32S10-4,8,4-g7

graph data
Name 32S10-4,8,4-g7
Type Hyperbolic
Degree 32
Genus 7
Galois orbit size for 32S10-4,8,4-g7-path1 1
Galois orbit size for 32S10-4,8,4-g7-path10 1
Galois orbit size for 32S10-4,8,4-g7-path11 1
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Galois orbit size for 32S10-4,8,4-g7-path14 1
Galois orbit size for 32S10-4,8,4-g7-path15 1
Galois orbit size for 32S10-4,8,4-g7-path16 1
Galois orbit size for 32S10-4,8,4-g7-path17 1
Galois orbit size for 32S10-4,8,4-g7-path18 1
Galois orbit size for 32S10-4,8,4-g7-path19 1
Galois orbit size for 32S10-4,8,4-g7-path2 1
Galois orbit size for 32S10-4,8,4-g7-path20 1
Galois orbit size for 32S10-4,8,4-g7-path21 1
Galois orbit size for 32S10-4,8,4-g7-path22 1
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Galois orbit size for 32S10-4,8,4-g7-path24 1
Galois orbit size for 32S10-4,8,4-g7-path25 1
Galois orbit size for 32S10-4,8,4-g7-path26 1
Galois orbit size for 32S10-4,8,4-g7-path27 1
Galois orbit size for 32S10-4,8,4-g7-path28 1
Galois orbit size for 32S10-4,8,4-g7-path29 1
Galois orbit size for 32S10-4,8,4-g7-path3 1
Galois orbit size for 32S10-4,8,4-g7-path30 1
Galois orbit size for 32S10-4,8,4-g7-path31 1
Galois orbit size for 32S10-4,8,4-g7-path32 1
Galois orbit size for 32S10-4,8,4-g7-path33 1
Galois orbit size for 32S10-4,8,4-g7-path34 1
Galois orbit size for 32S10-4,8,4-g7-path4 1
Galois orbit size for 32S10-4,8,4-g7-path5 1
Galois orbit size for 32S10-4,8,4-g7-path6 1
Galois orbit size for 32S10-4,8,4-g7-path7 1
Galois orbit size for 32S10-4,8,4-g7-path8 1
Galois orbit size for 32S10-4,8,4-g7-path9 1
Passport size 2
Pointed size 2

Above

64S21-4,8,4-g13 64S13-4,8,8-g17 64S14-4,8,8-g17 64S7-4,8,8-g17 64S13-8,8,4-g17 64S14-8,8,4-g17 64S7-8,8,4-g17 64S9-4,8,4-g13

Below

16T14-4,8,4-g4 16T12-4,8,2-g2 16T12-2,8,4-g2 16T10-4,4,2-g1 16T10-2,4,4-g1

Belyi Curve 1: 32S10-4,8,4-g7-path10

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

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

Belyi Curve 1 Degree: 12

Belyi Curve 1 Naive Measure: 16

Belyi Map 1 Numerator:

\(-1/16x_{2}^{8} + 3/4x_{2}^{6} - 19/8x_{2}^{4} + 3/4x_{2}^{2} - 1/16\)

Belyi Map 1 Denominator:

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

Belyi Curve 2: 32S10-4,8,4-g7-path11

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

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

Belyi Curve 2 Degree: 11

Belyi Curve 2 Naive Measure: 22

Belyi Map 2 Numerator:

\(x_{1}^{8} + 2x_{1}^{4} + 1\)

Belyi Map 2 Denominator:

\(x_{1}^{8} - 2x_{1}^{4} + 1\)

Belyi Curve 3: 32S10-4,8,4-g7-path13

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

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

Belyi Curve 3 Degree: 12

Belyi Curve 3 Naive Measure: 16

Belyi Map 3 Numerator:

\(-16x_{2}^{6} + 32x_{2}^{4} - 16x_{2}^{2}\)

Belyi Map 3 Denominator:

\(x_{2}^{8} - 12x_{2}^{6} + 38x_{2}^{4} - 12x_{2}^{2} + 1\)

Belyi Curve 4: 32S10-4,8,4-g7-path14

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

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

Belyi Curve 4 Degree: 14

Belyi Curve 4 Naive Measure: 45

Belyi Map 4 Numerator:

\(x_{3}^{8} + 2x_{3}^{4} + 1\)

Belyi Map 4 Denominator:

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

Belyi Curve 5: 32S10-4,8,4-g7-path19

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

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

Belyi Curve 5 Degree: 11

Belyi Curve 5 Naive Measure: 23

Belyi Map 5 Numerator:

