32S13-8,4,4-g7

graph data
Name 32S13-8,4,4-g7
Type Hyperbolic
Degree 32
Genus 7
Galois orbit size for 32S13-8,4,4-g7-path1 1
Galois orbit size for 32S13-8,4,4-g7-path10 1
Galois orbit size for 32S13-8,4,4-g7-path11 1
Galois orbit size for 32S13-8,4,4-g7-path12 1
Galois orbit size for 32S13-8,4,4-g7-path13 1
Galois orbit size for 32S13-8,4,4-g7-path14 1
Galois orbit size for 32S13-8,4,4-g7-path15 1
Galois orbit size for 32S13-8,4,4-g7-path16 1
Galois orbit size for 32S13-8,4,4-g7-path17 1
Galois orbit size for 32S13-8,4,4-g7-path2 1
Galois orbit size for 32S13-8,4,4-g7-path3 1
Galois orbit size for 32S13-8,4,4-g7-path4 1
Galois orbit size for 32S13-8,4,4-g7-path5 1
Galois orbit size for 32S13-8,4,4-g7-path6 1
Galois orbit size for 32S13-8,4,4-g7-path7 1
Galois orbit size for 32S13-8,4,4-g7-path8 1
Galois orbit size for 32S13-8,4,4-g7-path9 1
Passport size 1
Pointed size 1

Above

64S46-16,8,4-g19 64S46-16,4,8-g19 64S15-8,8,8-g21 64S21-8,4,4-g13

Below

16T12-8,2,4-g2 16T8-4,4,4-g3 16T12-8,4,2-g2

Belyi Curve 1: 32S13-8,4,4-g7-path1

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

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

Belyi Curve 1 Degree: 14

Belyi Curve 1 Naive Measure: 13

Belyi Map 1 Numerator:

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

Belyi Map 1 Denominator:

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

Belyi Curve 2: 32S13-8,4,4-g7-path10

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

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

Belyi Curve 2 Degree: 16

Belyi Curve 2 Naive Measure: 22269841419212633690445

Belyi Map 2 Numerator:

\(-604462909807316734836736/79228153069531371854287077375\nu x_{1}^{15} + 564165382486833533812736/5281876871302091456952471825x_{1}^{14} + 1934281311383468527058944/2263661516272324910122487925\nu x_{1}^{13} - 743954350532145568546816/174127808944024993086345225x_{1}^{12} - 3967756536172176040001536/290213014906708321810575375\nu x_{1}^{11} + 23806539217050648426053632/870639044720124965431726125x_{1}^{10} + 38090462747435848718876672/1218894662608174951604416575\nu x_{1}^{9} - 423227363877599567675392/27086548057959443368987035x_{1}^{8} - 3096224743817216/1218894662608174951604416575\nu x_{1}^{7} + 6192449487634432/870639044720124965431726125x_{1}^{6} + 4503599627370496/290213014906708321810575375\nu x_{1}^{5} - 4503599627370496/174127808944024993086345225x_{1}^{4} - 72057594037927936/2263661516272324910122487925\nu x_{1}^{3} + 144115188075855872/5281876871302091456952471825x_{1}^{2} + 1152921504606846976/79228153069531371854287077375\nu x_{1} + 287108874291380224/280371170181375x_{2}^{2} - 288230376151711744/79228153069531371854287077375\)

Belyi Map 2 Denominator:

\(-1073741824/281474976710655\nu x_{1}^{15} + 252201529740623872/4722366201394651725825x_{1}^{14} + 288230221532889088/674623743056378817975\nu x_{1}^{13} - 96076648884994048/44974916203758587865x_{1}^{12} - 4611664852828553216/674623743056378817975\nu x_{1}^{11} + 9223215356447817728/674623743056378817975x_{1}^{10} + 29524086229041152/1889702361502461675\nu x_{1}^{9} - 36865188917143404544/4722366201394651725825x_{1}^{8} + 1548112371908608/72651787713763872705\nu x_{1}^{7} - 3096224743817216/51894134081259909075x_{1}^{6} - 2251799813685248/17298044693753303025\nu x_{1}^{5} + 2251799813685248/10378826816251981815x_{1}^{4} + 36028797018963968/134924748611275763595\nu x_{1}^{3} - 72057594037927936/314824413426310115055x_{1}^{2} - 576460752303423488/4722366201394651725825\nu x_{1} - 93826423914496/21845x_{2}^{2} + 144115188075855872/4722366201394651725825\)

