32S16-16,2,16-g7

graph data
Name 32S16-16,2,16-g7
Type Hyperbolic
Degree 32
Genus 7
Galois orbit size for 32S16-16,2,16-g7-path1 1
Galois orbit size for 32S16-16,2,16-g7-path2 1
Galois orbit size for 32S16-16,2,16-g7-path3 1
Galois orbit size for 32S16-16,2,16-g7-path4 1
Galois orbit size for 32S16-16,2,16-g7-path5 1
Galois orbit size for 32S16-16,2,16-g7-path6 1
Galois orbit size for 32S16-16,2,16-g7-path7 1
Galois orbit size for 32S16-16,2,16-g7-path8 1
Galois orbit size for 32S16-16,2,16-g7-path9 1
Passport size 1
Pointed size 1

Above

64S29-16,2,16-g13 64S44-16,4,16-g21 64S51-32,2,32-g15 64S50-32,4,32-g23 64S50-32,2,32-g15 64S51-32,4,32-g23 64S26-16,4,16-g21

Below

16T5-8,2,8-g3 16T1-16,1,16-g0 16T1-16,2,16-g4

Belyi Curve 1: 32S16-16,2,16-g7-path1

\(-x_{1}^{16} + x_{2}^{2} + x_{3}^{16}\)

Belyi Curve 1 Base Field: Rationals

Belyi Curve 1 Degree: 16

Belyi Curve 1 Naive Measure: 3

Belyi Map 1 Numerator:

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

Belyi Map 1 Denominator:

\(1\)

Belyi Curve 2: 32S16-16,2,16-g7-path3

\(x_{1}^{16} + x_{2}^{2} - x_{3}^{16}\)

Belyi Curve 2 Base Field: Rationals

Belyi Curve 2 Degree: 16

Belyi Curve 2 Naive Measure: 3

Belyi Map 2 Numerator:

\(1\)

Belyi Map 2 Denominator:

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

Belyi Curve 3: 32S16-16,2,16-g7-path5

\(x_{1}^{8}x_{2} + x_{2}^{2} + 4x_{3}^{16}\)

Belyi Curve 3 Base Field: Rationals

Belyi Curve 3 Degree: 16

Belyi Curve 3 Naive Measure: 6

Belyi Map 3 Numerator:

\(x_{1}^{16}\)

Belyi Map 3 Denominator:

\(16\)

Belyi Curve 4: 32S16-16,2,16-g7-path7

\(21845/93826423914496x_{1}^{16} - 1/18890042405425158030336\nu x_{1}^{15}x_{3} + 5/3148340400904193005056x_{1}^{14}x_{3}^{2} + 5/168661092905581768128\nu x_{1}^{13}x_{3}^{3} - 5/12973930223506289856x_{1}^{12}x_{3}^{4} - 1/270290212989714372\nu x_{1}^{11}x_{3}^{5} + 11/405435319484571558x_{1}^{10}x_{3}^{6} + 220/1419023618196000453\nu x_{1}^{9}x_{3}^{7} - 110/157669290910666717x_{1}^{8}x_{3}^{8} - 3520/1419023618196000453\nu x_{1}^{7}x_{3}^{9} + 1408/202717659742285779x_{1}^{6}x_{3}^{10} + 1024/67572553247428593\nu x_{1}^{5}x_{3}^{11} - 5120/202717659742285779x_{1}^{4}x_{3}^{12} - 81920/2635329576649715127\nu x_{1}^{3}x_{3}^{13} + 163840/6149102345516001963x_{1}^{2}x_{3}^{14} + 262144/18447307036548005889\nu x_{1}x_{3}^{15} + x_{2}^{2} - 65536/18447307036548005889x_{3}^{16}\)

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

Belyi Curve 4 Degree: 16

Belyi Curve 4 Naive Measure: 22269841419212633690445

Belyi Map 4 Numerator:

\(64/281474976710655\nu x_{1}^{15} - 128/18764998447377x_{1}^{14} - 1024/8042142191733\nu x_{1}^{13} + 1024/618626322441x_{1}^{12} + 16384/1031043870735\nu x_{1}^{11} - 360448/3093131612205x_{1}^{10} - 2883584/4330384257087\nu x_{1}^{9} + 1441792/481153806343x_{1}^{8} + 46137344/4330384257087\nu x_{1}^{7} - 92274688/3093131612205x_{1}^{6} - 67108864/1031043870735\nu x_{1}^{5} + 67108864/618626322441x_{1}^{4} + 1073741824/8042142191733\nu x_{1}^{3} - 2147483648/18764998447377x_{1}^{2} - 17179869184/281474976710655\nu x_{1} - 1431677611/93823560581120x_{2}^{2} + 4294967296/281474976710655\)

Belyi Map 4 Denominator:

\(64/281474976710655\nu x_{1}^{15} - 128/18764998447377x_{1}^{14} - 1024/8042142191733\nu x_{1}^{13} + 1024/618626322441x_{1}^{12} + 16384/1031043870735\nu x_{1}^{11} - 360448/3093131612205x_{1}^{10} - 2883584/4330384257087\nu x_{1}^{9} + 1441792/481153806343x_{1}^{8} + 46137344/4330384257087\nu x_{1}^{7} - 92274688/3093131612205x_{1}^{6} - 67108864/1031043870735\nu x_{1}^{5} + 67108864/618626322441x_{1}^{4} + 1073741824/8042142191733\nu x_{1}^{3} - 2147483648/18764998447377x_{1}^{2} - 17179869184/281474976710655\nu x_{1} - 93826423914496/21845x_{2}^{2} + 4294967296/281474976710655\)

Belyi Curve 5: 32S16-16,2,16-g7-path8

\(x_{1}^{16} + x_{2}^{2} - x_{3}^{16}\)

Belyi Curve 5 Base Field: Rationals

Belyi Curve 5 Degree: 16

Belyi Curve 5 Naive Measure: 3

Belyi Map 5 Numerator:

\(1\)

Belyi Map 5 Denominator:

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

Belyi Curve 6: 32S16-16,2,16-g7-path9

\(x_{1}^{8}x_{2} + x_{2}^{2} - x_{3}^{16}\)

Belyi Curve 6 Base Field: Rationals

Belyi Curve 6 Degree: 16

Belyi Curve 6 Naive Measure: 3

Belyi Map 6 Numerator:

\(-x_{1}^{16}\)

Belyi Map 6 Denominator:

\(4\)