32S9-8,4,2-g3

graph data
Name 32S9-8,4,2-g3
Type Hyperbolic
Degree 32
Genus 3
Galois orbit size for 32S9-8,4,2-g3-path1 1
Galois orbit size for 32S9-8,4,2-g3-path10 1
Galois orbit size for 32S9-8,4,2-g3-path11 1
Galois orbit size for 32S9-8,4,2-g3-path12 1
Galois orbit size for 32S9-8,4,2-g3-path13 1
Galois orbit size for 32S9-8,4,2-g3-path14 1
Galois orbit size for 32S9-8,4,2-g3-path15 1
Galois orbit size for 32S9-8,4,2-g3-path16 1
Galois orbit size for 32S9-8,4,2-g3-path17 1
Galois orbit size for 32S9-8,4,2-g3-path2 1
Galois orbit size for 32S9-8,4,2-g3-path3 1
Galois orbit size for 32S9-8,4,2-g3-path4 1
Galois orbit size for 32S9-8,4,2-g3-path5 1
Galois orbit size for 32S9-8,4,2-g3-path6 1
Galois orbit size for 32S9-8,4,2-g3-path7 1
Galois orbit size for 32S9-8,4,2-g3-path8 1
Galois orbit size for 32S9-8,4,2-g3-path9 1
Passport size 1
Pointed size 1

Above

64S41-16,4,2-g7 64S39-16,4,4-g15 64S8-8,4,2-g5 64S8-8,4,4-g13 64S40-16,8,4-g19 64S21-8,4,4-g13 64S6-8,8,2-g9 64S43-16,8,4-g19 64S12-8,8,2-g9 64S13-8,8,4-g17 64S40-16,8,2-g11 64S38-16,4,2-g7 64S6-8,8,4-g17 64S42-16,8,2-g11 64S41-16,4,4-g15

Below

16T10-4,4,2-g1 16T13-8,2,2-g0 16T12-8,4,2-g2

Belyi Curve 1: 32S9-8,4,2-g3-path10

\(-128/65537x_{1}^{8} + 4096/4295098369\nu x_{1}^{7}x_{3} + 57344/4295098369x_{1}^{6}x_{3}^{2} - 458752/4295098369\nu x_{1}^{5}x_{3}^{3} - 2293760/4295098369x_{1}^{4}x_{3}^{4} + 7340032/4295098369\nu x_{1}^{3}x_{3}^{5} + 14680064/4295098369x_{1}^{2}x_{3}^{6} - 16777216/4295098369\nu x_{1}x_{3}^{7} + x_{2}^{2} - 8388608/4295098369x_{3}^{8}\)

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

Belyi Curve 1 Degree: 8

Belyi Curve 1 Naive Measure: 34360852490

Belyi Map 1 Numerator:

\(65536/65535\nu x_{1}^{7}x_{2}^{2} - 47947011751746898719233241849280016249717260288/17196235911533697689775860335577335152326148867\nu x_{1}^{7} + 3940512234078208/281470681677825x_{1}^{6}x_{2}^{2} - 43910801206958070900536869370712787246587683224420352/5634776602311804390497305035460303296038470829994225x_{1}^{6} - 229534962215826751488/2049638229457735225\nu x_{1}^{5}x_{2}^{2} + 31812960794629138268615607554813261469508447678496768/1878258867437268130165768345153434432012823609998075\nu x_{1}^{5} - 676771199636814106253590528/1208944265795744340967425x_{1}^{4}x_{2}^{2} + 157823732825922840913260591374888984960530336760987648/5634776602311804390497305035460303296038470829994225x_{1}^{4} + 15757636707613984297407890849792/8803397816383966319331348025\nu x_{1}^{3}x_{2}^{2} - 63755088232551135810639013060853070410077697126432768/1878258867437268130165768345153434432012823609998075\nu x_{1}^{3} + 18529697117833019806943436013387644928/5192534544231204006030166999629825x_{1}^{2}x_{2}^{2} - 159170583171986157387281605803814288253016709227610112/5634776602311804390497305035460303296038470829994225x_{1}^{2} - 18180573941678347607126473651723465392128/4537375152337072225909320728729864547\nu x_{1}x_{2}^{2} + 5355396786183494322014340594047935958187535209857024/375651773487453626033153669030686886402564721999615\nu x_{1} - 68721573904/4294836225x_{2}^{4} - 36715009147245839747774486416061245288005763072/22302446651903602685206436444907684961255425x_{2}^{2} + 307993666083658402891183312718102741305305859272736768/95791202239300674638454185602825156032654004109901825\)

