32S17-2,16,16-g7

graph data
Name 32S17-2,16,16-g7
Type Hyperbolic
Degree 32
Genus 7
Galois orbit size for 32S17-2,16,16-g7-path1 1
Galois orbit size for 32S17-2,16,16-g7-path2 1
Galois orbit size for 32S17-2,16,16-g7-path3 1
Galois orbit size for 32S17-2,16,16-g7-path4 1
Galois orbit size for 32S17-2,16,16-g7-path5 1
Galois orbit size for 32S17-2,16,16-g7-path6 1
Galois orbit size for 32S17-2,16,16-g7-path7 1
Passport size 1
Pointed size 1

Above

64S27-4,16,16-g21 64S44-4,16,16-g21 64S29-2,16,16-g13

Below

16T5-2,8,8-g3

Belyi Curve 1: 32S17-2,16,16-g7-path1

\(-65537/281470681808896x_{1}^{16} - 1/18888889483920282747904\nu^{4}x_{1}^{15}x_{3} + 15/9444444741960141373952x_{1}^{14}x_{3}^{2} + 35/1180555592745017671744\nu^{4}x_{1}^{13}x_{3}^{3} - 455/1180555592745017671744x_{1}^{12}x_{3}^{4} - 273/73784724546563604484\nu^{4}x_{1}^{11}x_{3}^{5} + 1001/36892362273281802242x_{1}^{10}x_{3}^{6} + 2860/18446181136640901121\nu^{4}x_{1}^{9}x_{3}^{7} - 12870/18446181136640901121x_{1}^{8}x_{3}^{8} - 45760/18446181136640901121\nu^{4}x_{1}^{7}x_{3}^{9} + 128128/18446181136640901121x_{1}^{6}x_{3}^{10} + 279552/18446181136640901121\nu^{4}x_{1}^{5}x_{3}^{11} - 465920/18446181136640901121x_{1}^{4}x_{3}^{12} - 573440/18446181136640901121\nu^{4}x_{1}^{3}x_{3}^{13} + 491520/18446181136640901121x_{1}^{2}x_{3}^{14} + 262144/18446181136640901121\nu^{4}x_{1}x_{3}^{15} + x_{2}^{2} - 65536/18446181136640901121x_{3}^{16}\)

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

Belyi Curve 1 Degree: 16

Belyi Curve 1 Naive Measure: 30989584591027395692177

Belyi Map 1 Numerator:

\(18446181136640901121/4294967296x_{2}^{2}\)

Belyi Map 1 Denominator:

\(-64/281474976710657\nu^{4}x_{1}^{15} + 1920/281474976710657x_{1}^{14} + 35840/281474976710657\nu^{4}x_{1}^{13} - 465920/281474976710657x_{1}^{12} - 4472832/281474976710657\nu^{4}x_{1}^{11} + 32800768/281474976710657x_{1}^{10} + 187432960/281474976710657\nu^{4}x_{1}^{9} - 843448320/281474976710657x_{1}^{8} - 2998927360/281474976710657\nu^{4}x_{1}^{7} + 8396996608/281474976710657x_{1}^{6} + 18320719872/281474976710657\nu^{4}x_{1}^{5} - 30534533120/281474976710657x_{1}^{4} - 37580963840/281474976710657\nu^{4}x_{1}^{3} + 32212254720/281474976710657x_{1}^{2} + 17179869184/281474976710657\nu^{4}x_{1} + 281470681808896/65537x_{2}^{2} - 4294967296/281474976710657\)

Belyi Curve 2: 32S17-2,16,16-g7-path3

\(-3949508/61681x_{1}^{16} - 14868736/3804545761\nu^{2}x_{1}^{15}x_{3} + 446062080/3804545761x_{1}^{14}x_{3}^{2} + 8326492160/3804545761\nu^{2}x_{1}^{13}x_{3}^{3} - 108244398080/3804545761x_{1}^{12}x_{3}^{4} - 1039146221568/3804545761\nu^{2}x_{1}^{11}x_{3}^{5} + 7620405624832/3804545761x_{1}^{10}x_{3}^{6} + 43545174999040/3804545761\nu^{2}x_{1}^{9}x_{3}^{7} - 195953287495680/3804545761x_{1}^{8}x_{3}^{8} - 696722799984640/3804545761\nu^{2}x_{1}^{7}x_{3}^{9} + 1950823839956992/3804545761x_{1}^{6}x_{3}^{10} + 4256342923542528/3804545761\nu^{2}x_{1}^{5}x_{3}^{11} - 7093904872570880/3804545761x_{1}^{4}x_{3}^{12} - 8730959843164160/3804545761\nu^{2}x_{1}^{3}x_{3}^{13} + 7483679865569280/3804545761x_{1}^{2}x_{3}^{14} + 3991295928303616/3804545761\nu^{2}x_{1}x_{3}^{15} + x_{2}^{2} - 997823982075904/3804545761x_{3}^{16}\)

