32S1-4,32,32-g12

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

Above

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

Below

16T1-2,16,16-g4

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

\((-2\nu^{6} + 2\nu^{2)}x_{1}^{4}x_{2} - 8x_{1}^{2}x_{2} - 8x_{1}^{2}x_{3}^{2} - x_{1}x_{2}^{2}x_{3}^{2} + x_{2}^{2}x_{3}^{6} + (-8\nu^{6} + 8\nu^{2)}x_{2} + (8\nu^{6} - 8\nu^{2)}x_{3}^{2}\)
\(-x_{1}^{2}x_{2} - 4x_{1}^{2}x_{3}^{2} + x_{1}x_{2}x_{3}^{4} + (-2\nu^{6} + 2\nu^{2)}x_{2} + (2\nu^{6} - 2\nu^{2)}x_{3}^{2}\)
\(x_{1}^{5} + (\nu^{6} - \nu^{2)}x_{1}^{3} + x_{1} - x_{2}x_{3}^{2}\)
\(x_{1}^{3}x_{3}^{2} + 1/4(\nu^{6} - \nu^{2)}x_{1}x_{2} + 1/4(-\nu^{6} + \nu^{2)}x_{2}x_{3}^{4}\)

Belyi Curve 1 Base Field: \(\nu^{8}+1\), discriminant [ <2, 24> ]

Belyi Curve 1 Degree: 22

Belyi Curve 1 Naive Measure: 59

Belyi Map 1 Numerator:

\(-8000x_{1}x_{3}^{19} + (-40\nu^{6} + 40\nu^{2)}x_{1}x_{3}^{11} - 8x_{1}x_{3}^{3} + (50\nu^{6} - 50\nu^{2)}x_{2}^{4}x_{3}^{28} + 13/2x_{2}^{4}x_{3}^{20} + (-350\nu^{6} + 350\nu^{2)}x_{2}^{3}x_{3}^{27} + 1677/2x_{2}^{3}x_{3}^{19} + 1/2(17\nu^{6} - 17\nu^{2)}x_{2}^{3}x_{3}^{11} - 13/2x_{2}^{3}x_{3}^{3} + (1100\nu^{6} - 1100\nu^{2)}x_{2}^{2}x_{3}^{26} + 4503x_{2}^{2}x_{3}^{18} + (31\nu^{6} - 31\nu^{2)}x_{2}^{2}x_{3}^{10} + 4x_{2}^{2}x_{3}^{2} + (-1600\nu^{6} + 1600\nu^{2)}x_{2}x_{3}^{25} + 2880x_{2}x_{3}^{17} + (-30\nu^{6} + 30\nu^{2)}x_{2}x_{3}^{9} + 4x_{2}x_{3} + (800\nu^{6} - 800\nu^{2)}x_{3}^{24} - 728x_{3}^{16} + (8\nu^{6} - 8\nu^{2)}x_{3}^{8}\)

Belyi Map 1 Denominator:

\(1\)