\(8x_{2}^{5}x_{3}^{12} + 60x_{2}^{5}x_{3}^{8} + 102x_{2}^{5}x_{3}^{4} + 45x_{2}^{5} + 24x_{2}^{4}x_{3}^{12} + 108x_{2}^{4}x_{3}^{8} + 90x_{2}^{4}x_{3}^{4} + 13x_{2}^{4} - 16x_{2}^{3}x_{3}^{12} - 120x_{2}^{3}x_{3}^{8} - 204x_{2}^{3}x_{3}^{4} - 106x_{2}^{3} - 48x_{2}^{2}x_{3}^{12} - 216x_{2}^{2}x_{3}^{8} - 244x_{2}^{2}x_{3}^{4} - 74x_{2}^{2} + 40x_{2}x_{3}^{12} + 172x_{2}x_{3}^{8} + 126x_{2}x_{3}^{4} - 15x_{2} - 8x_{3}^{12} - 36x_{3}^{8} - 30x_{3}^{4} + 1\)

Belyi Map 5 Denominator:

\(8x_{2}^{5}x_{3}^{12} + 60x_{2}^{5}x_{3}^{8} + 70x_{2}^{5}x_{3}^{4} - 3x_{2}^{5} + 24x_{2}^{4}x_{3}^{12} + 108x_{2}^{4}x_{3}^{8} - 6x_{2}^{4}x_{3}^{4} + 13x_{2}^{4} - 16x_{2}^{3}x_{3}^{12} - 120x_{2}^{3}x_{3}^{8} - 140x_{2}^{3}x_{3}^{4} - 10x_{2}^{3} - 48x_{2}^{2}x_{3}^{12} - 216x_{2}^{2}x_{3}^{8} - 52x_{2}^{2}x_{3}^{4} - 10x_{2}^{2} + 40x_{2}x_{3}^{12} + 172x_{2}x_{3}^{8} - 34x_{2}x_{3}^{4} + x_{2} - 8x_{3}^{12} - 36x_{3}^{8} + 2x_{3}^{4} + 1\)

Belyi Curve 6: 32S10-4,8,4-g7-path2

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

Belyi Curve 6 Base Field: Rationals

Belyi Curve 6 Degree: 12

Belyi Curve 6 Naive Measure: 19

Belyi Map 6 Numerator:

\(x_{2}^{8} + 12x_{2}^{6} + 38x_{2}^{4} + 12x_{2}^{2} + 1\)

Belyi Map 6 Denominator:

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

Belyi Curve 7: 32S10-4,8,4-g7-path20

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

Belyi Curve 7 Base Field: \(\nu^{4}+1\), discriminant [ <2, 8> ]

Belyi Curve 7 Degree: 12

Belyi Curve 7 Naive Measure: 14

Belyi Map 7 Numerator:

\(x_{2}^{8} + 4x_{2}^{6} + 6x_{2}^{4} + 4x_{2}^{2} + 1\)

Belyi Map 7 Denominator:

\(x_{2}^{8} - 12x_{2}^{6} + 38x_{2}^{4} - 12x_{2}^{2} + 1\)

Belyi Curve 8: 32S10-4,8,4-g7-path21

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

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

Belyi Curve 8 Degree: 18

Belyi Curve 8 Naive Measure: 18

Belyi Map 8 Numerator:

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

Belyi Map 8 Denominator:

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

Belyi Curve 9: 32S10-4,8,4-g7-path22

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

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

Belyi Curve 9 Degree: 12

Belyi Curve 9 Naive Measure: 16

Belyi Map 9 Numerator:

\(-16x_{2}^{6} + 32x_{2}^{4} - 16x_{2}^{2}\)

Belyi Map 9 Denominator:

\(x_{2}^{8} - 12x_{2}^{6} + 38x_{2}^{4} - 12x_{2}^{2} + 1\)

Belyi Curve 10: 32S10-4,8,4-g7-path23

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

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

Belyi Curve 10 Degree: 14

Belyi Curve 10 Naive Measure: 13

Belyi Map 10 Numerator:

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

Belyi Map 10 Denominator:

\(x_{3}^{8} + 2x_{3}^{4} + 1\)

Belyi Curve 11: 32S10-4,8,4-g7-path24

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

Belyi Curve 11 Base Field: \(\nu^{8}+16\), discriminant [ <2, 52> ]

Belyi Curve 11 Degree: 14

Belyi Curve 11 Naive Measure: 19

Belyi Map 11 Numerator:

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

Belyi Map 11 Denominator:

\(x_{3}^{8} + 2x_{3}^{4} + 1\)