Belyi Map 1 Denominator:

\(65536/65535\nu x_{1}^{7}x_{2}^{2} - 47947011751746898719233241849280016249717260288/17196235911533697689775860335577335152326148867\nu x_{1}^{7} + 3940512234078208/281470681677825x_{1}^{6}x_{2}^{2} - 43910801206958070900536869370712787246587683224420352/5634776602311804390497305035460303296038470829994225x_{1}^{6} - 229534962215826751488/2049638229457735225\nu x_{1}^{5}x_{2}^{2} + 31812960794629138268615607554813261469508447678496768/1878258867437268130165768345153434432012823609998075\nu x_{1}^{5} - 676771199636814106253590528/1208944265795744340967425x_{1}^{4}x_{2}^{2} + 157823732825922840913260591374888984960530336760987648/5634776602311804390497305035460303296038470829994225x_{1}^{4} + 15757636707613984297407890849792/8803397816383966319331348025\nu x_{1}^{3}x_{2}^{2} - 63755088232551135810639013060853070410077697126432768/1878258867437268130165768345153434432012823609998075\nu x_{1}^{3} + 18529697117833019806943436013387644928/5192534544231204006030166999629825x_{1}^{2}x_{2}^{2} - 159170583171986157387281605803814288253016709227610112/5634776602311804390497305035460303296038470829994225x_{1}^{2} - 18180573941678347607126473651723465392128/4537375152337072225909320728729864547\nu x_{1}x_{2}^{2} + 5355396786183494322014340594047935958187535209857024/375651773487453626033153669030686886402564721999615\nu x_{1} + 4295098369/16384x_{2}^{4} - 36715009147245839747774486416061245288005763072/22302446651903602685206436444907684961255425x_{2}^{2} + 307993666083658402891183312718102741305305859272736768/95791202239300674638454185602825156032654004109901825\)

Belyi Curve 2: 32S9-8,4,2-g3-path11

\(-4/4097x_{1}^{8} - 65536/16785409\nu x_{1}^{7}x_{3} + 114688/16785409x_{1}^{6}x_{3}^{2} + 114688/16785409\nu x_{1}^{5}x_{3}^{3} - 71680/16785409x_{1}^{4}x_{3}^{4} - 28672/16785409\nu x_{1}^{3}x_{3}^{5} + 7168/16785409x_{1}^{2}x_{3}^{6} + 1024/16785409\nu x_{1}x_{3}^{7} + x_{2}^{2} - 64/16785409x_{3}^{8}\)

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

Belyi Curve 2 Degree: 8

Belyi Curve 2 Naive Measure: 134287370

Belyi Map 2 Numerator:

\(16384/4095\nu x_{1}^{7}x_{2}^{2} - 1380595303167693507267848568832/266365256860644908139935563479036723\nu x_{1}^{7} - 481304743936/68702695425x_{1}^{6}x_{2}^{2} + 89336747843735789449722212323426304/5453828634221704494165180662233276903425x_{1}^{6} - 656752313184256/93824981052075\nu x_{1}^{5}x_{2}^{2} + 40685165732320527053538397189046272/1817942878073901498055060220744425634475\nu x_{1}^{5} + 5053522706079660544/1153202842111053825x_{1}^{4}x_{2}^{2} - 93357383070902920915262951984267264/5453828634221704494165180662233276903425x_{1}^{4} + 915974942564270851072/524963560458776391225\nu x_{1}^{3}x_{2}^{2} - 1597360359521367043016134019121152/201993653119322388672784468971602848275\nu x_{1}^{3} - 8598673843176912944363776/19356981364796461873639425x_{1}^{2}x_{2}^{2} + 245370145178479329540646631407616/111302625188198050901330217596597487825x_{1}^{2} - 10976940908965329361584896/195816179386595319250125245\nu x_{1}x_{2}^{2} + 41585362627490380700373073362944/121196191871593433203670681382961708965\nu x_{1} - 17188258816/16769025x_{2}^{4} + 3228751834148423843187244531696/324914849213486814301944067149825x_{2}^{2} - 125371728095392837782416671112192/5453828634221704494165180662233276903425\)

