32S17-16,16,8-g13

graph data
Name 32S17-16,16,8-g13
Type Hyperbolic
Degree 32
Genus 13
Galois orbit size for 32S17-16,16,8-g13-path1 1
Galois orbit size for 32S17-16,16,8-g13-path10 1
Galois orbit size for 32S17-16,16,8-g13-path11 1
Galois orbit size for 32S17-16,16,8-g13-path12 1
Galois orbit size for 32S17-16,16,8-g13-path13 1
Galois orbit size for 32S17-16,16,8-g13-path14 1
Galois orbit size for 32S17-16,16,8-g13-path2 1
Galois orbit size for 32S17-16,16,8-g13-path3 1
Galois orbit size for 32S17-16,16,8-g13-path4 1
Galois orbit size for 32S17-16,16,8-g13-path5 1
Galois orbit size for 32S17-16,16,8-g13-path6 1
Galois orbit size for 32S17-16,16,8-g13-path7 1
Galois orbit size for 32S17-16,16,8-g13-path8 1
Galois orbit size for 32S17-16,16,8-g13-path9 1
Passport size 2
Pointed size 2

Above

64S27-16,16,8-g25 64S44-16,16,8-g25 64S29-16,16,8-g25

Below

16T5-8,8,4-g5

Belyi Curve 1: 32S17-16,16,8-g13-path10

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

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

Belyi Curve 1 Degree: 20

Belyi Curve 1 Naive Measure: 13

Belyi Map 1 Numerator:

\(-4x_{2}^{3}x_{4}^{12} - 4x_{2}^{2}x_{4}^{16} - x_{2}^{2} + 4x_{2}x_{4}^{4} - 3x_{4}^{8}\)

Belyi Map 1 Denominator:

\(x_{4}^{8}\)

Belyi Curve 2: 32S17-16,16,8-g13-path11

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

Belyi Curve 2 Base Field: Rationals

Belyi Curve 2 Degree: 22

Belyi Curve 2 Naive Measure: 18

Belyi Map 2 Numerator:

\(-2x_{2}^{3}x_{3}^{2} + 4x_{2}^{2}x_{3}^{8} + x_{2}^{2} + 8x_{2}x_{3}^{6} + 4x_{3}^{4}\)

Belyi Map 2 Denominator:

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

Belyi Curve 3: 32S17-16,16,8-g13-path12

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

Belyi Curve 3 Base Field: Rationals

Belyi Curve 3 Degree: 22

Belyi Curve 3 Naive Measure: 18

Belyi Map 3 Numerator:

\(-2x_{2}^{3}x_{3}^{2} + 4x_{2}^{2}x_{3}^{8} + x_{2}^{2} + 8x_{2}x_{3}^{6} + 4x_{3}^{4}\)

Belyi Map 3 Denominator:

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

Belyi Curve 4: 32S17-16,16,8-g13-path13

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

Belyi Curve 4 Base Field: Rationals

Belyi Curve 4 Degree: 21

Belyi Curve 4 Naive Measure: 51

Belyi Map 4 Numerator:

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

Belyi Map 4 Denominator:

\(4\)

Belyi Curve 5: 32S17-16,16,8-g13-path14

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

Belyi Curve 5 Base Field: Rationals

Belyi Curve 5 Degree: 20

Belyi Curve 5 Naive Measure: 41

Belyi Map 5 Numerator:

\(32x_{2} - 16x_{3}^{16} + 32x_{3}^{12} - 72x_{3}^{8} + 16x_{3}^{4}x_{4}^{24} - 2160x_{3}^{4}x_{4}^{16} + 456x_{3}^{4}x_{4}^{8} + 16x_{3}^{4} - 2080x_{3}^{3}x_{4}^{26} + 5848x_{3}^{3}x_{4}^{18} - 296x_{3}^{3}x_{4}^{10} + 110x_{3}^{3}x_{4}^{2} + 2080x_{3}^{2}x_{4}^{28} - 2776x_{3}^{2}x_{4}^{20} - 212x_{3}^{2}x_{4}^{12} - 154x_{3}^{2}x_{4}^{4} - 2064x_{3}x_{4}^{14} + 64x_{3}x_{4}^{6} - 2080x_{4}^{24} + 3280x_{4}^{16} - 264x_{4}^{8} + 16\)

Belyi Map 5 Denominator:

\(32x_{2} + 64x_{3}^{12} - 64x_{3}^{4}x_{4}^{16} - 832x_{3}^{4}x_{4}^{8} + 96x_{3}^{4} - 1920x_{3}^{3}x_{4}^{18} + 3232x_{3}^{3}x_{4}^{10} + 32x_{3}^{3}x_{4}^{2} + 1920x_{3}^{2}x_{4}^{20} - 1184x_{3}^{2}x_{4}^{12} - 304x_{3}^{2}x_{4}^{4} - 960x_{3}x_{4}^{6} - 1920x_{4}^{16} + 1728x_{4}^{8} + 16\)

Belyi Curve 6: 32S17-16,16,8-g13-path5

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

Belyi Curve 6 Base Field: Rationals

Belyi Curve 6 Degree: 21

Belyi Curve 6 Naive Measure: 51

Belyi Map 6 Numerator:

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

Belyi Map 6 Denominator:

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

Belyi Curve 7: 32S17-16,16,8-g13-path6

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

Belyi Curve 7 Base Field: Rationals

Belyi Curve 7 Degree: 22

Belyi Curve 7 Naive Measure: 18

Belyi Map 7 Numerator:

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

Belyi Map 7 Denominator:

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