32S3-8,8,4-g9

graph data
Name 32S3-8,8,4-g9
Type Hyperbolic
Degree 32
Genus 9
Galois orbit size for 32S3-8,8,4-g9-path1 1
Galois orbit size for 32S3-8,8,4-g9-path10 1
Galois orbit size for 32S3-8,8,4-g9-path11 1
Galois orbit size for 32S3-8,8,4-g9-path12 1
Galois orbit size for 32S3-8,8,4-g9-path13 1
Galois orbit size for 32S3-8,8,4-g9-path14 1
Galois orbit size for 32S3-8,8,4-g9-path15 1
Galois orbit size for 32S3-8,8,4-g9-path16 1
Galois orbit size for 32S3-8,8,4-g9-path17 1
Galois orbit size for 32S3-8,8,4-g9-path18 1
Galois orbit size for 32S3-8,8,4-g9-path19 1
Galois orbit size for 32S3-8,8,4-g9-path2 1
Galois orbit size for 32S3-8,8,4-g9-path20 1
Galois orbit size for 32S3-8,8,4-g9-path21 1
Galois orbit size for 32S3-8,8,4-g9-path22 1
Galois orbit size for 32S3-8,8,4-g9-path23 1
Galois orbit size for 32S3-8,8,4-g9-path24 1
Galois orbit size for 32S3-8,8,4-g9-path25 1
Galois orbit size for 32S3-8,8,4-g9-path26 1
Galois orbit size for 32S3-8,8,4-g9-path27 1
Galois orbit size for 32S3-8,8,4-g9-path28 1
Galois orbit size for 32S3-8,8,4-g9-path29 1
Galois orbit size for 32S3-8,8,4-g9-path3 1
Galois orbit size for 32S3-8,8,4-g9-path4 1
Galois orbit size for 32S3-8,8,4-g9-path5 1
Galois orbit size for 32S3-8,8,4-g9-path6 1
Galois orbit size for 32S3-8,8,4-g9-path7 1
Galois orbit size for 32S3-8,8,4-g9-path8 1
Galois orbit size for 32S3-8,8,4-g9-path9 1
Passport size 1
Pointed size 1

Above

64S27-16,16,8-g25 64S26-16,16,4-g21 64S3-8,8,8-g21 64S26-16,16,8-g25 64S2-8,8,8-g21 64S27-16,16,4-g21 64S17-8,8,4-g17

Below

16T5-8,8,2-g3 16T4-4,4,4-g3 16T5-8,8,4-g5

Belyi Curve 1: 32S3-8,8,4-g9-path2

\(x_{1}^{4}x_{3}^{2} + (-4\nu^{2} - 16)x_{1} + 1/4\nu^{2}x_{2}x_{3}^{2} + (2\nu^{2} - 4)x_{3}^{2}\)
\(-x_{1}^{4}x_{2} + (-\nu^{2} - 8)x_{1}^{4} + x_{1}^{3}x_{2}x_{3}^{2} + 8x_{1}^{3}x_{3}^{2} + 1/4\nu^{2}x_{2}^{2} + 4\nu^{2}\)
\(x_{1}^{5} - 1/4\nu^{2}x_{1}x_{2} + (-2\nu^{2} - 20)x_{1} + 1/4\nu^{2}x_{2}x_{3}^{2} + 2\nu^{2}x_{3}^{2}\)
\((-4\nu^{2} + 16)x_{1}^{2} - 2x_{1}x_{2}x_{3}^{2} + (4\nu^{2} - 16)x_{1}x_{3}^{2} + x_{2}x_{3}^{4} + 8x_{3}^{4}\)

Belyi Curve 1 Base Field: \(\nu^{4}+16\), discriminant [ <2, 20> ]

Belyi Curve 1 Degree: 20

Belyi Curve 1 Naive Measure: 125

Belyi Map 1 Numerator:

\(1/91(-358205489152\nu^{2} - 15272835547136)x_{1}x_{3}^{33} + 1/91(-95662988544\nu^{2} - 264042096640)x_{1}x_{3}^{25} + 1/91(-795433432\nu^{2} + 1005282272)x_{1}x_{3}^{17} + 1/182(-1888271\nu^{2} + 11776834)x_{1}x_{3}^{9} - 1/16384\nu^{2}x_{2}^{5}x_{3}^{3} - 1441792x_{2}^{4}x_{3}^{36} + (361984\nu^{2} + 1714944)x_{2}^{4}x_{3}^{28} + 1/364(-14986885\nu^{2} - 35126180)x_{2}^{4}x_{3}^{20} + 1/46592(1785731\nu^{2} + 40692412)x_{2}^{4}x_{3}^{12} + 1/1024(-5\nu^{2} + 43)x_{2}^{4}x_{3}^{4} + (15990784\nu^{2} - 23068672)x_{2}^{3}x_{3}^{37} + (-690176\nu^{2} + 57217024)x_{2}^{3}x_{3}^{29} + 1/91(-25559552\nu^{2} - 118995296)x_{2}^{3}x_{3}^{21} + 1/11648(9974387\nu^{2} - 86928540)x_{2}^{3}x_{3}^{13} + 1/745472(-9752319\nu^{2} + 9402636)x_{2}^{3}x_{3}^{5} - 268435456x_{2}^{2}x_{3}^{46} + (232783872\nu^{2} + 1623195648)x_{2}^{2}x_{3}^{38} + (-165867520\nu^{2} + 186204160)x_{2}^{2}x_{3}^{30} + 1/7(-7072848\nu^{2} + 188928704)x_{2}^{2}x_{3}^{22} + 1/1456(73144807\nu^{2} - 348232564)x_{2}^{2}x_{3}^{14} + 1/46592(-9720287\nu^{2} + 9152204)x_{2}^{2}x_{3}^{6} + (240123904\nu^{2} - 369098752)x_{2}x_{3}^{39} + 1/91(137639661568\nu^{2} + 496825712640)x_{2}x_{3}^{31} + 1/91(4144700496\nu^{2} + 4566908352)x_{2}x_{3}^{23} + 1/364(137257103\nu^{2} - 1205668332)x_{2}x_{3}^{15} + 1/11648(-21514593\nu^{2} - 20809700)x_{2}x_{3}^{7} - 4294967296x_{3}^{48} + (3724541952\nu^{2} + 26491224064)x_{3}^{40} + 1/91(1216452182016\nu^{2} + 1538811756544)x_{3}^{32} + 1/91(39593173632\nu^{2} - 65831844864)x_{3}^{24} + 1/7(5045744\nu^{2} - 134094624)x_{3}^{16} + 1/728(-5900065\nu^{2} - 14992600)x_{3}^{8}\)

Belyi Map 1 Denominator:

\(1/7(174625652736\nu^{2} + 476338716672)x_{1}x_{3}^{33} + 1/7(1462960128\nu^{2} - 8706785280)x_{1}x_{3}^{25} + 1/7(-26373120\nu^{2} - 41902080)x_{1}x_{3}^{17} + 1/7(-79056\nu^{2} + 107520)x_{1}x_{3}^{9} - 1/16384\nu^{2}x_{2}^{5}x_{3}^{3} + (131072\nu^{2} - 1441792)x_{2}^{4}x_{3}^{36} + (-361984\nu^{2} + 1714944)x_{2}^{4}x_{3}^{28} + 1/7(97536\nu^{2} - 838608)x_{2}^{4}x_{3}^{20} + 1/56(-3681\nu^{2} + 29151)x_{2}^{4}x_{3}^{12} + 1/1024(-3\nu^{2} + 43)x_{2}^{4}x_{3}^{4} + (15990784\nu^{2} + 23068672)x_{2}^{3}x_{3}^{37} + (-12273664\nu^{2} - 2306048)x_{2}^{3}x_{3}^{29} + 1/7(1334256\nu^{2} - 8419072)x_{2}^{3}x_{3}^{21} + 1/14(24769\nu^{2} + 46686)x_{2}^{3}x_{3}^{13} + 1/448(-3335\nu^{2} - 6592)x_{2}^{3}x_{3}^{5} - 268435456x_{2}^{2}x_{3}^{46} + (-239075328\nu^{2} + 1623195648)x_{2}^{2}x_{3}^{38} + (12767232\nu^{2} - 580829184)x_{2}^{2}x_{3}^{30} + 1/7(-25522368\nu^{2} - 30451968)x_{2}^{2}x_{3}^{22} + 1/7(403013\nu^{2} + 349136)x_{2}^{2}x_{3}^{14} + 1/56(-6649\nu^{2} - 13709)x_{2}^{2}x_{3}^{6} + (240123904\nu^{2} + 369098752)x_{2}x_{3}^{39} + 1/7(-9927589888\nu^{2} + 8166572032)x_{2}x_{3}^{31} + 1/7(-113967360\nu^{2} + 186593280)x_{2}x_{3}^{23} + 1/7(3593696\nu^{2} - 1731456)x_{2}x_{3}^{15} + 1/28(-20025\nu^{2} - 108112)x_{2}x_{3}^{7} - 4294967296x_{3}^{48} + (-3858759680\nu^{2} + 26491224064)x_{3}^{40} + 1/7(-63620513792\nu^{2} + 129335754752)x_{3}^{32} + 1/7(159735808\nu^{2} + 3773313024)x_{3}^{24} + 1/7(13725632\nu^{2} - 33711360)x_{3}^{16} + 1/7(-13468\nu^{2} - 160044)x_{3}^{8} + 1\)

