8T4-4,2,2-g0

graph data
Name 8T4-4,2,2-g0
Type Spherical
Degree 8
Genus 0
Galois orbit size for 8T4-4,2,2-g0-path1 1
Galois orbit size for 8T4-4,2,2-g0-path2 1
Galois orbit size for 8T4-4,2,2-g0-path3 1
Passport size 1
Pointed size 1

Above

16T13-8,2,2-g0 16T12-8,4,2-g2 16T12-8,2,4-g2 16T14-8,4,4-g4 16T8-4,4,4-g3 16T10-4,4,2-g1 16T10-4,2,4-g1

Below

4T2-2,2,2-g0

Belyi Curve 1: 8T4-4,2,2-g0-path1

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

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

Belyi Curve 1 Degree: 2

Belyi Curve 1 Naive Measure: 2

Belyi Map 1 Numerator:

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

Belyi Map 1 Denominator:

\(x_{2}^{8} - 2x_{2}^{4} + 1\)

Belyi Curve 2: 8T4-4,2,2-g0-path2

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

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

Belyi Curve 2 Degree: 2

Belyi Curve 2 Naive Measure: 2

Belyi Map 2 Numerator:

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

Belyi Map 2 Denominator:

\(x_{2}^{8} - 2x_{2}^{4} + 1\)

Belyi Curve 3: 8T4-4,2,2-g0-path3

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

Belyi Curve 3 Base Field: Rationals

Belyi Curve 3 Degree: 2

Belyi Curve 3 Naive Measure: 3

Belyi Map 3 Numerator:

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

Belyi Map 3 Denominator:

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