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

Belyi Curve 2 Degree: 16

Belyi Curve 2 Naive Measure: 35449836253440391

Belyi Map 2 Numerator:

\(3804545761/232324x_{2}^{2}\)

Belyi Map 2 Denominator:

\(67108864/1048577\nu^{2}x_{1}^{15} - 2013265920/1048577x_{1}^{14} - 37580963840/1048577\nu^{2}x_{1}^{13} + 488552529920/1048577x_{1}^{12} + 4690104287232/1048577\nu^{2}x_{1}^{11} - 34394098106368/1048577x_{1}^{10} - 196537703464960/1048577\nu^{2}x_{1}^{9} + 884419665592320/1048577x_{1}^{8} + 3144603255439360/1048577\nu^{2}x_{1}^{7} - 8804889115230208/1048577x_{1}^{6} - 19210667160502272/1048577\nu^{2}x_{1}^{5} + 32017778600837120/1048577x_{1}^{4} + 39406496739491840/1048577\nu^{2}x_{1}^{3} - 33776997205278720/1048577x_{1}^{2} - 18014398509481984/1048577\nu^{2}x_{1} + 61681/3949508x_{2}^{2} + 4503599627370496/1048577\)

Belyi Curve 3: 32S17-2,16,16-g7-path5

\(-65537/281470681808896x_{1}^{16} - 1/18888889483920282747904\nu x_{1}^{15}x_{3} + 15/9444444741960141373952x_{1}^{14}x_{3}^{2} + 35/1180555592745017671744\nu x_{1}^{13}x_{3}^{3} - 455/1180555592745017671744x_{1}^{12}x_{3}^{4} - 273/73784724546563604484\nu x_{1}^{11}x_{3}^{5} + 1001/36892362273281802242x_{1}^{10}x_{3}^{6} + 2860/18446181136640901121\nu x_{1}^{9}x_{3}^{7} - 12870/18446181136640901121x_{1}^{8}x_{3}^{8} - 45760/18446181136640901121\nu x_{1}^{7}x_{3}^{9} + 128128/18446181136640901121x_{1}^{6}x_{3}^{10} + 279552/18446181136640901121\nu x_{1}^{5}x_{3}^{11} - 465920/18446181136640901121x_{1}^{4}x_{3}^{12} - 573440/18446181136640901121\nu x_{1}^{3}x_{3}^{13} + 491520/18446181136640901121x_{1}^{2}x_{3}^{14} + 262144/18446181136640901121\nu x_{1}x_{3}^{15} + x_{2}^{2} - 65536/18446181136640901121x_{3}^{16}\)

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

Belyi Curve 3 Degree: 16

Belyi Curve 3 Naive Measure: 30989584591027395692177

Belyi Map 3 Numerator:

\(18446181136640901121/4294967296x_{2}^{2}\)

Belyi Map 3 Denominator:

\(-64/281474976710657\nu x_{1}^{15} + 1920/281474976710657x_{1}^{14} + 35840/281474976710657\nu x_{1}^{13} - 465920/281474976710657x_{1}^{12} - 4472832/281474976710657\nu x_{1}^{11} + 32800768/281474976710657x_{1}^{10} + 187432960/281474976710657\nu x_{1}^{9} - 843448320/281474976710657x_{1}^{8} - 2998927360/281474976710657\nu x_{1}^{7} + 8396996608/281474976710657x_{1}^{6} + 18320719872/281474976710657\nu x_{1}^{5} - 30534533120/281474976710657x_{1}^{4} - 37580963840/281474976710657\nu x_{1}^{3} + 32212254720/281474976710657x_{1}^{2} + 17179869184/281474976710657\nu x_{1} + 281470681808896/65537x_{2}^{2} - 4294967296/281474976710657\)

Belyi Curve 4: 32S17-2,16,16-g7-path6

\(x_{1}^{8}x_{2} + 3x_{1}^{8}x_{3}^{8} + x_{2}^{2} - x_{3}^{16}\)

Belyi Curve 4 Base Field: Rationals

Belyi Curve 4 Degree: 16

Belyi Curve 4 Naive Measure: 6

Belyi Map 4 Numerator:

\(x_{1}^{32} - 8x_{1}^{24} + 8x_{1}^{16} - 32x_{1}^{8} - x_{2}^{4} + 4x_{2}^{3} - 6x_{2}^{2} + 4x_{2} + 15\)

Belyi Map 4 Denominator:

\(16x_{1}^{16}\)

Belyi Curve 5: 32S17-2,16,16-g7-path7

\(x_{1}^{8}x_{2} + x_{2}^{2} + x_{3}^{16}\)

Belyi Curve 5 Base Field: Rationals

Belyi Curve 5 Degree: 16

Belyi Curve 5 Naive Measure: 3

Belyi Map 5 Numerator:

\(-x_{1}^{16} + 4\)

Belyi Map 5 Denominator:

\(4\)