32S4-4,8,8-g9

graph data
Name 32S4-4,8,8-g9
Type Hyperbolic
Degree 32
Genus 9
Galois orbit size for 32S4-4,8,8-g9-path1 1
Galois orbit size for 32S4-4,8,8-g9-path10 1
Galois orbit size for 32S4-4,8,8-g9-path11 1
Galois orbit size for 32S4-4,8,8-g9-path12 1
Galois orbit size for 32S4-4,8,8-g9-path13 1
Galois orbit size for 32S4-4,8,8-g9-path14 1
Galois orbit size for 32S4-4,8,8-g9-path15 1
Galois orbit size for 32S4-4,8,8-g9-path16 1
Galois orbit size for 32S4-4,8,8-g9-path17 1
Galois orbit size for 32S4-4,8,8-g9-path18 1
Galois orbit size for 32S4-4,8,8-g9-path19 1
Galois orbit size for 32S4-4,8,8-g9-path2 1
Galois orbit size for 32S4-4,8,8-g9-path20 1
Galois orbit size for 32S4-4,8,8-g9-path21 1
Galois orbit size for 32S4-4,8,8-g9-path22 1
Galois orbit size for 32S4-4,8,8-g9-path23 1
Galois orbit size for 32S4-4,8,8-g9-path24 1
Galois orbit size for 32S4-4,8,8-g9-path25 1
Galois orbit size for 32S4-4,8,8-g9-path3 1
Galois orbit size for 32S4-4,8,8-g9-path4 1
Galois orbit size for 32S4-4,8,8-g9-path5 1
Galois orbit size for 32S4-4,8,8-g9-path6 1
Galois orbit size for 32S4-4,8,8-g9-path7 1
Galois orbit size for 32S4-4,8,8-g9-path8 1
Galois orbit size for 32S4-4,8,8-g9-path9 1
Passport size 1
Pointed size 1

Above

64S28-8,16,16-g25 64S17-4,8,8-g17 64S28-4,16,16-g21 64S3-8,8,8-g21

Below

16T6-2,8,8-g3 16T4-4,4,4-g3 16T6-4,8,8-g5

Belyi Curve 1: 32S4-4,8,8-g9-path1

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

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

Belyi Curve 1 Degree: 20

Belyi Curve 1 Naive Measure: 7

Belyi Map 1 Numerator:

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

Belyi Map 1 Denominator:

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

Belyi Curve 2: 32S4-4,8,8-g9-path10

\(x_{1}^{6} - 143848/960015\nu^{2}x_{1}^{5} + 16565776/14400225x_{1}^{4} - 1413010688/216003375\nu^{2}x_{1}^{3} - 153718528/14529375x_{1}^{2} + 16320255/2097152\nu^{2}x_{1}x_{2}^{2}x_{3}^{2} - 16320255/2097152\nu^{2}x_{1}x_{2}^{2} + 37933285376/6942965625\nu^{2}x_{1}x_{3}^{2} + 20285188096/3240050625\nu^{2}x_{1} - 20672323/1048576x_{2}^{2}x_{3}^{2} + 12480195/1048576x_{2}^{2} + 240149069824/48600759375x_{3}^{2} + 17236815872/3240050625\)
\(536870912/3672057375\nu^{2}x_{1}^{5} + 15778548593721344/59928912734630625x_{1}^{4} - 45745207043424256/299644563673153125\nu^{2}x_{1}^{3} + 10546236824609619968/13484005365291890625x_{1}^{2} + 64/255\nu^{2}x_{1}x_{2}^{2}x_{3}^{2} - 64/255\nu^{2}x_{1}x_{2}^{2} - 422282833810161664/699861870170859375\nu^{2}x_{1}x_{3}^{4} - 19057122560706609152/11897651792904609375\nu^{2}x_{1}x_{3}^{2} - 8965642663013384192/13484005365291890625\nu^{2}x_{1} + x_{2}^{2}x_{3}^{4} - 10082/3825x_{2}^{2}x_{3}^{2} + 5999/4335x_{2}^{2} - 353215911399784448/699861870170859375x_{3}^{4} - 19111517599955943424/11897651792904609375x_{3}^{2} - 11830292528395976704/13484005365291890625\)
\(x_{1}^{2}x_{3}^{2} - x_{1}^{2} + 8/15\nu^{2}x_{1}x_{3}^{2} + 8/17\nu^{2}x_{1} + 16/15x_{3}^{2} + 16/17\)

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

Belyi Curve 2 Degree: 20

Belyi Curve 2 Naive Measure: 80379953794214208189

Belyi Map 2 Numerator:

