16T10-4,4,2-g1

graph data
Name 16T10-4,4,2-g1
Type Euclidean
Degree 16
Genus 1
Galois orbit size for 16T10-4,4,2-g1-path1 1
Galois orbit size for 16T10-4,4,2-g1-path10 1
Galois orbit size for 16T10-4,4,2-g1-path11 1
Galois orbit size for 16T10-4,4,2-g1-path2 1
Galois orbit size for 16T10-4,4,2-g1-path3 1
Galois orbit size for 16T10-4,4,2-g1-path4 1
Galois orbit size for 16T10-4,4,2-g1-path5 1
Galois orbit size for 16T10-4,4,2-g1-path6 1
Galois orbit size for 16T10-4,4,2-g1-path7 1
Galois orbit size for 16T10-4,4,2-g1-path8 1
Galois orbit size for 16T10-4,4,2-g1-path9 1
Passport size 1
Pointed size 1

Above

32S6-4,4,4-g5 32S2-4,4,4-g5 32S8-8,8,4-g9 32S5-8,8,2-g5 32S10-8,4,4-g7 32S5-8,8,4-g9 32S6-4,4,2-g1 32S10-4,8,4-g7 32S11-8,4,4-g7 32S9-8,4,2-g3 32S11-8,4,2-g3 32S11-4,8,4-g7 32S9-4,8,2-g3 32S11-4,8,2-g3 32S7-8,8,2-g5

Below

8T4-4,2,2-g0 8T4-2,4,2-g0 8T2-4,4,2-g1

Belyi Curve 1: 16T10-4,4,2-g1-path10

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

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

Belyi Curve 1 Degree: 3

Belyi Curve 1 Naive Measure: 5

Belyi Map 1 Numerator:

\(-16x_{2}^{6} + 32x_{2}^{4} - 16x_{2}^{2}\)

Belyi Map 1 Denominator:

\(x_{2}^{8} - 12x_{2}^{6} + 38x_{2}^{4} - 12x_{2}^{2} + 1\)

Belyi Curve 2: 16T10-4,4,2-g1-path11

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

Belyi Curve 2 Base Field: \(\nu^{4}+6\nu^{2}+1\), discriminant [ <2, 14> ]

Belyi Curve 2 Degree: 6

Belyi Curve 2 Naive Measure: 15

Belyi Map 2 Numerator:

\(x_{3}^{8} + 2x_{3}^{4} + 1\)

Belyi Map 2 Denominator:

\(x_{3}^{8} - 2x_{3}^{4} + 1\)

Belyi Curve 3: 16T10-4,4,2-g1-path6

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

Belyi Curve 3 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 3 Degree: 3

Belyi Curve 3 Naive Measure: 5

Belyi Map 3 Numerator:

\(x_{2}^{8} + 4x_{2}^{6} + 6x_{2}^{4} + 4x_{2}^{2} + 1\)

Belyi Map 3 Denominator:

\(x_{2}^{8} - 12x_{2}^{6} + 38x_{2}^{4} - 12x_{2}^{2} + 1\)

Belyi Curve 4: 16T10-4,4,2-g1-path7

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

Belyi Curve 4 Base Field: \(\nu^{4}+1\), discriminant [ <2, 8> ]

Belyi Curve 4 Degree: 3

Belyi Curve 4 Naive Measure: 5

Belyi Map 4 Numerator:

\(x_{2}^{8} + 4x_{2}^{6} + 6x_{2}^{4} + 4x_{2}^{2} + 1\)

Belyi Map 4 Denominator:

\(x_{2}^{8} - 12x_{2}^{6} + 38x_{2}^{4} - 12x_{2}^{2} + 1\)

Belyi Curve 5: 16T10-4,4,2-g1-path8

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

Belyi Curve 5 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 5 Degree: 6

Belyi Curve 5 Naive Measure: 7

Belyi Map 5 Numerator:

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

Belyi Map 5 Denominator:

\(x_{3}^{8} - 2x_{3}^{4} + 1\)

Belyi Curve 6: 16T10-4,4,2-g1-path9

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

Belyi Curve 6 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 6 Degree: 3

Belyi Curve 6 Naive Measure: 5

Belyi Map 6 Numerator:

\(-16x_{2}^{6} + 32x_{2}^{4} - 16x_{2}^{2}\)

Belyi Map 6 Denominator:

\(x_{2}^{8} - 12x_{2}^{6} + 38x_{2}^{4} - 12x_{2}^{2} + 1\)