Belyi Curve 2: 32S3-8,8,4-g9-path22

\(x_{1}^{3}x_{3}^{2} + x_{1}x_{3}^{2} - x_{2}2\)
\(-5x_{1}^{2}x_{3}^{2} - x_{1}x_{2} + x_{2}x_{3}^{4} - x_{3}^{2}\)
\(x_{1}^{4} + 6x_{1}^{2} - x_{2}x_{3}^{2} + 1\)

Belyi Curve 2 Base Field: Rationals

Belyi Curve 2 Degree: 17

Belyi Curve 2 Naive Measure: 20

Belyi Map 2 Numerator:

\(-384x_{1}^{2} + 200/3x_{1}x_{3}^{12} - 64x_{1}x_{3}^{4} - 5/6x_{2}^{3}x_{3}^{6} + 5/6x_{2}^{2}x_{3}^{20} - 35/3x_{2}^{2}x_{3}^{12} + 7/3x_{2}^{2}x_{3}^{4} + 8x_{2}^{2} + 5/2x_{2}x_{3}^{18} - 248/3x_{2}x_{3}^{10} + 144x_{2}x_{3}^{2} - 10/3x_{3}^{16} + 8/3x_{3}^{8} - 64\)

Belyi Map 2 Denominator:

\(16x_{2}^{2}\)

Belyi Curve 3: 32S3-8,8,4-g9-path3

\(x_{1}^{3}x_{3}^{2} + x_{1}x_{3}^{2} - x_{2}2\)
\(-5x_{1}^{2}x_{3}^{2} - x_{1}x_{2} + x_{2}x_{3}^{4} - x_{3}^{2}\)
\(x_{1}^{4} + 6x_{1}^{2} - x_{2}x_{3}^{2} + 1\)

Belyi Curve 3 Base Field: Rationals

Belyi Curve 3 Degree: 17

Belyi Curve 3 Naive Measure: 20

Belyi Map 3 Numerator:

\(-384x_{1}^{2} + 200/3x_{1}x_{3}^{12} - 64x_{1}x_{3}^{4} - 5/6x_{2}^{3}x_{3}^{6} + 5/6x_{2}^{2}x_{3}^{20} - 35/3x_{2}^{2}x_{3}^{12} + 10/3x_{2}^{2}x_{3}^{4} + 5/2x_{2}x_{3}^{18} - 248/3x_{2}x_{3}^{10} + 144x_{2}x_{3}^{2} - 10/3x_{3}^{16} + 8/3x_{3}^{8} - 64\)

Belyi Map 3 Denominator:

\(-384x_{1}^{2} + 200/3x_{1}x_{3}^{12} - 64x_{1}x_{3}^{4} - 5/6x_{2}^{3}x_{3}^{6} + 5/6x_{2}^{2}x_{3}^{20} - 35/3x_{2}^{2}x_{3}^{12} + 13/3x_{2}^{2}x_{3}^{4} + 5/2x_{2}x_{3}^{18} - 248/3x_{2}x_{3}^{10} + 144x_{2}x_{3}^{2} - 10/3x_{3}^{16} + 8/3x_{3}^{8} - 64\)

Belyi Curve 4: 32S3-8,8,4-g9-path5

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

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

Belyi Curve 4 Degree: 20

Belyi Curve 4 Naive Measure: 7

Belyi Map 4 Numerator:

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

Belyi Map 4 Denominator:

\(x_{2}x_{3}^{2} - 1\)

Belyi Curve 5: 32S3-8,8,4-g9-path6

\(x_{1}^{3}x_{3}^{2} + x_{1}x_{3}^{2} - x_{2}2\)
\(-5x_{1}^{2}x_{3}^{2} - x_{1}x_{2} + x_{2}x_{3}^{4} - x_{3}^{2}\)
\(x_{1}^{4} + 6x_{1}^{2} - x_{2}x_{3}^{2} + 1\)

Belyi Curve 5 Base Field: Rationals

Belyi Curve 5 Degree: 17

Belyi Curve 5 Naive Measure: 20

Belyi Map 5 Numerator:

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

Belyi Map 5 Denominator:

\(-384x_{1}^{2} + 200/3x_{1}x_{3}^{12} - 64x_{1}x_{3}^{4} - 5/6x_{2}^{3}x_{3}^{6} + 5/6x_{2}^{2}x_{3}^{20} - 35/3x_{2}^{2}x_{3}^{12} + 13/3x_{2}^{2}x_{3}^{4} + 5/2x_{2}x_{3}^{18} - 248/3x_{2}x_{3}^{10} + 144x_{2}x_{3}^{2} - 10/3x_{3}^{16} + 8/3x_{3}^{8} - 64\)

Belyi Curve 6: 32S3-8,8,4-g9-path7

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

Belyi Curve 6 Base Field: Rationals

Belyi Curve 6 Degree: 20

Belyi Curve 6 Naive Measure: 7

Belyi Map 6 Numerator:

\(x_{2}^{2} - 2x_{2}x_{3}^{2}\)

Belyi Map 6 Denominator:

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