8T2-4,2,4-g1

graph data
Name 8T2-4,2,4-g1
Type Euclidean
Degree 8
Genus 1
Galois orbit size for 8T2-4,2,4-g1-path1 1
Galois orbit size for 8T2-4,2,4-g1-path2 1
Galois orbit size for 8T2-4,2,4-g1-path3 1
Galois orbit size for 8T2-4,2,4-g1-path4 1
Galois orbit size for 8T2-4,2,4-g1-path5 1
Passport size 1
Pointed size 1

Above

16T5-8,4,8-g5 16T6-8,2,8-g3 16T5-8,2,8-g3 16T4-4,4,4-g3 16T8-4,4,4-g3 16T6-8,4,8-g5 16T10-4,2,4-g1

Below

4T1-4,2,4-g1 4T1-4,1,4-g0 4T2-2,2,2-g0

Belyi Curve 1: 8T2-4,2,4-g1-path1

\(x_{1}^{2} - 1/2x_{2}^{3} - 1/2x_{2}2\)

Belyi Curve 1 Base Field: Rationals

Belyi Curve 1 Degree: 3

Belyi Curve 1 Naive Measure: 5

Belyi Map 1 Numerator:

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

Belyi Map 1 Denominator:

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

Belyi Curve 2: 8T2-4,2,4-g1-path3

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

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

Belyi Curve 2 Degree: 4

Belyi Curve 2 Naive Measure: 5

Belyi Map 2 Numerator:

\(x_{3}^{4}\)

Belyi Map 2 Denominator:

\(1\)

Belyi Curve 3: 8T2-4,2,4-g1-path4

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

Belyi Curve 3 Base Field: Rationals

Belyi Curve 3 Degree: 6

Belyi Curve 3 Naive Measure: 5

Belyi Map 3 Numerator:

\(1\)

Belyi Map 3 Denominator:

\(x_{3}^{4}\)

Belyi Curve 4: 8T2-4,2,4-g1-path5

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

Belyi Curve 4 Base Field: Rationals

Belyi Curve 4 Degree: 3

Belyi Curve 4 Naive Measure: 3

Belyi Map 4 Numerator:

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

Belyi Map 4 Denominator:

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