{3} + 139345300827662139310892697335710631126939224628460275361020\nu + 112513409761008349202484250721085860149506572045922318202881)x_{2}^{3}x_{3}^{18} + 1/139511754322793670178494092410880000000(-4483314683669540676213271834779887118887157172209771020\nu^{3} - 4483314683669540676213271834779887118887157172209771020\nu - 8728508357930878638674761064496333498546155372773661497)x_{2}^{3}x_{3}^{14} + 1/104633815742095252633870569308160000000(-1735820632889999308817440736365223270428211014768820\nu^{3} - 1735820632889999308817440736365223270428211014768820\nu + 6079731670145690789745946957048410909245942075501397)x_{2}^{3}x_{3}^{10} + 1/52316907871047626316935284654080000000(1648649628788269404998706012949478969177946904460\nu^{3} + 1648649628788269404998706012949478969177946904460\nu - 1407877295774035319315365277817518685110549480703)x_{2}^{3}x_{3}^{6} + 1/4359742322587302193077940387840000000(-46759716232914273723255542293678227334291292\nu^{3} - 46759716232914273723255542293678227334291292\nu + 21671261794203742137885573235613292459539911)x_{2}^{3}x_{3}^{2} + 1/209267631484190505267741138616320000000(-16548857768869795286768833805972831042820643293506630164\nu^{3} - 16548857768869795286768833805972831042820643293506630164\nu - 13734118174866456343037221866665249454617057268132259371)x_{2}^{2}x_{3}^{20} + 1/13079226967761906579233821163520000000(715479629828655835105658553443535422827315423204456\nu^{3} + 715479629828655835105658553443535422827315423204456\nu - 9647538204787821738613752374798842978194161068085355)x_{2}^{2}x_{3}^{16} + 1/6539613483880953289616910581760000000(3499715262960023963716698309770545222773040956700\nu^{3} + 3499715262960023963716698309770545222773040956700\nu + 635427166005260261235485303128979796522040190679)x_{2}^{2}x_{3}^{12} + 1/817451685485119161202113822720000000(-64165662813927275969379868198544512902065984\nu^{3} - 64165662813927275969379868198544512902065984\nu + 598690514748355704166495733938926173629469205)x_{2}^{2}x_{3}^{8} + 1/272483895161706387067371274240000000(-6409383925540723827560436922123985174252\nu^{3} - 6409383925540723827560436922123985174252\nu - 22998098628136177156840317226768000435897)x_{2}^{2}x_{3}^{4} + 1/1549536846840320(-14135994799968296\nu^{3} - 14135994799968296\nu + 1657319184211565113)x_{2}^{2} + 1/6539613483880953289616910581760000000(6302231771146007814146428993056083123620838546188\nu^{3} + 6302231771146007814146428993056083123620838546188\nu - 164770850806069950851136755257550508698751694635)x_{2}x_{3}^{18} + 1/1634903370970238322404227645440000000(-3878707189608154571098765654956766786581930076\nu^{3} - 3878707189608154571098765654956766786581930076\nu + 6131325985184726121021618242925545639341072851)x_{2}x_{3}^{14} + 1/408725842742559580601056911360000000(-878755817720954195612469168328339134097292\nu^{3} - 878755817720954195612469168328339134097292\nu - 1771494066618603264548749537781761241091117)x_{2}x_{3}^{10} + 1/34060486895213298383421409280000000(57973380007520018428074064888449236148\nu^{3} + 57973380007520018428074064888449236148\nu + 24863416109290448170565096729624369735)x_{2}x_{3}^{6} + 1/1665021423178354266655240(-1148329773315364086631216\nu^{3} - 1148329773315364086631216\nu - 1110320583517213436858553)x_{2}x_{3}^{2} + 1/12772682585704986893783028480000000(-23188888296404562964621037496449672415229\nu^{3} - 23188888296404562964621037496449672415229\nu - 102090381292454291278465072958544404095864)x_{3}^{16} + 1/6386341292852493446891514240000000(87703142132361040352001805295007607700\nu^{3} + 87703142132361040352001805295007607700\nu + 4195024913832685504942968265673542549)x_{3}^{12} + 1/266097553868853893620479760000000(-1030808425351791752294139159039873\nu^{3} - 1030808425351791752294139159039873\nu + 2451888257098113431803714309625768)x_{3}^{8} + 1/203200076053008819460(49861378728497224\nu^{3} + 49861378728497224\nu - 804180718572343367)x_{3}^{4} + 1/295508369114357825792(4418202712824832\nu^{3} + 4418202712824832\nu + 8320922350612865)\)

Belyi Curve 9: 32S12-4,8,8-g9-path30

\(536870912/281462092005375\nu x_{1}^{3}x_{2} + 215501057818624/18445618199572250625x_{1}^{2}x_{2} - 52401070514315984896/239885264685437119378125x_{1}^{2}x_{3}^{2} - 157078438757269504/4703632640890923909375\nu x_{1}x_{2} + 180089941899291394048/239885264685437119378125\nu x_{1}x_{3}^{2} + x_{2}^{2}x_{3}^{6} + 256/65535x_{2}^{2}x_{3}^{2} + 31645788798976/277098404709375x_{2}x_{3}^{4} + 1877286233206423552/4703632640890923909375x_{2} + 36189800705642463232/44423197163969836921875x_{3}^{2}\)
\(-8388608/858967245\nu x_{1}^{2}x_{3}^{2} + x_{1}x_{2}x_{3}^{4} + 256/65535x_{1}x_{2} - 33554432/858967245x_{1}x_{3}^{2} + 1546/255\nu x_{2}x_{3}^{4} + 390656/16842495\nu x_{2} + 67108864/1431612075\nu x_{3}^{2}\)
\(x_{1}^{3}x_{3}^{2} - 6\nu x_{1}^{2}x_{3}^{2} - 16x_{1}x_{3}^{2} + 4294836225/2097152\nu x_{2}x_{3}^{4} + 65535/8192\nu x_{2} + 16\nu x_{3}^{2}\)
\(x_{1}^{4} - 16/257\nu x_{1}^{3} - 96/257x_{1}^{2} + 256/257\nu x_{1} + 65535/256x_{2}x_{3}^{2} + 256/257\)

Belyi Curve 9 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 9 Degree: 20

Belyi Curve 9 Naive Measure: 533619437993393453952291

Belyi Map 9 Numerator:

\(-319229886726144/95298165909845\nu x_{1}^{3} - 155732211323109376/24301032307010475x_{1}^{2} + 206842649490594874221386675/188885016576\nu x_{1}x_{3}^{16} + 158366007427330836593047/18814718448\nu x_{1}x_{3}^{12} + 621370562173022888/38428755\nu x_{1}x_{3}^{8} - 38867598602928128/647236113943725\nu x_{1}x_{3}^{4} + 54867038975295488/8100344102336825\nu x_{1} + 748155095279074544632061172796795133116683761179078125/1492470414882768742460583357448192x_{2}^{3}x_{3}^{22} + 56757597840747395171075292062747456911483522209375/5829962558135815400236653740032x_{2}^{3}x_{3}^{18} + 861137114161178139432437302467880137106910625/11386645621359014453587214336x_{2}^{3}x_{3}^{14} + 13064908828358926204301134945306929057375/44479084458433650209325056x_{2}^{3}x_{3}^{10} + 5357033306186489530763362698885325/9391698576527375466496x_{2}^{3}x_{3}^{6} + 601396916968120783660082925075/1357393934888722235392x_{2}^{3}x_{3}^{2} + 2740130601308450740519362185296150775527634335/133437253375300950627975168x_{2}^{2}x_{3}^{20} + 13130229179927805291822140520894407616715/43436605916439111532544x_{2}^{2}x_{3}^{16} + 1695673905168933207373239724005802205/1018045451166541676544x_{2}^{2}x_{3}^{12} + 2698129303541582307435425319115/662790007269883904x_{2}^{2}x_{3}^{8} + 115661183175627798200989087/31068281590775808x_{2}^{2}x_{3}^{4} - 9652497235/19289728x_{2}^{2} + 22445203605195785512233589955142851677/67604580741528158208x_{2}x_{3}^{18} + 60427677880153177284139628626265/15534140795387904x_{2}x_{3}^{14} + 234977350211958477337993073753/15473460557905920x_{2}x_{3}^{10} + 1560649479991815979729/79010725888x_{2}x_{3}^{6} - 65522676639203328/217437491873905x_{2}x_{3}^{2} + 2684866068406259863475564774377/1541301735260160x_{3}^{16} + 40384339012524969958431767/3010354951680x_{3}^{12} + 3036065512903273239437/117591990300x_{3}^{8} - 71730489328664576/647236113943725x_{3}^{4} + 215727978120740864/72903096921031425\)