Belyi Curve 3: 32S13-8,4,4-g7-path11

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

Belyi Curve 3 Base Field: Rationals

Belyi Curve 3 Degree: 16

Belyi Curve 3 Naive Measure: 5

Belyi Map 3 Numerator:

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

Belyi Map 3 Denominator:

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

Belyi Curve 4: 32S13-8,4,4-g7-path14

\(21845/375305695657984\nu x_{1}^{16} + 1/75560169621700632121344x_{1}^{15}x_{3} + 5/12593361603616772020224\nu x_{1}^{14}x_{3}^{2} - 5/674644371622327072512x_{1}^{13}x_{3}^{3} - 5/51895720894025159424\nu x_{1}^{12}x_{3}^{4} + 1/1081160851958857488x_{1}^{11}x_{3}^{5} + 11/1621741277938286232\nu x_{1}^{10}x_{3}^{6} - 55/1419023618196000453x_{1}^{9}x_{3}^{7} - 55/315338581821333434\nu x_{1}^{8}x_{3}^{8} + 880/1419023618196000453x_{1}^{7}x_{3}^{9} + 352/202717659742285779\nu x_{1}^{6}x_{3}^{10} - 256/67572553247428593x_{1}^{5}x_{3}^{11} - 1280/202717659742285779\nu x_{1}^{4}x_{3}^{12} + 20480/2635329576649715127x_{1}^{3}x_{3}^{13} + 40960/6149102345516001963\nu x_{1}^{2}x_{3}^{14} - 65536/18447307036548005889x_{1}x_{3}^{15} + x_{2}^{2} - 16384/18447307036548005889\nu x_{3}^{16}\)

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

Belyi Curve 4 Degree: 16

Belyi Curve 4 Naive Measure: 88932080034955556238568

Belyi Map 4 Numerator:

\(-604462909807316734836736/79228153069531371854287077375\nu x_{1}^{15} + 564165382486833533812736/5281876871302091456952471825x_{1}^{14} + 1934281311383468527058944/2263661516272324910122487925\nu x_{1}^{13} - 743954350532145568546816/174127808944024993086345225x_{1}^{12} - 3967756536172176040001536/290213014906708321810575375\nu x_{1}^{11} + 23806539217050648426053632/870639044720124965431726125x_{1}^{10} + 38090462747435848718876672/1218894662608174951604416575\nu x_{1}^{9} - 423227363877599567675392/27086548057959443368987035x_{1}^{8} - 3096224743817216/1218894662608174951604416575\nu x_{1}^{7} + 6192449487634432/870639044720124965431726125x_{1}^{6} + 4503599627370496/290213014906708321810575375\nu x_{1}^{5} - 4503599627370496/174127808944024993086345225x_{1}^{4} - 72057594037927936/2263661516272324910122487925\nu x_{1}^{3} + 144115188075855872/5281876871302091456952471825x_{1}^{2} + 1152921504606846976/79228153069531371854287077375\nu x_{1} - 1148435497165520896/280371170181375\nu x_{2}^{2} - 288230376151711744/79228153069531371854287077375\)

Belyi Map 4 Denominator:

\(-1073741824/281474976710655\nu x_{1}^{15} + 252201529740623872/4722366201394651725825x_{1}^{14} + 288230221532889088/674623743056378817975\nu x_{1}^{13} - 96076648884994048/44974916203758587865x_{1}^{12} - 4611664852828553216/674623743056378817975\nu x_{1}^{11} + 9223215356447817728/674623743056378817975x_{1}^{10} + 29524086229041152/1889702361502461675\nu x_{1}^{9} - 36865188917143404544/4722366201394651725825x_{1}^{8} + 1548112371908608/72651787713763872705\nu x_{1}^{7} - 3096224743817216/51894134081259909075x_{1}^{6} - 2251799813685248/17298044693753303025\nu x_{1}^{5} + 2251799813685248/10378826816251981815x_{1}^{4} + 36028797018963968/134924748611275763595\nu x_{1}^{3} - 72057594037927936/314824413426310115055x_{1}^{2} - 576460752303423488/4722366201394651725825\nu x_{1} + 375305695657984/21845\nu x_{2}^{2} + 144115188075855872/4722366201394651725825\)

