32S1-32,8,32-g14

graph data
Name 32S1-32,8,32-g14
Type Hyperbolic
Degree 32
Genus 14
Galois orbit size for 32S1-32,8,32-g14-path1 2
Galois orbit size for 32S1-32,8,32-g14-path2 2
Passport size 4
Pointed size 4

Above

64S50-32,8,32-g27 64S1-64,16,64-g30

Below

16T1-16,4,16-g6

Belyi Curve 1: 32S1-32,8,32-g14-path1

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

Belyi Curve 1 Base Field: Rationals

Belyi Curve 1 Degree: 28

Belyi Curve 1 Naive Measure: 17

Belyi Map 1 Numerator:

\(x_{2}^{2}x_{3}^{20} + 2x_{2}^{2}x_{3}^{12} + 4x_{2}x_{3}^{18} + 8x_{2}x_{3}^{10} - 2x_{2}x_{3}^{2} + 4x_{3}^{16} + 12x_{3}^{8} + 1\)

Belyi Map 1 Denominator:

\(1\)

Belyi Curve 2: 32S1-32,8,32-g14-path2

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

Belyi Curve 2 Base Field: Rationals

Belyi Curve 2 Degree: 28

Belyi Curve 2 Naive Measure: 17

Belyi Map 2 Numerator:

\(x_{2}^{2}x_{3}^{20} + 2x_{2}^{2}x_{3}^{12} + 4x_{2}x_{3}^{18} + 8x_{2}x_{3}^{10} - 2x_{2}x_{3}^{2} + 4x_{3}^{16} + 12x_{3}^{8} + 1\)

Belyi Map 2 Denominator:

\(1\)