Belyi Map 9 Denominator:

\(-319229886726144/95298165909845\nu x_{1}^{3} - 155732211323109376/24301032307010475x_{1}^{2} + 206842649490594874221386675/188885016576\nu x_{1}x_{3}^{16} + 158366007427330836593047/18814718448\nu x_{1}x_{3}^{12} + 621370562173022888/38428755\nu x_{1}x_{3}^{8} - 38867598602928128/647236113943725\nu x_{1}x_{3}^{4} + 54867038975295488/8100344102336825\nu x_{1} + 748155095279074544632061172796795133116683761179078125/1492470414882768742460583357448192x_{2}^{3}x_{3}^{22} + 56757597840747395171075292062747456911483522209375/5829962558135815400236653740032x_{2}^{3}x_{3}^{18} + 861137114161178139432437302467880137106910625/11386645621359014453587214336x_{2}^{3}x_{3}^{14} + 13064908828358926204301134945306929057375/44479084458433650209325056x_{2}^{3}x_{3}^{10} + 5357033306186489530763362698885325/9391698576527375466496x_{2}^{3}x_{3}^{6} + 601396916968120783660082925075/1357393934888722235392x_{2}^{3}x_{3}^{2} + 2740130601308450740519362185296150775527634335/133437253375300950627975168x_{2}^{2}x_{3}^{20} + 13130229179927805291822140520894407616715/43436605916439111532544x_{2}^{2}x_{3}^{16} + 1695673905168933207373239724005802205/1018045451166541676544x_{2}^{2}x_{3}^{12} + 2698129303541582307435425319115/662790007269883904x_{2}^{2}x_{3}^{8} + 115663251267346085747635615/31068281590775808x_{2}^{2}x_{3}^{4} - 9652497235/19289728x_{2}^{2} + 22445203605195785512233589955142851677/67604580741528158208x_{2}x_{3}^{18} + 60427677880153177284139628626265/15534140795387904x_{2}x_{3}^{14} + 234977350211958477337993073753/15473460557905920x_{2}x_{3}^{10} + 1560649479991815979729/79010725888x_{2}x_{3}^{6} - 65522676639203328/217437491873905x_{2}x_{3}^{2} + 2684866068406259863475564774377/1541301735260160x_{3}^{16} + 40384339012524969958431767/3010354951680x_{3}^{12} + 3036065512903273239437/117591990300x_{3}^{8} - 71730489328664576/647236113943725x_{3}^{4} + 215727978120740864/72903096921031425\)

Belyi Curve 10: 32S12-4,8,8-g9-path31

\(536870912/281462092005375\nu x_{1}^{3}x_{2} + 215501057818624/18445618199572250625x_{1}^{2}x_{2} - 52401070514315984896/239885264685437119378125x_{1}^{2}x_{3}^{2} - 157078438757269504/4703632640890923909375\nu x_{1}x_{2} + 180089941899291394048/239885264685437119378125\nu x_{1}x_{3}^{2} + x_{2}^{2}x_{3}^{6} + 256/65535x_{2}^{2}x_{3}^{2} + 31645788798976/277098404709375x_{2}x_{3}^{4} + 1877286233206423552/4703632640890923909375x_{2} + 36189800705642463232/44423197163969836921875x_{3}^{2}\)
\(-8388608/858967245\nu x_{1}^{2}x_{3}^{2} + x_{1}x_{2}x_{3}^{4} + 256/65535x_{1}x_{2} - 33554432/858967245x_{1}x_{3}^{2} + 1546/255\nu x_{2}x_{3}^{4} + 390656/16842495\nu x_{2} + 67108864/1431612075\nu x_{3}^{2}\)
\(x_{1}^{3}x_{3}^{2} - 6\nu x_{1}^{2}x_{3}^{2} - 16x_{1}x_{3}^{2} + 4294836225/2097152\nu x_{2}x_{3}^{4} + 65535/8192\nu x_{2} + 16\nu x_{3}^{2}\)
\(x_{1}^{4} - 16/257\nu x_{1}^{3} - 96/257x_{1}^{2} + 256/257\nu x_{1} + 65535/256x_{2}x_{3}^{2} + 256/257\)

Belyi Curve 10 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 10 Degree: 20

Belyi Curve 10 Naive Measure: 533619437993393453952291

Belyi Map 10 Numerator:

\(-319229886726144/95298165909845\nu x_{1}^{3} - 155732211323109376/24301032307010475x_{1}^{2} + 206842649490594874221386675/188885016576\nu x_{1}x_{3}^{16} + 158366007427330836593047/18814718448\nu x_{1}x_{3}^{12} + 621370562173022888/38428755\nu x_{1}x_{3}^{8} - 38867598602928128/647236113943725\nu x_{1}x_{3}^{4} + 54867038975295488/8100344102336825\nu x_{1} + 748155095279074544632061172796795133116683761179078125/1492470414882768742460583357448192x_{2}^{3}x_{3}^{22} + 56757597840747395171075292062747456911483522209375/5829962558135815400236653740032x_{2}^{3}x_{3}^{18} + 861137114161178139432437302467880137106910625/11386645621359014453587214336x_{2}^{3}x_{3}^{14} + 13064908828358926204301134945306929057375/44479084458433650209325056x_{2}^{3}x_{3}^{10} + 5357033306186489530763362698885325/9391698576527375466496x_{2}^{3}x_{3}^{6} + 601396916968120783660082925075/1357393934888722235392x_{2}^{3}x_{3}^{2} + 2740130601308450740519362185296150775527634335/133437253375300950627975168x_{2}^{2}x_{3}^{20} + 13130229179927805291822140520894407616715/43436605916439111532544x_{2}^{2}x_{3}^{16} + 1695673905168933207373239724005802205/1018045451166541676544x_{2}^{2}x_{3}^{12} + 2698129303541582307435425319115/662790007269883904x_{2}^{2}x_{3}^{8} + 115661183175627798200989087/31068281590775808x_{2}^{2}x_{3}^{4} - 9652497235/19289728x_{2}^{2} + 22445203605195785512233589955142851677/67604580741528158208x_{2}x_{3}^{18} + 60427677880153177284139628626265/15534140795387904x_{2}x_{3}^{14} + 234977350211958477337993073753/15473460557905920x_{2}x_{3}^{10} + 1560649479991815979729/79010725888x_{2}x_{3}^{6} - 65522676639203328/217437491873905x_{2}x_{3}^{2} + 2684866068406259863475564774377/1541301735260160x_{3}^{16} + 40384339012524969958431767/3010354951680x_{3}^{12} + 3036065512903273239437/117591990300x_{3}^{8} - 71730489328664576/647236113943725x_{3}^{4} + 215727978120740864/72903096921031425\)

Belyi Map 10 Denominator:

\(-319229886726144/95298165909845\nu x_{1}^{3} - 155732211323109376/24301032307010475x_{1}^{2} + 206842649490594874221386675/188885016576\nu x_{1}x_{3}^{16} + 158366007427330836593047/18814718448\nu x_{1}x_{3}^{12} + 621370562173022888/38428755\nu x_{1}x_{3}^{8} - 38867598602928128/647236113943725\nu x_{1}x_{3}^{4} + 54867038975295488/8100344102336825\nu x_{1} + 748155095279074544632061172796795133116683761179078125/1492470414882768742460583357448192x_{2}^{3}x_{3}^{22} + 56757597840747395171075292062747456911483522209375/5829962558135815400236653740032x_{2}^{3}x_{3}^{18} + 861137114161178139432437302467880137106910625/11386645621359014453587214336x_{2}^{3}x_{3}^{14} + 13064908828358926204301134945306929057375/44479084458433650209325056x_{2}^{3}x_{3}^{10} + 5357033306186489530763362698885325/9391698576527375466496x_{2}^{3}x_{3}^{6} + 601396916968120783660082925075/1357393934888722235392x_{2}^{3}x_{3}^{2} + 2740130601308450740519362185296150775527634335/133437253375300950627975168x_{2}^{2}x_{3}^{20} + 13130229179927805291822140520894407616715/43436605916439111532544x_{2}^{2}x_{3}^{16} + 1695673905168933207373239724005802205/1018045451166541676544x_{2}^{2}x_{3}^{12} + 2698129303541582307435425319115/662790007269883904x_{2}^{2}x_{3}^{8} + 115663251267346085747635615/31068281590775808x_{2}^{2}x_{3}^{4} - 9652497235/19289728x_{2}^{2} + 22445203605195785512233589955142851677/67604580741528158208x_{2}x_{3}^{18} + 60427677880153177284139628626265/15534140795387904x_{2}x_{3}^{14} + 234977350211958477337993073753/15473460557905920x_{2}x_{3}^{10} + 1560649479991815979729/79010725888x_{2}x_{3}^{6} - 65522676639203328/217437491873905x_{2}x_{3}^{2} + 2684866068406259863475564774377/1541301735260160x_{3}^{16} + 40384339012524969958431767/3010354951680x_{3}^{12} + 3036065512903273239437/117591990300x_{3}^{8} - 71730489328664576/647236113943725x_{3}^{4} + 215727978120740864/72903096921031425\)

Belyi Curve 11: 32S12-4,8,8-g9-path32

\(536870912/281462092005375\nu x_{1}^{3}x_{2} + 215501057818624/18445618199572250625x_{1}^{2}x_{2} - 52401070514315984896/239885264685437119378125x_{1}^{2}x_{3}^{2} - 157078438757269504/4703632640890923909375\nu x_{1}x_{2} + 180089941899291394048/239885264685437119378125\nu x_{1}x_{3}^{2} + x_{2}^{2}x_{3}^{6} + 256/65535x_{2}^{2}x_{3}^{2} + 31645788798976/277098404709375x_{2}x_{3}^{4} + 1877286233206423552/4703632640890923909375x_{2} + 36189800705642463232/44423197163969836921875x_{3}^{2}\)
\(-8388608/858967245\nu x_{1}^{2}x_{3}^{2} + x_{1}x_{2}x_{3}^{4} + 256/65535x_{1}x_{2} - 33554432/858967245x_{1}x_{3}^{2} + 1546/255\nu x_{2}x_{3}^{4} + 390656/16842495\nu x_{2} + 67108864/1431612075\nu x_{3}^{2}\)
\(x_{1}^{3}x_{3}^{2} - 6\nu x_{1}^{2}x_{3}^{2} - 16x_{1}x_{3}^{2} + 4294836225/2097152\nu x_{2}x_{3}^{4} + 65535/8192\nu x_{2} + 16\nu x_{3}^{2}\)
\(x_{1}^{4} - 16/257\nu x_{1}^{3} - 96/257x_{1}^{2} + 256/257\nu x_{1} + 65535/256x_{2}x_{3}^{2} + 256/257\)

Belyi Curve 11 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 11 Degree: 20

Belyi Curve 11 Naive Measure: 533619437993393453952291

Belyi Map 11 Numerator:

\(-319229886726144/95298165909845\nu x_{1}^{3} - 155732211323109376/24301032307010475x_{1}^{2} + 206842649490594874221386675/188885016576\nu x_{1}x_{3}^{16} + 158366007427330836593047/18814718448\nu x_{1}x_{3}^{12} + 621370562173022888/38428755\nu x_{1}x_{3}^{8} - 38867598602928128/647236113943725\nu x_{1}x_{3}^{4} + 54867038975295488/8100344102336825\nu x_{1} + 748155095279074544632061172796795133116683761179078125/1492470414882768742460583357448192x_{2}^{3}x_{3}^{22} + 56757597840747395171075292062747456911483522209375/5829962558135815400236653740032x_{2}^{3}x_{3}^{18} + 861137114161178139432437302467880137106910625/11386645621359014453587214336x_{2}^{3}x_{3}^{14} + 13064908828358926204301134945306929057375/44479084458433650209325056x_{2}^{3}x_{3}^{10} + 5357033306186489530763362698885325/9391698576527375466496x_{2}^{3}x_{3}^{6} + 601396916968120783660082925075/1357393934888722235392x_{2}^{3}x_{3}^{2} + 2740130601308450740519362185296150775527634335/133437253375300950627975168x_{2}^{2}x_{3}^{20} + 13130229179927805291822140520894407616715/43436605916439111532544x_{2}^{2}x_{3}^{16} + 1695673905168933207373239724005802205/1018045451166541676544x_{2}^{2}x_{3}^{12} + 2698129303541582307435425319115/662790007269883904x_{2}^{2}x_{3}^{8} + 115661183175627798200989087/31068281590775808x_{2}^{2}x_{3}^{4} - 9652497235/19289728x_{2}^{2} + 22445203605195785512233589955142851677/67604580741528158208x_{2}x_{3}^{18} + 60427677880153177284139628626265/15534140795387904x_{2}x_{3}^{14} + 234977350211958477337993073753/15473460557905920x_{2}x_{3}^{10} + 1560649479991815979729/79010725888x_{2}x_{3}^{6} - 65522676639203328/217437491873905x_{2}x_{3}^{2} + 2684866068406259863475564774377/1541301735260160x_{3}^{16} + 40384339012524969958431767/3010354951680x_{3}^{12} + 3036065512903273239437/117591990300x_{3}^{8} - 71730489328664576/647236113943725x_{3}^{4} + 215727978120740864/72903096921031425\)

Belyi Map 11 Denominator:

\(-319229886726144/95298165909845\nu x_{1}^{3} - 155732211323109376/24301032307010475x_{1}^{2} + 206842649490594874221386675/188885016576\nu x_{1}x_{3}^{16} + 158366007427330836593047/18814718448\nu x_{1}x_{3}^{12} + 621370562173022888/38428755\nu x_{1}x_{3}^{8} - 38867598602928128/647236113943725\nu x_{1}x_{3}^{4} + 54867038975295488/8100344102336825\nu x_{1} + 748155095279074544632061172796795133116683761179078125/1492470414882768742460583357448192x_{2}^{3}x_{3}^{22} + 56757597840747395171075292062747456911483522209375/5829962558135815400236653740032x_{2}^{3}x_{3}^{18} + 861137114161178139432437302467880137106910625/11386645621359014453587214336x_{2}^{3}x_{3}^{14} + 13064908828358926204301134945306929057375/44479084458433650209325056x_{2}^{3}x_{3}^{10} + 5357033306186489530763362698885325/9391698576527375466496x_{2}^{3}x_{3}^{6} + 601396916968120783660082925075/1357393934888722235392x_{2}^{3}x_{3}^{2} + 2740130601308450740519362185296150775527634335/133437253375300950627975168x_{2}^{2}x_{3}^{20} + 13130229179927805291822140520894407616715/43436605916439111532544x_{2}^{2}x_{3}^{16} + 1695673905168933207373239724005802205/1018045451166541676544x_{2}^{2}x_{3}^{12} + 2698129303541582307435425319115/662790007269883904x_{2}^{2}x_{3}^{8} + 115663251267346085747635615/31068281590775808x_{2}^{2}x_{3}^{4} - 9652497235/19289728x_{2}^{2} + 22445203605195785512233589955142851677/67604580741528158208x_{2}x_{3}^{18} + 60427677880153177284139628626265/15534140795387904x_{2}x_{3}^{14} + 234977350211958477337993073753/15473460557905920x_{2}x_{3}^{10} + 1560649479991815979729/79010725888x_{2}x_{3}^{6} - 65522676639203328/217437491873905x_{2}x_{3}^{2} + 2684866068406259863475564774377/1541301735260160x_{3}^{16} + 40384339012524969958431767/3010354951680x_{3}^{12} + 3036065512903273239437/117591990300x_{3}^{8} - 71730489328664576/647236113943725x_{3}^{4} + 215727978120740864/72903096921031425\)

Belyi Curve 12: 32S12-4,8,8-g9-path33

\(x_{1}^{3}x_{3}^{2} + x_{1}x_{3}^{2} - x_{2}2\)
\(10x_{1}^{2}x_{3}^{2} + 2x_{1}x_{2} + x_{2}x_{3}^{4} + 2x_{3}^{2}\)
\(x_{1}^{4} + 6x_{1}^{2} + 1/2x_{2}x_{3}^{2} + 1\)