Belyi Map 2 Denominator:

\(16384/4095\nu x_{1}^{7}x_{2}^{2} - 1380595303167693507267848568832/266365256860644908139935563479036723\nu x_{1}^{7} - 481304743936/68702695425x_{1}^{6}x_{2}^{2} + 89336747843735789449722212323426304/5453828634221704494165180662233276903425x_{1}^{6} - 656752313184256/93824981052075\nu x_{1}^{5}x_{2}^{2} + 40685165732320527053538397189046272/1817942878073901498055060220744425634475\nu x_{1}^{5} + 5053522706079660544/1153202842111053825x_{1}^{4}x_{2}^{2} - 93357383070902920915262951984267264/5453828634221704494165180662233276903425x_{1}^{4} + 915974942564270851072/524963560458776391225\nu x_{1}^{3}x_{2}^{2} - 1597360359521367043016134019121152/201993653119322388672784468971602848275\nu x_{1}^{3} - 8598673843176912944363776/19356981364796461873639425x_{1}^{2}x_{2}^{2} + 245370145178479329540646631407616/111302625188198050901330217596597487825x_{1}^{2} - 10976940908965329361584896/195816179386595319250125245\nu x_{1}x_{2}^{2} + 41585362627490380700373073362944/121196191871593433203670681382961708965\nu x_{1} + 16785409/16x_{2}^{4} + 3228751834148423843187244531696/324914849213486814301944067149825x_{2}^{2} - 125371728095392837782416671112192/5453828634221704494165180662233276903425\)

Belyi Curve 3: 32S9-8,4,2-g3-path15

\(-256/65537x_{1}^{8} + 8192/4295098369\nu x_{1}^{7}x_{3} + 114688/4295098369x_{1}^{6}x_{3}^{2} - 917504/4295098369\nu x_{1}^{5}x_{3}^{3} - 4587520/4295098369x_{1}^{4}x_{3}^{4} + 14680064/4295098369\nu x_{1}^{3}x_{3}^{5} + 29360128/4295098369x_{1}^{2}x_{3}^{6} - 33554432/4295098369\nu x_{1}x_{3}^{7} + x_{2}^{2} - 16777216/4295098369x_{3}^{8}\)

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

Belyi Curve 3 Degree: 8

Belyi Curve 3 Naive Measure: 34360852490

Belyi Map 3 Numerator:

\(32768/65535\nu x_{1}^{7}x_{2}^{2} - 47947011751746898719233241849280016249717260288/17196235911533697689775860335577335152326148867\nu x_{1}^{7} + 1970256117039104/281470681677825x_{1}^{6}x_{2}^{2} - 43910801206958070900536869370712787246587683224420352/5634776602311804390497305035460303296038470829994225x_{1}^{6} - 114767481107913375744/2049638229457735225\nu x_{1}^{5}x_{2}^{2} + 31812960794629138268615607554813261469508447678496768/1878258867437268130165768345153434432012823609998075\nu x_{1}^{5} - 338385599818407053126795264/1208944265795744340967425x_{1}^{4}x_{2}^{2} + 157823732825922840913260591374888984960530336760987648/5634776602311804390497305035460303296038470829994225x_{1}^{4} + 7878818353806992148703945424896/8803397816383966319331348025\nu x_{1}^{3}x_{2}^{2} - 63755088232551135810639013060853070410077697126432768/1878258867437268130165768345153434432012823609998075\nu x_{1}^{3} + 9264848558916509903471718006693822464/5192534544231204006030166999629825x_{1}^{2}x_{2}^{2} - 159170583171986157387281605803814288253016709227610112/5634776602311804390497305035460303296038470829994225x_{1}^{2} - 9090286970839173803563236825861732696064/4537375152337072225909320728729864547\nu x_{1}x_{2}^{2} + 5355396786183494322014340594047935958187535209857024/375651773487453626033153669030686886402564721999615\nu x_{1} - 17180393476/4294836225x_{2}^{4} - 18357504573622919873887243208030622644002881536/22302446651903602685206436444907684961255425x_{2}^{2} + 307993666083658402891183312718102741305305859272736768/95791202239300674638454185602825156032654004109901825\)

Belyi Map 3 Denominator:

