32S1-32,32,4-g12

graph data
Name 32S1-32,32,4-g12
Type Hyperbolic
Degree 32
Genus 12
Galois orbit size for 32S1-32,32,4-g12-path1 2
Passport size 2
Pointed size 2

Above

64S50-32,32,4-g23 64S1-64,64,8-g28

Below

16T1-16,16,2-g4

Belyi Curve 1: 32S1-32,32,4-g12-path1

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

Belyi Curve 1 Base Field: Rationals

Belyi Curve 1 Degree: 22

Belyi Curve 1 Naive Measure: 10

Belyi Map 1 Numerator:

\(-1/4x_{2}^{4}x_{3}^{21} + 2x_{2}^{3}x_{3}^{20} + 1/4x_{2}^{3}x_{3}^{4} - 23/4x_{2}^{2}x_{3}^{19} + 1/4x_{2}^{2}x_{3}^{3} + 7x_{2}x_{3}^{18} - 3x_{3}^{17} - x_{3}3\)

Belyi Map 1 Denominator:

\(-1/2x_{2}^{4}x_{3}^{21} + 7/2x_{2}^{3}x_{3}^{20} + 1/2x_{2}^{3}x_{3}^{4} - 9x_{2}^{2}x_{3}^{19} + x_{2}^{2}x_{3}^{3} + 10x_{2}x_{3}^{18} - 2x_{2}x_{3}^{2} - 4x_{3}^{17}\)