8T5-4,4,4-g2

graph data
Name 8T5-4,4,4-g2
Type Hyperbolic
Degree 8
Genus 2
Galois orbit size for 8T5-4,4,4-g2-path1 1
Galois orbit size for 8T5-4,4,4-g2-path2 1
Galois orbit size for 8T5-4,4,4-g2-path3 1
Passport size 1
Pointed size 1

Above

16T8-4,4,4-g3

Below

4T2-2,2,2-g0

Belyi Curve 1: 8T5-4,4,4-g2-path1

\(-9x_{1}^{5}x_{3} + 9x_{1}x_{3}^{5} + x_{2}^{2}\)

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

Belyi Curve 1 Degree: 5

Belyi Curve 1 Naive Measure: 19

Belyi Map 1 Numerator:

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

Belyi Map 1 Denominator:

\(x_{1}^{2}\)

Belyi Curve 2: 8T5-4,4,4-g2-path2

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

Belyi Curve 2 Base Field: Rationals

Belyi Curve 2 Degree: 5

Belyi Curve 2 Naive Measure: 3

Belyi Map 2 Numerator:

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

Belyi Map 2 Denominator:

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

Belyi Curve 3: 8T5-4,4,4-g2-path3

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

Belyi Curve 3 Base Field: Rationals

Belyi Curve 3 Degree: 5

Belyi Curve 3 Naive Measure: 3

Belyi Map 3 Numerator:

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

Belyi Map 3 Denominator:

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