\(32768/65535\nu x_{1}^{7}x_{2}^{2} - 47947011751746898719233241849280016249717260288/17196235911533697689775860335577335152326148867\nu x_{1}^{7} + 1970256117039104/281470681677825x_{1}^{6}x_{2}^{2} - 43910801206958070900536869370712787246587683224420352/5634776602311804390497305035460303296038470829994225x_{1}^{6} - 114767481107913375744/2049638229457735225\nu x_{1}^{5}x_{2}^{2} + 31812960794629138268615607554813261469508447678496768/1878258867437268130165768345153434432012823609998075\nu x_{1}^{5} - 338385599818407053126795264/1208944265795744340967425x_{1}^{4}x_{2}^{2} + 157823732825922840913260591374888984960530336760987648/5634776602311804390497305035460303296038470829994225x_{1}^{4} + 7878818353806992148703945424896/8803397816383966319331348025\nu x_{1}^{3}x_{2}^{2} - 63755088232551135810639013060853070410077697126432768/1878258867437268130165768345153434432012823609998075\nu x_{1}^{3} + 9264848558916509903471718006693822464/5192534544231204006030166999629825x_{1}^{2}x_{2}^{2} - 159170583171986157387281605803814288253016709227610112/5634776602311804390497305035460303296038470829994225x_{1}^{2} - 9090286970839173803563236825861732696064/4537375152337072225909320728729864547\nu x_{1}x_{2}^{2} + 5355396786183494322014340594047935958187535209857024/375651773487453626033153669030686886402564721999615\nu x_{1} + 4295098369/65536x_{2}^{4} - 18357504573622919873887243208030622644002881536/22302446651903602685206436444907684961255425x_{2}^{2} + 307993666083658402891183312718102741305305859272736768/95791202239300674638454185602825156032654004109901825\)

Belyi Curve 4: 32S9-8,4,2-g3-path16

\(-256/65537x_{1}^{8} + 8192/4295098369\nu x_{1}^{7}x_{3} + 114688/4295098369x_{1}^{6}x_{3}^{2} - 917504/4295098369\nu x_{1}^{5}x_{3}^{3} - 4587520/4295098369x_{1}^{4}x_{3}^{4} + 14680064/4295098369\nu x_{1}^{3}x_{3}^{5} + 29360128/4295098369x_{1}^{2}x_{3}^{6} - 33554432/4295098369\nu x_{1}x_{3}^{7} + x_{2}^{2} - 16777216/4295098369x_{3}^{8}\)

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

Belyi Curve 4 Degree: 8

Belyi Curve 4 Naive Measure: 34360852490

Belyi Map 4 Numerator:

\(32768/65535\nu x_{1}^{7}x_{2}^{2} - 47947011751746898719233241849280016249717260288/17196235911533697689775860335577335152326148867\nu x_{1}^{7} + 1970256117039104/281470681677825x_{1}^{6}x_{2}^{2} - 43910801206958070900536869370712787246587683224420352/5634776602311804390497305035460303296038470829994225x_{1}^{6} - 114767481107913375744/2049638229457735225\nu x_{1}^{5}x_{2}^{2} + 31812960794629138268615607554813261469508447678496768/1878258867437268130165768345153434432012823609998075\nu x_{1}^{5} - 338385599818407053126795264/1208944265795744340967425x_{1}^{4}x_{2}^{2} + 157823732825922840913260591374888984960530336760987648/5634776602311804390497305035460303296038470829994225x_{1}^{4} + 7878818353806992148703945424896/8803397816383966319331348025\nu x_{1}^{3}x_{2}^{2} - 63755088232551135810639013060853070410077697126432768/1878258867437268130165768345153434432012823609998075\nu x_{1}^{3} + 9264848558916509903471718006693822464/5192534544231204006030166999629825x_{1}^{2}x_{2}^{2} - 159170583171986157387281605803814288253016709227610112/5634776602311804390497305035460303296038470829994225x_{1}^{2} - 9090286970839173803563236825861732696064/4537375152337072225909320728729864547\nu x_{1}x_{2}^{2} + 5355396786183494322014340594047935958187535209857024/375651773487453626033153669030686886402564721999615\nu x_{1} - 17180393476/4294836225x_{2}^{4} - 18357504573622919873887243208030622644002881536/22302446651903602685206436444907684961255425x_{2}^{2} + 307993666083658402891183312718102741305305859272736768/95791202239300674638454185602825156032654004109901825\)

Belyi Map 4 Denominator:

\(32768/65535\nu x_{1}^{7}x_{2}^{2} - 47947011751746898719233241849280016249717260288/17196235911533697689775860335577335152326148867\nu x_{1}^{7} + 1970256117039104/281470681677825x_{1}^{6}x_{2}^{2} - 43910801206958070900536869370712787246587683224420352/5634776602311804390497305035460303296038470829994225x_{1}^{6} - 114767481107913375744/2049638229457735225\nu x_{1}^{5}x_{2}^{2} + 31812960794629138268615607554813261469508447678496768/1878258867437268130165768345153434432012823609998075\nu x_{1}^{5} - 338385599818407053126795264/1208944265795744340967425x_{1}^{4}x_{2}^{2} + 157823732825922840913260591374888984960530336760987648/5634776602311804390497305035460303296038470829994225x_{1}^{4} + 7878818353806992148703945424896/8803397816383966319331348025\nu x_{1}^{3}x_{2}^{2} - 63755088232551135810639013060853070410077697126432768/1878258867437268130165768345153434432012823609998075\nu x_{1}^{3} + 9264848558916509903471718006693822464/5192534544231204006030166999629825x_{1}^{2}x_{2}^{2} - 159170583171986157387281605803814288253016709227610112/5634776602311804390497305035460303296038470829994225x_{1}^{2} - 9090286970839173803563236825861732696064/4537375152337072225909320728729864547\nu x_{1}x_{2}^{2} + 5355396786183494322014340594047935958187535209857024/375651773487453626033153669030686886402564721999615\nu x_{1} + 4295098369/65536x_{2}^{4} - 18357504573622919873887243208030622644002881536/22302446651903602685206436444907684961255425x_{2}^{2} + 307993666083658402891183312718102741305305859272736768/95791202239300674638454185602825156032654004109901825\)

Belyi Curve 5: 32S9-8,4,2-g3-path17

\(-256/65537x_{1}^{8} + 8192/4295098369\nu^{4}x_{1}^{7}x_{3} + 114688/4295098369x_{1}^{6}x_{3}^{2} - 917504/4295098369\nu^{4}x_{1}^{5}x_{3}^{3} - 4587520/4295098369x_{1}^{4}x_{3}^{4} + 14680064/4295098369\nu^{4}x_{1}^{3}x_{3}^{5} + 29360128/4295098369x_{1}^{2}x_{3}^{6} - 33554432/4295098369\nu^{4}x_{1}x_{3}^{7} + x_{2}^{2} - 16777216/4295098369x_{3}^{8}\)

Belyi Curve 5 Base Field: \(\nu^{8}+1\), discriminant [ <2, 24> ]

Belyi Curve 5 Degree: 8

Belyi Curve 5 Naive Measure: 34360852490

Belyi Map 5 Numerator:

\(32768/65535\nu^{4}x_{1}^{7}x_{2}^{2} - 47947011751746898719233241849280016249717260288/17196235911533697689775860335577335152326148867\nu^{4}x_{1}^{7} + 1970256117039104/281470681677825x_{1}^{6}x_{2}^{2} - 43910801206958070900536869370712787246587683224420352/5634776602311804390497305035460303296038470829994225x_{1}^{6} - 114767481107913375744/2049638229457735225\nu^{4}x_{1}^{5}x_{2}^{2} + 31812960794629138268615607554813261469508447678496768/1878258867437268130165768345153434432012823609998075\nu^{4}x_{1}^{5} - 338385599818407053126795264/1208944265795744340967425x_{1}^{4}x_{2}^{2} + 157823732825922840913260591374888984960530336760987648/5634776602311804390497305035460303296038470829994225x_{1}^{4} + 7878818353806992148703945424896/8803397816383966319331348025\nu^{4}x_{1}^{3}x_{2}^{2} - 63755088232551135810639013060853070410077697126432768/1878258867437268130165768345153434432012823609998075\nu^{4}x_{1}^{3} + 9264848558916509903471718006693822464/5192534544231204006030166999629825x_{1}^{2}x_{2}^{2} - 159170583171986157387281605803814288253016709227610112/5634776602311804390497305035460303296038470829994225x_{1}^{2} - 9090286970839173803563236825861732696064/4537375152337072225909320728729864547\nu^{4}x_{1}x_{2}^{2} + 5355396786183494322014340594047935958187535209857024/375651773487453626033153669030686886402564721999615\nu^{4}x_{1} - 17180393476/4294836225x_{2}^{4} - 18357504573622919873887243208030622644002881536/22302446651903602685206436444907684961255425x_{2}^{2} + 307993666083658402891183312718102741305305859272736768/95791202239300674638454185602825156032654004109901825\)