Belyi Curve 12 Base Field: Rationals

Belyi Curve 12 Degree: 17

Belyi Curve 12 Naive Measure: 28

Belyi Map 12 Numerator:

\(384x_{1}^{2} + 25/3x_{1}x_{3}^{12} - 32x_{1}x_{3}^{4} - 5/48x_{2}^{3}x_{3}^{6} - 5/384x_{2}^{2}x_{3}^{20} + 35/48x_{2}^{2}x_{3}^{12} - 13/12x_{2}^{2}x_{3}^{4} + 5/64x_{2}x_{3}^{18} - 31/3x_{2}x_{3}^{10} + 72x_{2}x_{3}^{2} + 5/24x_{3}^{16} - 2/3x_{3}^{8} + 64\)

Belyi Map 12 Denominator:

\(384x_{1}^{2} + 25/3x_{1}x_{3}^{12} - 32x_{1}x_{3}^{4} - 5/48x_{2}^{3}x_{3}^{6} - 5/384x_{2}^{2}x_{3}^{20} + 35/48x_{2}^{2}x_{3}^{12} - 5/6x_{2}^{2}x_{3}^{4} + 5/64x_{2}x_{3}^{18} - 31/3x_{2}x_{3}^{10} + 72x_{2}x_{3}^{2} + 5/24x_{3}^{16} - 2/3x_{3}^{8} + 64\)

Belyi Curve 13: 32S12-4,8,8-g9-path34

\(x_{1}^{3}x_{3}^{2} + x_{1}x_{3}^{2} - x_{2}2\)
\(10x_{1}^{2}x_{3}^{2} + 2x_{1}x_{2} + x_{2}x_{3}^{4} + 2x_{3}^{2}\)
\(x_{1}^{4} + 6x_{1}^{2} + 1/2x_{2}x_{3}^{2} + 1\)

Belyi Curve 13 Base Field: Rationals

Belyi Curve 13 Degree: 17

Belyi Curve 13 Naive Measure: 28

Belyi Map 13 Numerator:

\(384x_{1}^{2} + 25/3x_{1}x_{3}^{12} - 32x_{1}x_{3}^{4} - 5/48x_{2}^{3}x_{3}^{6} - 5/384x_{2}^{2}x_{3}^{20} + 35/48x_{2}^{2}x_{3}^{12} - 13/12x_{2}^{2}x_{3}^{4} + 5/64x_{2}x_{3}^{18} - 31/3x_{2}x_{3}^{10} + 72x_{2}x_{3}^{2} + 5/24x_{3}^{16} - 2/3x_{3}^{8} + 64\)

Belyi Map 13 Denominator:

\(384x_{1}^{2} + 25/3x_{1}x_{3}^{12} - 32x_{1}x_{3}^{4} - 5/48x_{2}^{3}x_{3}^{6} - 5/384x_{2}^{2}x_{3}^{20} + 35/48x_{2}^{2}x_{3}^{12} - 5/6x_{2}^{2}x_{3}^{4} + 5/64x_{2}x_{3}^{18} - 31/3x_{2}x_{3}^{10} + 72x_{2}x_{3}^{2} + 5/24x_{3}^{16} - 2/3x_{3}^{8} + 64\)

Belyi Curve 14: 32S12-4,8,8-g9-path39

\(-8589934592/281462092005375\nu x_{1}^{3}x_{2} - 3448016925097984/18445618199572250625x_{1}^{2}x_{2} + 838417128229055758336/239885264685437119378125x_{1}^{2}x_{3}^{2} + 2513255020116312064/4703632640890923909375\nu x_{1}x_{2} - 2881439070388662304768/239885264685437119378125\nu x_{1}x_{3}^{2} + x_{2}^{2}x_{3}^{6} - 1024/65535\nu x_{2}^{2}x_{3}^{2} - 126583155195904/277098404709375\nu x_{2}x_{3}^{4} - 30036579731302776832/4703632640890923909375x_{2} - 579036811290279411712/44423197163969836921875x_{3}^{2}\)
\(-33554432/858967245x_{1}^{2}x_{3}^{2} + x_{1}x_{2}x_{3}^{4} - 1024/65535\nu x_{1}x_{2} + 134217728/858967245\nu x_{1}x_{3}^{2} + 1546/255\nu x_{2}x_{3}^{4} + 1562624/16842495x_{2} + 268435456/1431612075x_{3}^{2}\)
\(x_{1}^{3}x_{3}^{2} - 6\nu x_{1}^{2}x_{3}^{2} - 16x_{1}x_{3}^{2} - 4294836225/8388608x_{2}x_{3}^{4} + 65535/8192\nu x_{2} + 16\nu x_{3}^{2}\)
\(x_{1}^{4} - 16/257\nu x_{1}^{3} - 96/257x_{1}^{2} + 256/257\nu x_{1} + 65535/1024\nu x_{2}x_{3}^{2} + 256/257\)

Belyi Curve 14 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 14 Degree: 20

Belyi Curve 14 Naive Measure: 533619437993393453952291

Belyi Map 14 Numerator:

\(-319229886726144/95298165909845\nu x_{1}^{3} - 155732211323109376/24301032307010475x_{1}^{2} + 206842649490594874221386675/48354564243456\nu x_{1}x_{3}^{16} + 158366007427330836593047/1204141980672x_{1}x_{3}^{12} - 77671320271627861/76857510\nu x_{1}x_{3}^{8} + 9716899650732032/647236113943725x_{1}x_{3}^{4} + 54867038975295488/8100344102336825\nu x_{1} - 748155095279074544632061172796795133116683761179078125/24452635277439283076474197728431177728\nu x_{2}^{3}x_{3}^{22} - 56757597840747395171075292062747456911483522209375/23879526638124299879369333719171072x_{2}^{3}x_{3}^{18} + 861137114161178139432437302467880137106910625/11659925116271630800473307480064\nu x_{2}^{3}x_{3}^{14} + 13064908828358926204301134945306929057375/11386645621359014453587214336x_{2}^{3}x_{3}^{10} - 5357033306186489530763362698885325/601068708897752029855744\nu x_{2}^{3}x_{3}^{6} - 601396916968120783660082925075/21718302958219555766272x_{2}^{3}x_{3}^{2} - 2740130601308450740519362185296150775527634335/546558989825232693772186288128x_{2}^{2}x_{3}^{20} + 13130229179927805291822140520894407616715/44479084458433650209325056\nu x_{2}^{2}x_{3}^{16} + 1695673905168933207373239724005802205/260619635498634669195264x_{2}^{2}x_{3}^{12} - 2698129303541582307435425319115/42418560465272569856\nu x_{2}^{2}x_{3}^{8} - 115661183175627798200989087/497092505452412928x_{2}^{2}x_{3}^{4} - 9652497235/77158912\nu x_{2}^{2} + 22445203605195785512233589955142851677/69227090679324834004992\nu x_{2}x_{3}^{18} + 60427677880153177284139628626265/3976740043619303424x_{2}x_{3}^{14} - 234977350211958477337993073753/990301475705978880\nu x_{2}x_{3}^{10} - 1560649479991815979729/1264171614208x_{2}x_{3}^{6} - 16380669159800832/217437491873905\nu x_{2}x_{3}^{2} + 2684866068406259863475564774377/394573244226600960x_{3}^{16} - 40384339012524969958431767/192662716907520\nu x_{3}^{12} - 3036065512903273239437/1881471844800x_{3}^{8} - 17932622332166144/647236113943725\nu x_{3}^{4} + 215727978120740864/72903096921031425\)

Belyi Map 14 Denominator:

\(-319229886726144/95298165909845\nu x_{1}^{3} - 155732211323109376/24301032307010475x_{1}^{2} + 206842649490594874221386675/48354564243456\nu x_{1}x_{3}^{16} + 158366007427330836593047/1204141980672x_{1}x_{3}^{12} - 77671320271627861/76857510\nu x_{1}x_{3}^{8} + 9716899650732032/647236113943725x_{1}x_{3}^{4} + 54867038975295488/8100344102336825\nu x_{1} - 748155095279074544632061172796795133116683761179078125/24452635277439283076474197728431177728\nu x_{2}^{3}x_{3}^{22} - 56757597840747395171075292062747456911483522209375/23879526638124299879369333719171072x_{2}^{3}x_{3}^{18} + 861137114161178139432437302467880137106910625/11659925116271630800473307480064\nu x_{2}^{3}x_{3}^{14} + 13064908828358926204301134945306929057375/11386645621359014453587214336x_{2}^{3}x_{3}^{10} - 5357033306186489530763362698885325/601068708897752029855744\nu x_{2}^{3}x_{3}^{6} - 601396916968120783660082925075/21718302958219555766272x_{2}^{3}x_{3}^{2} - 2740130601308450740519362185296150775527634335/546558989825232693772186288128x_{2}^{2}x_{3}^{20} + 13130229179927805291822140520894407616715/44479084458433650209325056\nu x_{2}^{2}x_{3}^{16} + 1695673905168933207373239724005802205/260619635498634669195264x_{2}^{2}x_{3}^{12} - 2698129303541582307435425319115/42418560465272569856\nu x_{2}^{2}x_{3}^{8} - 115663251267346085747635615/497092505452412928x_{2}^{2}x_{3}^{4} - 9652497235/77158912\nu x_{2}^{2} + 22445203605195785512233589955142851677/69227090679324834004992\nu x_{2}x_{3}^{18} + 60427677880153177284139628626265/3976740043619303424x_{2}x_{3}^{14} - 234977350211958477337993073753/990301475705978880\nu x_{2}x_{3}^{10} - 1560649479991815979729/1264171614208x_{2}x_{3}^{6} - 16380669159800832/217437491873905\nu x_{2}x_{3}^{2} + 2684866068406259863475564774377/394573244226600960x_{3}^{16} - 40384339012524969958431767/192662716907520\nu x_{3}^{12} - 3036065512903273239437/1881471844800x_{3}^{8} - 17932622332166144/647236113943725\nu x_{3}^{4} + 215727978120740864/72903096921031425\)

Belyi Curve 15: 32S12-4,8,8-g9-path40

\(-8589934592/281462092005375\nu x_{1}^{3}x_{2} - 3448016925097984/18445618199572250625x_{1}^{2}x_{2} + 838417128229055758336/239885264685437119378125x_{1}^{2}x_{3}^{2} + 2513255020116312064/4703632640890923909375\nu x_{1}x_{2} - 2881439070388662304768/239885264685437119378125\nu x_{1}x_{3}^{2} + x_{2}^{2}x_{3}^{6} - 1024/65535\nu x_{2}^{2}x_{3}^{2} - 126583155195904/277098404709375\nu x_{2}x_{3}^{4} - 30036579731302776832/4703632640890923909375x_{2} - 579036811290279411712/44423197163969836921875x_{3}^{2}\)
\(-33554432/858967245x_{1}^{2}x_{3}^{2} + x_{1}x_{2}x_{3}^{4} - 1024/65535\nu x_{1}x_{2} + 134217728/858967245\nu x_{1}x_{3}^{2} + 1546/255\nu x_{2}x_{3}^{4} + 1562624/16842495x_{2} + 268435456/1431612075x_{3}^{2}\)
\(x_{1}^{3}x_{3}^{2} - 6\nu x_{1}^{2}x_{3}^{2} - 16x_{1}x_{3}^{2} - 4294836225/8388608x_{2}x_{3}^{4} + 65535/8192\nu x_{2} + 16\nu x_{3}^{2}\)
\(x_{1}^{4} - 16/257\nu x_{1}^{3} - 96/257x_{1}^{2} + 256/257\nu x_{1} + 65535/1024\nu x_{2}x_{3}^{2} + 256/257\)

Belyi Curve 15 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 15 Degree: 20

Belyi Curve 15 Naive Measure: 533619437993393453952291

Belyi Map 15 Numerator:

\(-319229886726144/95298165909845\nu x_{1}^{3} - 155732211323109376/24301032307010475x_{1}^{2} + 206842649490594874221386675/48354564243456\nu x_{1}x_{3}^{16} + 158366007427330836593047/1204141980672x_{1}x_{3}^{12} - 77671320271627861/76857510\nu x_{1}x_{3}^{8} + 9716899650732032/647236113943725x_{1}x_{3}^{4} + 54867038975295488/8100344102336825\nu x_{1} - 748155095279074544632061172796795133116683761179078125/24452635277439283076474197728431177728\nu x_{2}^{3}x_{3}^{22} - 56757597840747395171075292062747456911483522209375/23879526638124299879369333719171072x_{2}^{3}x_{3}^{18} + 861137114161178139432437302467880137106910625/11659925116271630800473307480064\nu x_{2}^{3}x_{3}^{14} + 13064908828358926204301134945306929057375/11386645621359014453587214336x_{2}^{3}x_{3}^{10} - 5357033306186489530763362698885325/601068708897752029855744\nu x_{2}^{3}x_{3}^{6} - 601396916968120783660082925075/21718302958219555766272x_{2}^{3}x_{3}^{2} - 2740130601308450740519362185296150775527634335/546558989825232693772186288128x_{2}^{2}x_{3}^{20} + 13130229179927805291822140520894407616715/44479084458433650209325056\nu x_{2}^{2}x_{3}^{16} + 1695673905168933207373239724005802205/260619635498634669195264x_{2}^{2}x_{3}^{12} - 2698129303541582307435425319115/42418560465272569856\nu x_{2}^{2}x_{3}^{8} - 115661183175627798200989087/497092505452412928x_{2}^{2}x_{3}^{4} - 9652497235/77158912\nu x_{2}^{2} + 22445203605195785512233589955142851677/69227090679324834004992\nu x_{2}x_{3}^{18} + 60427677880153177284139628626265/3976740043619303424x_{2}x_{3}^{14} - 234977350211958477337993073753/990301475705978880\nu x_{2}x_{3}^{10} - 1560649479991815979729/1264171614208x_{2}x_{3}^{6} - 16380669159800832/217437491873905\nu x_{2}x_{3}^{2} + 2684866068406259863475564774377/394573244226600960x_{3}^{16} - 40384339012524969958431767/192662716907520\nu x_{3}^{12} - 3036065512903273239437/1881471844800x_{3}^{8} - 17932622332166144/647236113943725\nu x_{3}^{4} + 215727978120740864/72903096921031425\)

Belyi Map 15 Denominator:

\(-319229886726144/95298165909845\nu x_{1}^{3} - 155732211323109376/24301032307010475x_{1}^{2} + 206842649490594874221386675/48354564243456\nu x_{1}x_{3}^{16} + 158366007427330836593047/1204141980672x_{1}x_{3}^{12} - 77671320271627861/76857510\nu x_{1}x_{3}^{8} + 9716899650732032/647236113943725x_{1}x_{3}^{4} + 54867038975295488/8100344102336825\nu x_{1} - 748155095279074544632061172796795133116683761179078125/24452635277439283076474197728431177728\nu x_{2}^{3}x_{3}^{22} - 56757597840747395171075292062747456911483522209375/23879526638124299879369333719171072x_{2}^{3}x_{3}^{18} + 861137114161178139432437302467880137106910625/11659925116271630800473307480064\nu x_{2}^{3}x_{3}^{14} + 13064908828358926204301134945306929057375/11386645621359014453587214336x_{2}^{3}x_{3}^{10} - 5357033306186489530763362698885325/601068708897752029855744\nu x_{2}^{3}x_{3}^{6} - 601396916968120783660082925075/21718302958219555766272x_{2}^{3}x_{3}^{2} - 2740130601308450740519362185296150775527634335/546558989825232693772186288128x_{2}^{2}x_{3}^{20} + 13130229179927805291822140520894407616715/44479084458433650209325056\nu x_{2}^{2}x_{3}^{16} + 1695673905168933207373239724005802205/260619635498634669195264x_{2}^{2}x_{3}^{12} - 2698129303541582307435425319115/42418560465272569856\nu x_{2}^{2}x_{3}^{8} - 115663251267346085747635615/497092505452412928x_{2}^{2}x_{3}^{4} - 9652497235/77158912\nu x_{2}^{2} + 22445203605195785512233589955142851677/69227090679324834004992\nu x_{2}x_{3}^{18} + 60427677880153177284139628626265/3976740043619303424x_{2}x_{3}^{14} - 234977350211958477337993073753/990301475705978880\nu x_{2}x_{3}^{10} - 1560649479991815979729/1264171614208x_{2}x_{3}^{6} - 16380669159800832/217437491873905\nu x_{2}x_{3}^{2} + 2684866068406259863475564774377/394573244226600960x_{3}^{16} - 40384339012524969958431767/192662716907520\nu x_{3}^{12} - 3036065512903273239437/1881471844800x_{3}^{8} - 17932622332166144/647236113943725\nu x_{3}^{4} + 215727978120740864/72903096921031425\)