Belyi Curve 5: 32S13-8,4,4-g7-path16

\(-21845/375305695657984\nu^{2}x_{1}^{16} - 1/75560169621700632121344x_{1}^{15}x_{3} - 5/12593361603616772020224\nu^{2}x_{1}^{14}x_{3}^{2} + 5/674644371622327072512x_{1}^{13}x_{3}^{3} + 5/51895720894025159424\nu^{2}x_{1}^{12}x_{3}^{4} - 1/1081160851958857488x_{1}^{11}x_{3}^{5} - 11/1621741277938286232\nu^{2}x_{1}^{10}x_{3}^{6} + 55/1419023618196000453x_{1}^{9}x_{3}^{7} + 55/315338581821333434\nu^{2}x_{1}^{8}x_{3}^{8} - 880/1419023618196000453x_{1}^{7}x_{3}^{9} - 352/202717659742285779\nu^{2}x_{1}^{6}x_{3}^{10} + 256/67572553247428593x_{1}^{5}x_{3}^{11} + 1280/202717659742285779\nu^{2}x_{1}^{4}x_{3}^{12} - 20480/2635329576649715127x_{1}^{3}x_{3}^{13} - 40960/6149102345516001963\nu^{2}x_{1}^{2}x_{3}^{14} + 65536/18447307036548005889x_{1}x_{3}^{15} + x_{2}^{2} + 16384/18447307036548005889\nu^{2}x_{3}^{16}\)

Belyi Curve 5 Base Field: \(\nu^{4}+1\), discriminant [ <2, 8> ]

Belyi Curve 5 Degree: 16

Belyi Curve 5 Naive Measure: 88932080034955556238568

Belyi Map 5 Numerator:

\(-604462909807316734836736/79228153069531371854287077375\nu^{2}x_{1}^{15} + 564165382486833533812736/5281876871302091456952471825x_{1}^{14} + 1934281311383468527058944/2263661516272324910122487925\nu^{2}x_{1}^{13} - 743954350532145568546816/174127808944024993086345225x_{1}^{12} - 3967756536172176040001536/290213014906708321810575375\nu^{2}x_{1}^{11} + 23806539217050648426053632/870639044720124965431726125x_{1}^{10} + 38090462747435848718876672/1218894662608174951604416575\nu^{2}x_{1}^{9} - 423227363877599567675392/27086548057959443368987035x_{1}^{8} - 3096224743817216/1218894662608174951604416575\nu^{2}x_{1}^{7} + 6192449487634432/870639044720124965431726125x_{1}^{6} + 4503599627370496/290213014906708321810575375\nu^{2}x_{1}^{5} - 4503599627370496/174127808944024993086345225x_{1}^{4} - 72057594037927936/2263661516272324910122487925\nu^{2}x_{1}^{3} + 144115188075855872/5281876871302091456952471825x_{1}^{2} + 1152921504606846976/79228153069531371854287077375\nu^{2}x_{1} + 1148435497165520896/280371170181375\nu^{2}x_{2}^{2} - 288230376151711744/79228153069531371854287077375\)

Belyi Map 5 Denominator:

\(-1073741824/281474976710655\nu^{2}x_{1}^{15} + 252201529740623872/4722366201394651725825x_{1}^{14} + 288230221532889088/674623743056378817975\nu^{2}x_{1}^{13} - 96076648884994048/44974916203758587865x_{1}^{12} - 4611664852828553216/674623743056378817975\nu^{2}x_{1}^{11} + 9223215356447817728/674623743056378817975x_{1}^{10} + 29524086229041152/1889702361502461675\nu^{2}x_{1}^{9} - 36865188917143404544/4722366201394651725825x_{1}^{8} + 1548112371908608/72651787713763872705\nu^{2}x_{1}^{7} - 3096224743817216/51894134081259909075x_{1}^{6} - 2251799813685248/17298044693753303025\nu^{2}x_{1}^{5} + 2251799813685248/10378826816251981815x_{1}^{4} + 36028797018963968/134924748611275763595\nu^{2}x_{1}^{3} - 72057594037927936/314824413426310115055x_{1}^{2} - 576460752303423488/4722366201394651725825\nu^{2}x_{1} - 375305695657984/21845\nu^{2}x_{2}^{2} + 144115188075855872/4722366201394651725825\)