Belyi Map 5 Denominator:

\(32768/65535\nu^{4}x_{1}^{7}x_{2}^{2} - 47947011751746898719233241849280016249717260288/17196235911533697689775860335577335152326148867\nu^{4}x_{1}^{7} + 1970256117039104/281470681677825x_{1}^{6}x_{2}^{2} - 43910801206958070900536869370712787246587683224420352/5634776602311804390497305035460303296038470829994225x_{1}^{6} - 114767481107913375744/2049638229457735225\nu^{4}x_{1}^{5}x_{2}^{2} + 31812960794629138268615607554813261469508447678496768/1878258867437268130165768345153434432012823609998075\nu^{4}x_{1}^{5} - 338385599818407053126795264/1208944265795744340967425x_{1}^{4}x_{2}^{2} + 157823732825922840913260591374888984960530336760987648/5634776602311804390497305035460303296038470829994225x_{1}^{4} + 7878818353806992148703945424896/8803397816383966319331348025\nu^{4}x_{1}^{3}x_{2}^{2} - 63755088232551135810639013060853070410077697126432768/1878258867437268130165768345153434432012823609998075\nu^{4}x_{1}^{3} + 9264848558916509903471718006693822464/5192534544231204006030166999629825x_{1}^{2}x_{2}^{2} - 159170583171986157387281605803814288253016709227610112/5634776602311804390497305035460303296038470829994225x_{1}^{2} - 9090286970839173803563236825861732696064/4537375152337072225909320728729864547\nu^{4}x_{1}x_{2}^{2} + 5355396786183494322014340594047935958187535209857024/375651773487453626033153669030686886402564721999615\nu^{4}x_{1} + 4295098369/65536x_{2}^{4} - 18357504573622919873887243208030622644002881536/22302446651903602685206436444907684961255425x_{2}^{2} + 307993666083658402891183312718102741305305859272736768/95791202239300674638454185602825156032654004109901825\)

Belyi Curve 6: 32S9-8,4,2-g3-path2

\(-4/4097x_{1}^{8} - 65536/16785409\nu x_{1}^{7}x_{3} + 114688/16785409x_{1}^{6}x_{3}^{2} + 114688/16785409\nu x_{1}^{5}x_{3}^{3} - 71680/16785409x_{1}^{4}x_{3}^{4} - 28672/16785409\nu x_{1}^{3}x_{3}^{5} + 7168/16785409x_{1}^{2}x_{3}^{6} + 1024/16785409\nu x_{1}x_{3}^{7} + x_{2}^{2} - 64/16785409x_{3}^{8}\)

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

Belyi Curve 6 Degree: 8

Belyi Curve 6 Naive Measure: 134287370

Belyi Map 6 Numerator:

\(16384/4095\nu x_{1}^{7}x_{2}^{2} - 1380595303167693507267848568832/266365256860644908139935563479036723\nu x_{1}^{7} - 481304743936/68702695425x_{1}^{6}x_{2}^{2} + 89336747843735789449722212323426304/5453828634221704494165180662233276903425x_{1}^{6} - 656752313184256/93824981052075\nu x_{1}^{5}x_{2}^{2} + 40685165732320527053538397189046272/1817942878073901498055060220744425634475\nu x_{1}^{5} + 5053522706079660544/1153202842111053825x_{1}^{4}x_{2}^{2} - 93357383070902920915262951984267264/5453828634221704494165180662233276903425x_{1}^{4} + 915974942564270851072/524963560458776391225\nu x_{1}^{3}x_{2}^{2} - 1597360359521367043016134019121152/201993653119322388672784468971602848275\nu x_{1}^{3} - 8598673843176912944363776/19356981364796461873639425x_{1}^{2}x_{2}^{2} + 245370145178479329540646631407616/111302625188198050901330217596597487825x_{1}^{2} - 10976940908965329361584896/195816179386595319250125245\nu x_{1}x_{2}^{2} + 41585362627490380700373073362944/121196191871593433203670681382961708965\nu x_{1} - 17188258816/16769025x_{2}^{4} + 3228751834148423843187244531696/324914849213486814301944067149825x_{2}^{2} - 125371728095392837782416671112192/5453828634221704494165180662233276903425\)