Belyi Curve 16: 32S12-4,8,8-g9-path43

\(8589934592/281462092005375\nu^{2}x_{1}^{3}x_{2} - 3448016925097984/18445618199572250625x_{1}^{2}x_{2} + 838417128229055758336/239885264685437119378125x_{1}^{2}x_{3}^{2} - 2513255020116312064/4703632640890923909375\nu^{2}x_{1}x_{2} + 2881439070388662304768/239885264685437119378125\nu^{2}x_{1}x_{3}^{2} + x_{2}^{2}x_{3}^{6} + 1024/65535\nu^{2}x_{2}^{2}x_{3}^{2} + 126583155195904/277098404709375\nu^{2}x_{2}x_{3}^{4} - 30036579731302776832/4703632640890923909375x_{2} - 579036811290279411712/44423197163969836921875x_{3}^{2}\)
\(-33554432/858967245x_{1}^{2}x_{3}^{2} + x_{1}x_{2}x_{3}^{4} + 1024/65535\nu^{2}x_{1}x_{2} - 134217728/858967245\nu^{2}x_{1}x_{3}^{2} - 1546/255\nu^{2}x_{2}x_{3}^{4} + 1562624/16842495x_{2} + 268435456/1431612075x_{3}^{2}\)
\(x_{1}^{3}x_{3}^{2} + 6\nu^{2}x_{1}^{2}x_{3}^{2} - 16x_{1}x_{3}^{2} - 4294836225/8388608x_{2}x_{3}^{4} - 65535/8192\nu^{2}x_{2} - 16\nu^{2}x_{3}^{2}\)
\(x_{1}^{4} + 16/257\nu^{2}x_{1}^{3} - 96/257x_{1}^{2} - 256/257\nu^{2}x_{1} - 65535/1024\nu^{2}x_{2}x_{3}^{2} + 256/257\)

Belyi Curve 16 Base Field: \(\nu^{4}+1\), discriminant [ <2, 8> ]

Belyi Curve 16 Degree: 20

Belyi Curve 16 Naive Measure: 533619437993393453952291

Belyi Map 16 Numerator:

\(319229886726144/95298165909845\nu^{2}x_{1}^{3} - 155732211323109376/24301032307010475x_{1}^{2} - 206842649490594874221386675/48354564243456\nu^{2}x_{1}x_{3}^{16} + 158366007427330836593047/1204141980672x_{1}x_{3}^{12} + 77671320271627861/76857510\nu^{2}x_{1}x_{3}^{8} + 9716899650732032/647236113943725x_{1}x_{3}^{4} - 54867038975295488/8100344102336825\nu^{2}x_{1} + 748155095279074544632061172796795133116683761179078125/24452635277439283076474197728431177728\nu^{2}x_{2}^{3}x_{3}^{22} - 56757597840747395171075292062747456911483522209375/23879526638124299879369333719171072x_{2}^{3}x_{3}^{18} - 861137114161178139432437302467880137106910625/11659925116271630800473307480064\nu^{2}x_{2}^{3}x_{3}^{14} + 13064908828358926204301134945306929057375/11386645621359014453587214336x_{2}^{3}x_{3}^{10} + 5357033306186489530763362698885325/601068708897752029855744\nu^{2}x_{2}^{3}x_{3}^{6} - 601396916968120783660082925075/21718302958219555766272x_{2}^{3}x_{3}^{2} - 2740130601308450740519362185296150775527634335/546558989825232693772186288128x_{2}^{2}x_{3}^{20} - 13130229179927805291822140520894407616715/44479084458433650209325056\nu^{2}x_{2}^{2}x_{3}^{16} + 1695673905168933207373239724005802205/260619635498634669195264x_{2}^{2}x_{3}^{12} + 2698129303541582307435425319115/42418560465272569856\nu^{2}x_{2}^{2}x_{3}^{8} - 115661183175627798200989087/497092505452412928x_{2}^{2}x_{3}^{4} + 9652497235/77158912\nu^{2}x_{2}^{2} - 22445203605195785512233589955142851677/69227090679324834004992\nu^{2}x_{2}x_{3}^{18} + 60427677880153177284139628626265/3976740043619303424x_{2}x_{3}^{14} + 234977350211958477337993073753/990301475705978880\nu^{2}x_{2}x_{3}^{10} - 1560649479991815979729/1264171614208x_{2}x_{3}^{6} + 16380669159800832/217437491873905\nu^{2}x_{2}x_{3}^{2} + 2684866068406259863475564774377/394573244226600960x_{3}^{16} + 40384339012524969958431767/192662716907520\nu^{2}x_{3}^{12} - 3036065512903273239437/1881471844800x_{3}^{8} + 17932622332166144/647236113943725\nu^{2}x_{3}^{4} + 215727978120740864/72903096921031425\)

Belyi Map 16 Denominator:

\(319229886726144/95298165909845\nu^{2}x_{1}^{3} - 155732211323109376/24301032307010475x_{1}^{2} - 206842649490594874221386675/48354564243456\nu^{2}x_{1}x_{3}^{16} + 158366007427330836593047/1204141980672x_{1}x_{3}^{12} + 77671320271627861/76857510\nu^{2}x_{1}x_{3}^{8} + 9716899650732032/647236113943725x_{1}x_{3}^{4} - 54867038975295488/8100344102336825\nu^{2}x_{1} + 748155095279074544632061172796795133116683761179078125/24452635277439283076474197728431177728\nu^{2}x_{2}^{3}x_{3}^{22} - 56757597840747395171075292062747456911483522209375/23879526638124299879369333719171072x_{2}^{3}x_{3}^{18} - 861137114161178139432437302467880137106910625/11659925116271630800473307480064\nu^{2}x_{2}^{3}x_{3}^{14} + 13064908828358926204301134945306929057375/11386645621359014453587214336x_{2}^{3}x_{3}^{10} + 5357033306186489530763362698885325/601068708897752029855744\nu^{2}x_{2}^{3}x_{3}^{6} - 601396916968120783660082925075/21718302958219555766272x_{2}^{3}x_{3}^{2} - 2740130601308450740519362185296150775527634335/546558989825232693772186288128x_{2}^{2}x_{3}^{20} - 13130229179927805291822140520894407616715/44479084458433650209325056\nu^{2}x_{2}^{2}x_{3}^{16} + 1695673905168933207373239724005802205/260619635498634669195264x_{2}^{2}x_{3}^{12} + 2698129303541582307435425319115/42418560465272569856\nu^{2}x_{2}^{2}x_{3}^{8} - 115663251267346085747635615/497092505452412928x_{2}^{2}x_{3}^{4} + 9652497235/77158912\nu^{2}x_{2}^{2} - 22445203605195785512233589955142851677/69227090679324834004992\nu^{2}x_{2}x_{3}^{18} + 60427677880153177284139628626265/3976740043619303424x_{2}x_{3}^{14} + 234977350211958477337993073753/990301475705978880\nu^{2}x_{2}x_{3}^{10} - 1560649479991815979729/1264171614208x_{2}x_{3}^{6} + 16380669159800832/217437491873905\nu^{2}x_{2}x_{3}^{2} + 2684866068406259863475564774377/394573244226600960x_{3}^{16} + 40384339012524969958431767/192662716907520\nu^{2}x_{3}^{12} - 3036065512903273239437/1881471844800x_{3}^{8} + 17932622332166144/647236113943725\nu^{2}x_{3}^{4} + 215727978120740864/72903096921031425\)