Belyi Curve 12: 32S10-4,8,4-g7-path25

\(-144x_{1}^{3} - 576x_{1}^{2} - 252x_{1}x_{3}^{4} - 1080x_{1}x_{3}^{2} - 684x_{1} + x_{2}^{2}x_{3}^{4} - 2x_{2}^{2}x_{3}^{2} + x_{2}^{2} - 108x_{3}^{4} - 288x_{3}^{2} + 396\)
\(-36x_{1}^{3} - 72x_{1}^{2} + x_{1}x_{2}^{2}x_{3}^{2} - x_{1}x_{2}^{2} - 108x_{1}x_{3}^{2} - 72x_{1} - 2x_{2}^{2}x_{3}^{2} - 2x_{2}^{2} - 36x_{3}^{2} + 36\)
\(x_{1}^{4} + 2x_{1}^{3} + 5x_{1}^{2} + 7x_{1}x_{3}^{2} + 5x_{1} - 1/36x_{2}^{2}x_{3}^{2} + 1/36x_{2}^{2} + 3x_{3}^{2} - 3\)
\(x_{1}^{2}x_{3}^{2} - x_{1}^{2} - 2x_{1}x_{3}^{2} - 2x_{1} - x_{3}^{2} + 1\)

Belyi Curve 12 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 12 Degree: 14

Belyi Curve 12 Naive Measure: 4004

Belyi Map 12 Numerator:

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

Belyi Map 12 Denominator:

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

Belyi Curve 13: 32S10-4,8,4-g7-path26

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

Belyi Curve 13 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 13 Degree: 14

Belyi Curve 13 Naive Measure: 13

Belyi Map 13 Numerator:

\(1/4x_{3}^{8} + 1/2x_{3}^{4} + 1/4\)

Belyi Map 13 Denominator:

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

Belyi Curve 14: 32S10-4,8,4-g7-path27

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

Belyi Curve 14 Base Field: \(\nu^{4}+1\), discriminant [ <2, 8> ]

Belyi Curve 14 Degree: 14

Belyi Curve 14 Naive Measure: 13

Belyi Map 14 Numerator:

\(1/4x_{3}^{8} + 1/2x_{3}^{4} + 1/4\)

Belyi Map 14 Denominator:

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

Belyi Curve 15: 32S10-4,8,4-g7-path28

\(x_{1}^{5} + x_{1} + 8/9x_{2}^{2}\)
\(x_{1}^{2}x_{3}^{2} - x_{1}^{2} + x_{3}^{2} + 1\)
\(-9/4x_{1}^{3} + 9/4x_{1}x_{3}^{2} + x_{2}^{2}x_{3}^{2} - x_{2}^{2}\)

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

Belyi Curve 15 Degree: 14

Belyi Curve 15 Naive Measure: 35

Belyi Map 15 Numerator:

\(1/4x_{3}^{8} + 1/2x_{3}^{4} + 1/4\)

Belyi Map 15 Denominator:

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

Belyi Curve 16: 32S10-4,8,4-g7-path3

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

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

Belyi Curve 16 Degree: 12

Belyi Curve 16 Naive Measure: 103

Belyi Map 16 Numerator:

\(-136270082448/845185x_{1}x_{3}^{16} - 3867572052/845185\nu x_{1}x_{3}^{14} + 63174592281/3380740x_{1}x_{3}^{12} - 174578343147/13522960\nu x_{1}x_{3}^{10} + 19242770671/108183680x_{1}x_{3}^{8} - 11460116761/10818368\nu x_{1}x_{3}^{6} - 22296549719/108183680x_{1}x_{3}^{4} - 161296562857/3461877760\nu x_{1}x_{3}^{2} + 10014148055/5539004416x_{1} - x_{2}^{6}x_{3}^{4} + 1/2\nu x_{2}^{6}x_{3}^{2} + 1/16x_{2}^{6} + 22711680408/845185\nu x_{2}^{5}x_{3}^{16} + 7872284811/845185x_{2}^{5}x_{3}^{14} - 50550983023/13522960\nu x_{2}^{5}x_{3}^{12} - 105578523881/13522960x_{2}^{5}x_{3}^{10} + 76417098721/19669760\nu x_{2}^{5}x_{3}^{8} + 120377908253/216367360x_{2}^{5}x_{3}^{6} + 23658539559/692375552\nu x_{2}^{5}x_{3}^{4} + 40575296017/3461877760x_{2}^{5}x_{3}^{2} - 10047877987/11078008832\nu x_{2}^{5} + 11355840204/169037x_{2}^{4}x_{3}^{16} - 45039344157/1690370\nu x_{2}^{4}x_{3}^{14} - 287382149789/13522960x_{2}^{4}x_{3}^{12} + 25057387299/27045920\nu x_{2}^{4}x_{3}^{10} + 2840807898361/216367360x_{2}^{4}x_{3}^{8} - 1813936511383/432734720\nu x_{2}^{4}x_{3}^{6} + 2137569931969/3461877760x_{2}^{4}x_{3}^{4} - 117273423031/6923755520\nu x_{2}^{4}x_{3}^{2} + 34281022307/11078008832x_{2}^{4} - 136270082448/845185\nu x_{2}^{3}x_{3}^{16} - 37268550273/169037x_{2}^{3}x_{3}^{14} - 476113833399/6761480\nu x_{2}^{3}x_{3}^{12} + 222387388115/2704592x_{2}^{3}x_{3}^{10} - 1192767438701/54091840\nu x_{2}^{3}x_{3}^{8} + 1491145077677/216367360x_{2}^{3}x_{3}^{6} + 839473790093/1730938880\nu x_{2}^{3}x_{3}^{4} - 10014148055/692375552x_{2}^{3}x_{3}^{2} - 272540164896/845185x_{2}^{2}x_{3}^{16} - 135488346399/845185\nu x_{2}^{2}x_{3}^{14} + 58386644181/614680x_{2}^{2}x_{3}^{12} + 411190004421/27045920\nu x_{2}^{2}x_{3}^{10} + 1404956738813/108183680x_{2}^{2}x_{3}^{8} + 283758257169/108183680\nu x_{2}^{2}x_{3}^{6} - 1065623172719/1730938880x_{2}^{2}x_{3}^{4} - 462588362919/6923755520\nu x_{2}^{2}x_{3}^{2} + 10360335831/5539004416x_{2}^{2} + 22711680408/845185\nu x_{2}x_{3}^{16} + 4586971416/76835x_{2}x_{3}^{14} - 19857282559/13522960\nu x_{2}x_{3}^{12} - 42225888475/2704592x_{2}x_{3}^{10} + 343480614215/43273472\nu x_{2}x_{3}^{8} + 32627692561/54091840x_{2}x_{3}^{6} - 329009914229/3461877760\nu x_{2}x_{3}^{4} + 133961670707/3461877760x_{2}x_{3}^{2} - 10047877987/11078008832\nu x_{2} - 11355840204/845185x_{3}^{16} + 41939805423/1690370\nu x_{3}^{14} - 32925251173/2704592x_{3}^{12} - 5961877021/676148\nu x_{3}^{10} - 259611326783/216367360x_{3}^{8} - 485467975673/432734720\nu x_{3}^{6} + 310114062861/3461877760x_{3}^{4} + 13260495627/3461877760\nu x_{3}^{2} - 10031013021/11078008832\)

Belyi Map 16 Denominator:

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

Belyi Curve 17: 32S10-4,8,4-g7-path8

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

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

Belyi Curve 17 Degree: 12

Belyi Curve 17 Naive Measure: 16

Belyi Map 17 Numerator:

\(1/16x_{2}^{8} + 3/4x_{2}^{6} + 19/8x_{2}^{4} + 3/4x_{2}^{2} + 1/16\)

Belyi Map 17 Denominator:

\(x_{2}^{6} + 2x_{2}^{4} + x_{2}^{2}\)

Belyi Curve 18: 32S10-4,8,4-g7-path9

\(x_{1}^{3}x_{3}^{2} + 1/4x_{1}^{3} - 1/2x_{1}^{2}x_{2} - x_{1}^{2} + 3/4x_{1}x_{2}^{2} + x_{1}x_{2}x_{3}^{2} + 1/2x_{1}x_{2} - 2x_{1}x_{3}^{2} - 3/2x_{2}^{2}x_{3}^{2} + 1/8x_{2}^{2} + x_{2}x_{3}^{2} + 1/2x_{2} + 1/2x_{3}^{2} - 1/8\)
\(x_{1}^{2}x_{2}x_{3}^{2} + 1/4x_{1}^{2}x_{2} - 2x_{1}^{2}x_{3}^{2} + x_{1}^{2} - 1/2x_{1}x_{2}^{2} - 2x_{1}x_{2}x_{3}^{2} - 1/2x_{1}x_{2} + 2x_{1}x_{3}^{2} + 3/2x_{2}^{2}x_{3}^{2} + 1/8x_{2}^{2} - 1/2x_{2} - 1/2x_{3}^{2} + 1/8\)
\(2x_{1}^{2}x_{3}^{2} - 1/2x_{1}^{2} + x_{1}x_{2}^{2}x_{3}^{2} + 1/4x_{1}x_{2}^{2} + 1/2x_{1}x_{2} - x_{1}x_{3}^{2} + 1/4x_{1} - 2x_{2}^{2}x_{3}^{2} + 1/2x_{2}2\)
\(-2x_{1}^{2} + x_{2}^{3} + x_{2}2\)

Belyi Curve 18 Base Field: Rationals

Belyi Curve 18 Degree: 12

Belyi Curve 18 Naive Measure: 104

Belyi Map 18 Numerator:

\(x_{2}^{8} + 12x_{2}^{6} + 38x_{2}^{4} + 12x_{2}^{2} + 1\)

Belyi Map 18 Denominator:

\(16x_{2}^{6} + 32x_{2}^{4} + 16x_{2}^{2}\)