\(1/1666995368452984760434688(-1108462489395508348250625\nu^{3} + 1108462489395508348250625\nu )x_{2}^{3}x_{3}^{28} + 1/208374421056623095054336(1108462489395508348250625\nu^{3} - 1108462489395508348250625\nu )x_{2}^{3}x_{3}^{26} + 1/1666995368452984760434688(-30173959875690187459126875\nu^{3} + 30173959875690187459126875\nu )x_{2}^{3}x_{3}^{24} + 1/104187210528311547527168(3448123799192256072931875\nu^{3} - 3448123799192256072931875\nu )x_{2}^{3}x_{3}^{22} + 1/1666995368452984760434688(-52756781197640210641715625\nu^{3} + 52756781197640210641715625\nu )x_{2}^{3}x_{3}^{20} + 1/208374421056623095054336(1046430740788156831629375\nu^{3} - 1046430740788156831629375\nu )x_{2}^{3}x_{3}^{18} + 1/481761661482912595765624832(13774269130319577118163833125\nu^{3} - 13774269130319577118163833125\nu )x_{2}^{3}x_{3}^{16} + 1/15055051921341018617675776(-658379803375444798481911875\nu^{3} + 658379803375444798481911875\nu )x_{2}^{3}x_{3}^{14} + 1/481761661482912595765624832(16022227077315041132400913125\nu^{3} - 16022227077315041132400913125\nu )x_{2}^{3}x_{3}^{12} + 1/60220207685364074470703104(-550405356308840126531390625\nu^{3} + 550405356308840126531390625\nu )x_{2}^{3}x_{3}^{10} + 1/481761661482912595765624832(-4895836846716740598260015625\nu^{3} + 4895836846716740598260015625\nu )x_{2}^{3}x_{3}^{8} + 1/30110103842682037235351552(432017485386805872938671875\nu^{3} - 432017485386805872938671875\nu )x_{2}^{3}x_{3}^{6} + 1/481761661482912595765624832(-4038658016578678230535546875\nu^{3} + 4038658016578678230535546875\nu )x_{2}^{3}x_{3}^{4} + 1/60220207685364074470703104(151172525990717451650390625\nu^{3} - 151172525990717451650390625\nu )x_{2}^{3}x_{3}^{2} + 1/481761661482912595765624832(-151172525990717451650390625\nu^{3} + 151172525990717451650390625\nu )x_{2}^{3} + 1/2398554685440000(2393741243606531\nu^{3} - 2393741243606531\nu )x_{2}x_{3}^{28} + 1/2665060761600(-6345022467427\nu^{3} + 6345022467427\nu )x_{2}x_{3}^{26} + 1/10660243046400(-37543083049507\nu^{3} + 37543083049507\nu )x_{2}x_{3}^{24} + 1/5922357248(73559741353\nu^{3} - 73559741353\nu )x_{2}x_{3}^{22} + 1/47378857984(-321756643369\nu^{3} + 321756643369\nu )x_{2}x_{3}^{20} + 1/11844714496(-66773843325\nu^{3} + 66773843325\nu )x_{2}x_{3}^{18} + 1/13692489957376(132125074022025\nu^{3} - 132125074022025\nu )x_{2}x_{3}^{16} + 1/855780622336(-7494237095625\nu^{3} + 7494237095625\nu )x_{2}x_{3}^{14} + 1/3957129597681664(11715326449115625\nu^{3} - 11715326449115625\nu )x_{2}x_{3}^{12} + 1/989282399420416(4504561382671875\nu^{3} - 4504561382671875\nu )x_{2}x_{3}^{10} + 1/1143610453730000896(-5223810581765015625\nu^{3} + 5223810581765015625\nu )x_{2}x_{3}^{8} + 1/142951306716250112(106453888316015625\nu^{3} - 106453888316015625\nu )x_{2}x_{3}^{6} + 1/330503421127970258944(158085336369786328125\nu^{3} - 158085336369786328125\nu )x_{2}x_{3}^{4} + 1/82625855281992564736(-13101701585888671875\nu^{3} + 13101701585888671875\nu )x_{2}x_{3}^{2} + 1/95515488705983404834816(744139743876826171875\nu^{3} - 744139743876826171875\nu )x_{2} + 83521/405000x_{3}^{28} - 83521/317700x_{3}^{26} - 324547/211800x_{3}^{24} + 1445/706x_{3}^{22} + 9333/2824x_{3}^{20} - 6975/1412x_{3}^{18} - 2371725/816136x_{3}^{16} + 556875/102017x_{3}^{14} + 11491875/13874312x_{3}^{12} - 353109375/117931652x_{3}^{10} + 16641703125/68164494856x_{3}^{8} + 12814453125/17041123714x_{3}^{6} - 3221553515625/19699539013384x_{3}^{4} - 576650390625/9849769506692x_{3}^{2} + 92840712890625/5693166774867976\)

Belyi Map 2 Denominator:

\(x_{3}^{20} - 450/353x_{3}^{18} - 440325/102017x_{3}^{16} + 607500/102017x_{3}^{14} - 31033125/29482913x_{3}^{12} - 22781250/29482913x_{3}^{10} + 1833890625/8520561857x_{3}^{8}\)