Belyi Curve 17: 32S12-4,8,8-g9-path44

\(-8589934592/281462092005375\nu^{2}x_{1}^{3}x_{2} + 3307279436742656/18445618199572250625x_{1}^{2}x_{2} + 1357393934888722235392/406104878821182527176875x_{1}^{2}x_{3}^{2} + 2098923579520319488/4740523877290068410625\nu^{2}x_{1}x_{2} + 1547508889558540353536/135368292940394175725625\nu^{2}x_{1}x_{3}^{2} + x_{2}^{2}x_{3}^{6} + 1024/65535\nu^{2}x_{2}^{2}x_{3}^{2} - 39903735840768/95298165909845\nu^{2}x_{2}x_{3}^{4} + 3323387007211667456/526724875254452045625x_{2} - 15062144838552548016128/1218314636463547581530625x_{3}^{2}\)
\(33554432/858967245x_{1}^{2}x_{3}^{2} + x_{1}x_{2}x_{3}^{4} + 1024/65535\nu^{2}x_{1}x_{2} + 134217728/858967245\nu^{2}x_{1}x_{3}^{2} - 1526/257\nu^{2}x_{2}x_{3}^{4} + 1583104/16711425x_{2} - 268435456/1431612075x_{3}^{2}\)
\(x_{1}^{3}x_{3}^{2} + 6\nu^{2}x_{1}^{2}x_{3}^{2} - 16x_{1}x_{3}^{2} + 4294836225/8388608x_{2}x_{3}^{4} + 65535/8192\nu^{2}x_{2} - 16\nu^{2}x_{3}^{2}\)
\(x_{1}^{4} - 16/255\nu^{2}x_{1}^{3} + 32/85x_{1}^{2} + 256/255\nu^{2}x_{1} - 65535/1024\nu^{2}x_{2}x_{3}^{2} - 256/255\)

Belyi Curve 17 Base Field: \(\nu^{4}+1\), discriminant [ <2, 8> ]

Belyi Curve 17 Degree: 20

Belyi Curve 17 Naive Measure: 1765073502972636096413995

Belyi Map 17 Numerator:

\(-260254967082778624/70110209207109375\nu^{2}x_{1}^{3} + 20076639941558272/2596674415078125x_{1}^{2} + 781156878579618534894285/195209199616\nu^{2}x_{1}x_{3}^{16} - 60615007712845796799/476584960x_{1}x_{3}^{12} - 239803804887483007/237361650\nu^{2}x_{1}x_{3}^{8} + 5879397911363584/393578252926875x_{1}x_{3}^{4} + 660437567782518784/70110209207109375\nu^{2}x_{1} + 434109499662152431733084045828680965809751195693046875/15103580265093667504578255931649818624\nu^{2}x_{2}^{3}x_{3}^{22} - 33317573397647576469789939150139315696774209965625/14749590102630534672439703058251776x_{2}^{3}x_{3}^{18} - 511401769905418381635715828783519045438674375/7201948292300065758027198758912\nu^{2}x_{2}^{3}x_{3}^{14} + 7849392809816772654981351361894253741625/7033152629199282966823436288x_{2}^{3}x_{3}^{10} + 120474476457426734648697784563359175/13736626228904849544577024\nu^{2}x_{2}^{3}x_{3}^{6} - 369802078749028408198427508645/13414674051664892133376x_{2}^{3}x_{3}^{2} + 424664777570875566290372059956146867845921875/112530442067188527469174980608x_{2}^{2}x_{3}^{20} + 6920646187819884481223466149526914782125/27473252457809699089154048\nu^{2}x_{2}^{2}x_{3}^{16} - 337618268393357164076349357111776505/53658696206659568533504x_{2}^{2}x_{3}^{12} - 9132078627400405466564694786657/131002676285789962240\nu^{2}x_{2}^{2}x_{3}^{8} + 3206398111047251994951511844149/11091730501931630592000x_{2}^{2}x_{3}^{4} - 1614810006683/12152916480\nu^{2}x_{2}^{2} - 262299119752966866718830929707163625/838417128229055758336\nu^{2}x_{2}x_{3}^{18} + 12022724704324519000328720065605/818766726786187264x_{2}x_{3}^{14} + 918051955308746737194104487/3997884408135680\nu^{2}x_{2}x_{3}^{10} - 101252749369199615813092561/84623188033536000x_{2}x_{3}^{6} - 7818228627954466816/100362454496353125\nu^{2}x_{2}x_{3}^{2} - 39914179961376730576690665/6246694387712x_{3}^{16} - 3091444560261580425843/15250718720\nu^{2}x_{3}^{12} + 3112709130403807148941/1936871064000x_{3}^{8} + 10858089641148416/393578252926875\nu^{2}x_{3}^{4} - 362096168601124864/70110209207109375\)

Belyi Map 17 Denominator:

\(-4294836225/1048576x_{2}^{2}x_{3}^{4}\)

Belyi Curve 18: 32S12-4,8,8-g9-path45

\(x_{1}^{3}x_{3}^{2} + x_{1}x_{3}^{2} - x_{2}2\)
\(-10x_{1}^{2}x_{3}^{2} - 2x_{1}x_{2} + x_{2}x_{3}^{4} - 2x_{3}^{2}\)
\(x_{1}^{4} + 6x_{1}^{2} - 1/2x_{2}x_{3}^{2} + 1\)

Belyi Curve 18 Base Field: Rationals

Belyi Curve 18 Degree: 17

Belyi Curve 18 Naive Measure: 28

Belyi Map 18 Numerator:

\(384x_{1}^{2} - 25/3x_{1}x_{3}^{12} + 32x_{1}x_{3}^{4} + 5/48x_{2}^{3}x_{3}^{6} - 5/384x_{2}^{2}x_{3}^{20} + 35/48x_{2}^{2}x_{3}^{12} - 13/12x_{2}^{2}x_{3}^{4} - 5/64x_{2}x_{3}^{18} + 31/3x_{2}x_{3}^{10} - 72x_{2}x_{3}^{2} + 5/24x_{3}^{16} - 2/3x_{3}^{8} + 64\)

Belyi Map 18 Denominator:

\(384x_{1}^{2} - 25/3x_{1}x_{3}^{12} + 32x_{1}x_{3}^{4} + 5/48x_{2}^{3}x_{3}^{6} - 5/384x_{2}^{2}x_{3}^{20} + 35/48x_{2}^{2}x_{3}^{12} - 5/6x_{2}^{2}x_{3}^{4} - 5/64x_{2}x_{3}^{18} + 31/3x_{2}x_{3}^{10} - 72x_{2}x_{3}^{2} + 5/24x_{3}^{16} - 2/3x_{3}^{8} + 64\)

Belyi Curve 19: 32S12-4,8,8-g9-path46

\(x_{1}^{3}x_{3}^{2} + x_{1}x_{3}^{2} - x_{2}2\)
\(-10x_{1}^{2}x_{3}^{2} - 2x_{1}x_{2} + x_{2}x_{3}^{4} - 2x_{3}^{2}\)
\(x_{1}^{4} + 6x_{1}^{2} - 1/2x_{2}x_{3}^{2} + 1\)

Belyi Curve 19 Base Field: Rationals

Belyi Curve 19 Degree: 17

Belyi Curve 19 Naive Measure: 28

Belyi Map 19 Numerator:

\(384x_{1}^{2} - 25/3x_{1}x_{3}^{12} + 32x_{1}x_{3}^{4} + 5/48x_{2}^{3}x_{3}^{6} - 5/384x_{2}^{2}x_{3}^{20} + 35/48x_{2}^{2}x_{3}^{12} - 13/12x_{2}^{2}x_{3}^{4} - 5/64x_{2}x_{3}^{18} + 31/3x_{2}x_{3}^{10} - 72x_{2}x_{3}^{2} + 5/24x_{3}^{16} - 2/3x_{3}^{8} + 64\)

Belyi Map 19 Denominator:

\(384x_{1}^{2} - 25/3x_{1}x_{3}^{12} + 32x_{1}x_{3}^{4} + 5/48x_{2}^{3}x_{3}^{6} - 5/384x_{2}^{2}x_{3}^{20} + 35/48x_{2}^{2}x_{3}^{12} - 5/6x_{2}^{2}x_{3}^{4} - 5/64x_{2}x_{3}^{18} + 31/3x_{2}x_{3}^{10} - 72x_{2}x_{3}^{2} + 5/24x_{3}^{16} - 2/3x_{3}^{8} + 64\)