Belyi Map 6 Denominator:

\(16384/4095\nu x_{1}^{7}x_{2}^{2} - 1380595303167693507267848568832/266365256860644908139935563479036723\nu x_{1}^{7} - 481304743936/68702695425x_{1}^{6}x_{2}^{2} + 89336747843735789449722212323426304/5453828634221704494165180662233276903425x_{1}^{6} - 656752313184256/93824981052075\nu x_{1}^{5}x_{2}^{2} + 40685165732320527053538397189046272/1817942878073901498055060220744425634475\nu x_{1}^{5} + 5053522706079660544/1153202842111053825x_{1}^{4}x_{2}^{2} - 93357383070902920915262951984267264/5453828634221704494165180662233276903425x_{1}^{4} + 915974942564270851072/524963560458776391225\nu x_{1}^{3}x_{2}^{2} - 1597360359521367043016134019121152/201993653119322388672784468971602848275\nu x_{1}^{3} - 8598673843176912944363776/19356981364796461873639425x_{1}^{2}x_{2}^{2} + 245370145178479329540646631407616/111302625188198050901330217596597487825x_{1}^{2} - 10976940908965329361584896/195816179386595319250125245\nu x_{1}x_{2}^{2} + 41585362627490380700373073362944/121196191871593433203670681382961708965\nu x_{1} + 16785409/16x_{2}^{4} + 3228751834148423843187244531696/324914849213486814301944067149825x_{2}^{2} - 125371728095392837782416671112192/5453828634221704494165180662233276903425\)

Belyi Curve 7: 32S9-8,4,2-g3-path3

\(1/262143(128\nu^{3} + 640\nu )x_{1}^{8} - 8192/68718952449x_{1}^{7}x_{3} + 1/9816993207(8192\nu^{3} + 40960\nu )x_{1}^{6}x_{3}^{2} + 131072/9816993207x_{1}^{5}x_{3}^{3} + 1/9816993207(-327680\nu^{3} - 1638400\nu )x_{1}^{4}x_{3}^{4} - 2097152/9816993207x_{1}^{3}x_{3}^{5} + 1/9816993207(2097152\nu^{3} + 10485760\nu )x_{1}^{2}x_{3}^{6} + 33554432/68718952449x_{1}x_{3}^{7} + x_{2}^{2} + 1/68718952449(-8388608\nu^{3} - 41943040\nu )x_{3}^{8}\)

Belyi Curve 7 Base Field: \(\nu^{4}+6\nu^{2}+1\), discriminant [ <2, 14> ]

Belyi Curve 7 Degree: 8

Belyi Curve 7 Naive Measure: 255242085526

Belyi Map 7 Numerator:

\(131072/262145x_{1}^{7}x_{2}^{2} + 1/306489754683122061290103612409804135885125602516349747(-26761867251657688233688742484137209149902456249909248\nu^{3} - 133809336258288441168443712420686045749512281249546240\nu )x_{1}^{7} + 1/18014467228696575(-63050944538083328\nu^{3} - 315254722690416640\nu )x_{1}^{6}x_{2}^{2} - 28074714117483792101775332182420216778149089265204559085568/57389111958147880540638722482262932286861607908320360305225x_{1}^{6} - 264459584685465619398656/4722366482732206260225x_{1}^{5}x_{2}^{2} + 1/57389111958147880540638722482262932286861607908320360305225(30656145223469584259127309159558540812134318084690372722688\nu^{3} + 153280726117347921295636545797792704060671590423451863613440\nu )x_{1}^{5} + 1/1237935316882868745674162175(173326150461354606000365109248\nu^{3} + 866630752306773030001825546240\nu )x_{1}^{4}x_{2}^{2} + 102384823924843204356873212952897179164151232461768419704832/57389111958147880540638722482262932286861607908320360305225x_{1}^{4} + 290849596537877712582426727037272064/324516077773625861597261895041025x_{1}^{3}x_{2}^{2} + 1/57389111958147880540638722482262932286861607908320360305225(-63243333993740521680418170878768042998517161797453095108608\nu^{3} - 316216669968702608402090854393840214992585808987265475543040\nu )x_{1}^{3} + 1/85069618175811604236691024951739416575(-76304668534088962180333419988764713811968\nu^{3} - 381523342670444810901667099943823569059840\nu )x_{1}^{2}x_{2}^{2} - 109177177979411507704130148280875828556496934933757205413888/57389111958147880540638722482262932286861607908320360305225x_{1}^{2} - 9183973779455176727912028608798029668262346752/4460080983492356273883779070784765175844045x_{1}x_{2}^{2} + 1/80344756741407032756894211475168105201606251071648504427315(41267996203360213544178137928601764723225798750645870657536\nu^{3} + 206339981016801067720890689643008823616128993753229353287680\nu )x_{1} - 1099503239184/68720001025x_{2}^{4} + 1/5845895046278183753523577484763653487456427442175(3140040423002292532721629990530931321831032369446912\nu^{3} + 15700202115011462663608149952654656609155161847234560\nu )x_{2}^{2} + 105361889737226838544249511839436999678781020185481143386112/401723783707035163784471057375840526008031255358242522136575\)

