32S17-16,8,16-g13

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

Above

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

Below

16T5-8,4,8-g5

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

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

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

Belyi Curve 1 Degree: 24

Belyi Curve 1 Naive Measure: 9

Belyi Map 1 Numerator:

\(x_{3}^{2} + x_{5}^{8}\)

Belyi Map 1 Denominator:

\(x_{5}^{8}\)

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

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

Belyi Curve 2 Base Field: Rationals

Belyi Curve 2 Degree: 26

Belyi Curve 2 Naive Measure: 41

Belyi Map 2 Numerator:

\(x_{5}^{4}\)

Belyi Map 2 Denominator:

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

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

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

Belyi Curve 3 Base Field: Rationals

Belyi Curve 3 Degree: 28

Belyi Curve 3 Naive Measure: 31

Belyi Map 3 Numerator:

\(x_{5}^{4}\)

Belyi Map 3 Denominator:

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

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

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

Belyi Curve 4 Base Field: Rationals

Belyi Curve 4 Degree: 20

Belyi Curve 4 Naive Measure: 45

Belyi Map 4 Numerator:

\(1/2048x_{2}x_{3}x_{4}^{22} + 9/512x_{2}x_{3}x_{4}^{18} + 5/32x_{2}x_{3}x_{4}^{14} - 13/8x_{2}x_{3}x_{4}^{6} - 1/2x_{2}x_{3}x_{4}^{2} - 1/512x_{2}x_{4}^{20} - 1/16x_{2}x_{4}^{16} - 7/16x_{2}x_{4}^{12} + 1/2x_{2}x_{4}^{8} + 7/2x_{2}x_{4}^{4} - 1/2048x_{3}x_{4}^{22} - 9/512x_{3}x_{4}^{18} - 11/64x_{3}x_{4}^{14} - 5/16x_{3}x_{4}^{10} + 7/8x_{3}x_{4}^{6} + 3/2x_{3}x_{4}^{2} + 1/512x_{4}^{20} + 1/16x_{4}^{16} + 1/2x_{4}^{12} + 1/2x_{4}^{8} - 5/2x_{4}^{4} - 4\)

Belyi Map 4 Denominator:

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

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

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

Belyi Curve 5 Base Field: Rationals

Belyi Curve 5 Degree: 20

Belyi Curve 5 Naive Measure: 45

Belyi Map 5 Numerator:

\(1/2048x_{2}x_{3}x_{4}^{22} + 9/512x_{2}x_{3}x_{4}^{18} + 5/32x_{2}x_{3}x_{4}^{14} - 13/8x_{2}x_{3}x_{4}^{6} - 1/2x_{2}x_{3}x_{4}^{2} - 1/512x_{2}x_{4}^{20} - 1/16x_{2}x_{4}^{16} - 7/16x_{2}x_{4}^{12} + 1/2x_{2}x_{4}^{8} + 7/2x_{2}x_{4}^{4} - 1/2048x_{3}x_{4}^{22} - 9/512x_{3}x_{4}^{18} - 11/64x_{3}x_{4}^{14} - 5/16x_{3}x_{4}^{10} + 7/8x_{3}x_{4}^{6} + 3/2x_{3}x_{4}^{2} + 1/512x_{4}^{20} + 1/16x_{4}^{16} + 1/2x_{4}^{12} + 1/2x_{4}^{8} - 5/2x_{4}^{4} - 4\)

Belyi Map 5 Denominator:

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

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

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

Belyi Curve 6 Base Field: Rationals

Belyi Curve 6 Degree: 18

Belyi Curve 6 Naive Measure: 11

Belyi Map 6 Numerator:

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

Belyi Map 6 Denominator:

\(2\)

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

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

Belyi Curve 7 Base Field: Rationals

Belyi Curve 7 Degree: 18

Belyi Curve 7 Naive Measure: 11

Belyi Map 7 Numerator:

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

Belyi Map 7 Denominator:

\(2\)

Belyi Curve 8: 32S17-16,8,16-g13-path9

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

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

Belyi Curve 8 Degree: 24

Belyi Curve 8 Naive Measure: 9

Belyi Map 8 Numerator:

\(x_{3}^{2} + x_{5}^{8}\)

Belyi Map 8 Denominator:

\(x_{5}^{8}\)