Belyi Curve 20: 32S12-4,8,8-g9-path5

\(536870912/281487861809153x_{1}^{3}x_{2} + 1/18447869999386460161(-211109453758464\nu - 4398046511104)x_{1}^{2}x_{2} + 1/79235416345888816038194577409(-377783554022048582860800\nu + 16922526508327728459022336)x_{1}^{2}x_{3}^{2} + 1/1209018056149790439571457(3458746921634496512\nu - 36876599657406398464)x_{1}x_{2} + 1/79235416345888816038194577409(-58018699478645680252125184\nu - 1435575199440775401177088)x_{1}x_{3}^{2} + x_{2}^{2}x_{3}^{6} - 256/65537x_{2}^{2}x_{3}^{2} + 1/1209018056149790439571457(132154493251801401262080\nu + 5754983331970573926400)x_{2}x_{3}^{4} + 1/1209018056149790439571457(-479650248684711444480\nu - 2882488479470583808)x_{2} + 1/79235416345888816038194577409(1662243026010995337199616\nu - 62852484301350030691794944)x_{3}^{2}\)
\(41943040/4295098369x_{1}^{2}x_{3}^{2} + x_{1}x_{2}x_{3}^{4} - 256/65537x_{1}x_{2} - 167772160/4295098369\nu x_{1}x_{3}^{2} + 1/65537(393206\nu + 4096)x_{2}x_{3}^{4} + 1/4295098369(-100660736\nu + 1048576)x_{2} - 201326592/4295098369x_{3}^{2}\)
\(x_{1}^{3}x_{3}^{2} - 6\nu x_{1}^{2}x_{3}^{2} - 16x_{1}x_{3}^{2} + 4295098369/2097152x_{2}x_{3}^{4} - 65537/8192x_{2} + 16\nu x_{3}^{2}\)
\(x_{1}^{4} + 1/65537(-16\nu - 4096)x_{1}^{3} + 1/65537(24576\nu - 96)x_{1}^{2} + 1/65537(256\nu + 65536)x_{1} - 65537/256x_{2}x_{3}^{2} + 1/65537(-65536\nu + 256)\)

Belyi Curve 20 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 20 Degree: 20

Belyi Curve 20 Naive Measure: 237709876110283048994627125301

Belyi Map 20 Numerator:

\(4295098369/16777216x_{2}^{2}\)

Belyi Map 20 Denominator:

\(1/1209018056149790439571457(1056860127415873522688000\nu - 54298819971388413050880)x_{1}^{3} + 1/1209018056149790439571457(198294717427640019451904\nu + 2111267008161106289541120)x_{1}^{2} + 1/1356079728538140278784(356037924580009071364953315830261419\nu + 11874168658730337214828848073048896)x_{1}x_{3}^{16} + 1/152218001137991680(-312252481958038637753759491841\nu - 5226732209515135007176691200)x_{1}x_{3}^{12} + 1/103460672648478720(414570349037226788675027287\nu + 54167170619845447250880)x_{1}x_{3}^{8} + 1/904080742081957724209(33427299738872446976\nu - 13430515443734709534720)x_{1}x_{3}^{4} + 1/1209018056149790439571457(-2407891072964571755839488\nu + 396567818254366011293696)x_{1} + 1/1639399797285755073653007869521289393926569984(197482611966494330768294649625274746961969171620312022454567816877\nu + 6172617363878532786160292292146310573643066963113162124554835968)x_{2}^{3}x_{3}^{22} + 1/368040543571694296348107010937789465231360(-865920442583905508529959236658868949890291201046060381967651\nu - 22036951283004348535936727387236703575824642525661185121280)x_{2}^{3}x_{3}^{18} + 1/62538139239721491762275995999194694287360(1149544051519665671054737851834021766068150608768160706277\nu + 22579593116601149165889554363218817401250056407197429760)x_{2}^{3}x_{3}^{14} + 1/244289606405162077196390609371854274560(-17540985568074396511155261878932526568441310221053669\nu - 242691258032046414148917054969306119972291138411520)x_{2}^{3}x_{3}^{10} + 1/636170850013442909365600545239203840(89219771940308869888922051499055373661588710647\nu + 716391884084716021263074335875046634894120960)x_{2}^{3}x_{3}^{6} + 1/7455127148595034094128131389521920(-816847023595502565510924858430362323257697\nu - 1816479533650177461823415645833906529280)x_{2}^{3}x_{3}^{2} + 1/48857921281032415439278121874370854912(30709988209134828897102862825030741260119224026009126400\nu - 215637065812307947120065582624421275339201178246700450805)x_{2}^{2}x_{3}^{20} + 1/15904271250336072734140013630980096(-87362552423932670036632877359495921872633214415360\nu + 1101014463932569976145619276164676545364986460477095)x_{2}^{2}x_{3}^{16} + 1/1863781787148758523532032847380480(12674581671005217319514080427058076613315426816\nu - 757455111358754474938518896935872870789092244315)x_{2}^{2}x_{3}^{12} + 1/1213399601008306330424500551680(58749885517197262808034766326165427496448\nu + 1284194469230200783043745068381713550405955)x_{2}^{2}x_{3}^{8} + 1/11375621259452871847729692672(-1272210855499482693226635193285835264\nu - 11734471490664975150668588747615224821)x_{2}^{2}x_{3}^{4} + 1/13794756353130496(53205329113448637\nu + 3531775394959016192)x_{2}^{2} + 1/50209638662412675741703471104(-4062935103583010058643451942206340427780573691\nu - 72558896888116648557463685636324185804529664)x_{2}x_{3}^{18} + 1/28439053148632179619324231680(26953337927588843554586522746423746920265089\nu + 461246047146572816271991765802462060221440)x_{2}x_{3}^{14} + 1/111090051361844451637985280(-411231126824765732009288886803536295297\nu - 6730369329116678091699973058003404800)x_{2}x_{3}^{10} + 1/433945513132204889210880(2092320589272918681982307334252331\nu + 32670607025043696381131980231680)x_{2}x_{3}^{6} + 1/59250739593825263371485233(-75379452938771231481419776\nu - 4501865546715175861656220020)x_{2}x_{3}^{2} + 1/43394551313220488921088(-571166458128825752376802594155950592\nu + 18159238658958685673091168429042819439)x_{3}^{16} + 1/423774915168168837120(23190888648645007323448398436864\nu - 1385429217060224081234707607217963)x_{3}^{12} + 1/3310741524751319040(-42839587725964666419902976\nu + 21143264877212490389049665323)x_{3}^{8} + 1/904080742081957724209(24794792886138333822976\nu + 53019541425683955712)x_{3}^{4} + 1/1209018056149790439571457(-330459731585146757840896\nu - 1199887584923845056987136)\)

Belyi Curve 21: 32S12-4,8,8-g9-path6

\(x_{1}^{4}x_{2} + 3x_{1}^{4} + x_{2}^{2} - 1\)
\(x_{1}^{2}x_{3}^{2} - x_{1}^{2} + 1/132(\nu^{6} + 6\nu^{5} + 35\nu^{4} + 100\nu^{3} + 241\nu^{2} + 298\nu + 375)x_{3}^{2} + 1/132(\nu^{6} + 6\nu^{5} + 35\nu^{4} + 100\nu^{3} + 241\nu^{2} + 298\nu + 375)\)
\(1/66(-\nu^{6} - 6\nu^{5} - 35\nu^{4} - 100\nu^{3} - 241\nu^{2} - 298\nu - 375)x_{1}^{2}x_{2} + 1/22(-\nu^{6} - 6\nu^{5} - 35\nu^{4} - 100\nu^{3} - 241\nu^{2} - 298\nu - 375)x_{1}^{2} + x_{2}^{2}x_{3}^{2} - x_{2}^{2} + 2x_{2}x_{3}^{2} + 2x_{2} + 5x_{3}^{2} + 7\)

Belyi Curve 21 Base Field: \(\nu^{8}+8\nu^{7}+44\nu^{6}+152\nu^{5}+402\nu^{4}+744\nu^{3}+1172\nu^{2}+1176\nu^{1}+657\), discriminant [ <2, 60>, <3, 4>, <7, 2>, <11, 4> ]

Belyi Curve 21 Degree: 14

Belyi Curve 21 Naive Measure: 1526

Belyi Map 21 Numerator:

\(-4x_{2}x_{3}^{8} - 4x_{2}x_{3}^{4} - 4x_{3}^{8} - 16x_{3}^{6} - 4x_{3}^{4}\)

Belyi Map 21 Denominator:

\(x_{3}^{12} + 2x_{3}^{10} - x_{3}^{8} - 4x_{3}^{6} - x_{3}^{4} + 2x_{3}^{2} + 1\)