Belyi Map 7 Denominator:

\(131072/262145x_{1}^{7}x_{2}^{2} + 1/306489754683122061290103612409804135885125602516349747(-26761867251657688233688742484137209149902456249909248\nu^{3} - 133809336258288441168443712420686045749512281249546240\nu )x_{1}^{7} + 1/18014467228696575(-63050944538083328\nu^{3} - 315254722690416640\nu )x_{1}^{6}x_{2}^{2} - 28074714117483792101775332182420216778149089265204559085568/57389111958147880540638722482262932286861607908320360305225x_{1}^{6} - 264459584685465619398656/4722366482732206260225x_{1}^{5}x_{2}^{2} + 1/57389111958147880540638722482262932286861607908320360305225(30656145223469584259127309159558540812134318084690372722688\nu^{3} + 153280726117347921295636545797792704060671590423451863613440\nu )x_{1}^{5} + 1/1237935316882868745674162175(173326150461354606000365109248\nu^{3} + 866630752306773030001825546240\nu )x_{1}^{4}x_{2}^{2} + 102384823924843204356873212952897179164151232461768419704832/57389111958147880540638722482262932286861607908320360305225x_{1}^{4} + 290849596537877712582426727037272064/324516077773625861597261895041025x_{1}^{3}x_{2}^{2} + 1/57389111958147880540638722482262932286861607908320360305225(-63243333993740521680418170878768042998517161797453095108608\nu^{3} - 316216669968702608402090854393840214992585808987265475543040\nu )x_{1}^{3} + 1/85069618175811604236691024951739416575(-76304668534088962180333419988764713811968\nu^{3} - 381523342670444810901667099943823569059840\nu )x_{1}^{2}x_{2}^{2} - 109177177979411507704130148280875828556496934933757205413888/57389111958147880540638722482262932286861607908320360305225x_{1}^{2} - 9183973779455176727912028608798029668262346752/4460080983492356273883779070784765175844045x_{1}x_{2}^{2} + 1/80344756741407032756894211475168105201606251071648504427315(41267996203360213544178137928601764723225798750645870657536\nu^{3} + 206339981016801067720890689643008823616128993753229353287680\nu )x_{1} - 68718952449/65536x_{2}^{4} + 1/5845895046278183753523577484763653487456427442175(3140040423002292532721629990530931321831032369446912\nu^{3} + 15700202115011462663608149952654656609155161847234560\nu )x_{2}^{2} + 105361889737226838544249511839436999678781020185481143386112/401723783707035163784471057375840526008031255358242522136575\)

Belyi Curve 8: 32S9-8,4,2-g3-path8

\(-\nu x_{1}^{8} + x_{2}^{2} + \nu x_{3}^{8}\)

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

Belyi Curve 8 Degree: 8

Belyi Curve 8 Naive Measure: 3

Belyi Map 8 Numerator:

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

Belyi Map 8 Denominator:

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

Belyi Curve 9: 32S9-8,4,2-g3-path9

\(-\nu^{2}x_{1}^{8} + x_{2}^{2} + \nu^{2}x_{3}^{8}\)

Belyi Curve 9 Base Field: \(\nu^{4}+1\), discriminant [ <2, 8> ]

Belyi Curve 9 Degree: 8

Belyi Curve 9 Naive Measure: 3

Belyi Map 9 Numerator:

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

Belyi Map 9 Denominator:

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