Belyi Curve 6: 32S13-8,4,4-g7-path17

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

Belyi Curve 6 Base Field: Rationals

Belyi Curve 6 Degree: 16

Belyi Curve 6 Naive Measure: 5

Belyi Map 6 Numerator:

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

Belyi Map 6 Denominator:

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

Belyi Curve 7: 32S13-8,4,4-g7-path2

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

Belyi Curve 7 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 7 Degree: 14

Belyi Curve 7 Naive Measure: 13

Belyi Map 7 Numerator:

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

Belyi Map 7 Denominator:

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

Belyi Curve 8: 32S13-8,4,4-g7-path3

\(x_{1}^{5} - x_{1} - x_{2}^{2}\)
\(x_{1}^{2}x_{3}^{2} - x_{1}^{2} + 1/1120(-\nu^{4} + 192)x_{3}^{2} + 1/1120(-\nu^{4} - 6528)\)
\(1/560(-\nu^{4} - 3168)x_{1}^{3} + 1/560(3\nu^{4} + 544)x_{1}x_{3}^{2} + x_{2}^{2}x_{3}^{2} - x_{2}^{2}\)

Belyi Curve 8 Base Field: \(\nu^{8}+6336\nu^{4}+1024\), discriminant [ <2, 106>, <5, 8>, <7, 8> ]

Belyi Curve 8 Degree: 14

Belyi Curve 8 Naive Measure: 11383

Belyi Map 8 Numerator:

\(x_{3}^{8} + 1/280(-\nu^{4} - 6528)x_{3}^{6} + 1/280(9\nu^{4} + 57072)x_{3}^{4} + 1/8(-\nu^{4} - 6336)x_{3}^{2} + 1/280(51\nu^{4} + 323128)\)

Belyi Map 8 Denominator:

\(x_{3}^{8} + 1/280(-\nu^{4} - 6528)x_{3}^{6} + 1/56(-3\nu^{4} - 19024)x_{3}^{4} + 1/8(-\nu^{4} - 6336)x_{3}^{2} + 1/280(51\nu^{4} + 323128)\)

Belyi Curve 9: 32S13-8,4,4-g7-path4

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

Belyi Curve 9 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 9 Degree: 14

Belyi Curve 9 Naive Measure: 13

Belyi Map 9 Numerator:

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

Belyi Map 9 Denominator:

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

Belyi Curve 10: 32S13-8,4,4-g7-path5

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

Belyi Curve 10 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 10 Degree: 14

Belyi Curve 10 Naive Measure: 13

Belyi Map 10 Numerator:

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

Belyi Map 10 Denominator:

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

Belyi Curve 11: 32S13-8,4,4-g7-path6

\(x_{1}^{5} + x_{1} - 8/9x_{2}^{2}\)
\(x_{1}^{2}x_{3}^{2} - x_{1}^{2} + x_{3}^{2} + 1\)
\(9/4x_{1}^{3} - 9/4x_{1}x_{3}^{2} + x_{2}^{2}x_{3}^{2} - x_{2}^{2}\)

Belyi Curve 11 Base Field: \(\nu^{4}+6\nu^{2}+1\), discriminant [ <2, 14> ]

Belyi Curve 11 Degree: 14

Belyi Curve 11 Naive Measure: 35

Belyi Map 11 Numerator:

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

Belyi Map 11 Denominator:

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

Belyi Curve 12: 32S13-8,4,4-g7-path7

\(-256/4294967295\nu^{2}x_{1}^{16} - 16384/18446744065119617025x_{1}^{15}x_{3} - 32768/1229782937674641135\nu^{2}x_{1}^{14}x_{3}^{2} + 1835008/3689348813023923405x_{1}^{13}x_{3}^{3} + 23855104/3689348813023923405\nu^{2}x_{1}^{12}x_{3}^{4} - 381681664/6148914688373205675x_{1}^{11}x_{3}^{5} - 8396996608/18446744065119617025\nu^{2}x_{1}^{10}x_{3}^{6} + 9596567552/3689348813023923405x_{1}^{9}x_{3}^{7} + 4798283776/409927645891547045\nu^{2}x_{1}^{8}x_{3}^{8} - 153545080832/3689348813023923405x_{1}^{7}x_{3}^{9} - 2149631131648/18446744065119617025\nu^{2}x_{1}^{6}x_{3}^{10} + 1563368095744/6148914688373205675x_{1}^{5}x_{3}^{11} + 1563368095744/3689348813023923405\nu^{2}x_{1}^{4}x_{3}^{12} - 1924145348608/3689348813023923405x_{1}^{3}x_{3}^{13} - 549755813888/1229782937674641135\nu^{2}x_{1}^{2}x_{3}^{14} + 4398046511104/18446744065119617025x_{1}x_{3}^{15} + x_{2}^{2} + 1099511627776/18446744065119617025\nu^{2}x_{3}^{16}\)

Belyi Curve 12 Base Field: \(\nu^{4}+1\), discriminant [ <2, 8> ]

Belyi Curve 12 Degree: 16

Belyi Curve 12 Naive Measure: 129537136106023833516

Belyi Map 12 Numerator:

\(-36028797027352576/18446181123756261375\nu^{2}x_{1}^{15} + 33626877243424768/1229745408250417425x_{1}^{14} + 807045054915936256/3689236224751252275\nu^{2}x_{1}^{13} - 4035225289612066816/3689236224751252275x_{1}^{12} - 7173733935053012992/2049575680417362375\nu^{2}x_{1}^{11} + 129127217084426616832/18446181123756261375x_{1}^{10} + 5902960067589701632/737847244950250455\nu^{2}x_{1}^{9} - 4919146492171649024/1229745408250417425x_{1}^{8} - 157230162771968/3689236224751252275\nu^{2}x_{1}^{7} + 2201222278807552/18446181123756261375x_{1}^{6} + 1600888930041856/6148727041252087125\nu^{2}x_{1}^{5} - 1600888930041856/3689236224751252275x_{1}^{4} - 1970324836974592/3689236224751252275\nu^{2}x_{1}^{3} + 562949953421312/1229745408250417425x_{1}^{2} + 4503599627370496/18446181123756261375\nu^{2}x_{1} + 67109888/65535\nu^{2}x_{2}^{2} - 1125899906842624/18446181123756261375\)

Belyi Map 12 Denominator:

\(-4194304/4294967295\nu^{2}x_{1}^{15} + 3848097759232/281470681677825x_{1}^{14} + 30782097719296/281470681677825\nu^{2}x_{1}^{13} - 3419397947392/6254904037285x_{1}^{12} - 492002462400512/281470681677825\nu^{2}x_{1}^{11} + 980878188609536/281470681677825x_{1}^{10} + 7198365188096/1839677658025\nu^{2}x_{1}^{9} - 452406085156864/281470681677825x_{1}^{8} + 78615081385984/56294136335565\nu^{2}x_{1}^{7} - 1100611139403776/281470681677825x_{1}^{6} - 800444465020928/93823560559275\nu^{2}x_{1}^{5} + 800444465020928/56294136335565x_{1}^{4} + 985162418487296/56294136335565\nu^{2}x_{1}^{3} - 281474976710656/18764712111855x_{1}^{2} - 2251799813685248/281470681677825\nu^{2}x_{1} - 4294967295/256\nu^{2}x_{2}^{2} + 562949953421312/281470681677825\)

Belyi Curve 13: 32S13-8,4,4-g7-path9

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

Belyi Curve 13 Base Field: \(\nu^{2}+1\), discriminant [ <2, 2> ]

Belyi Curve 13 Degree: 16

Belyi Curve 13 Naive Measure: 22269841419212633690445

Belyi Map 13 Numerator:

\(-604462909807316734836736/79228153069531371854287077375\nu x_{1}^{15} + 564165382486833533812736/5281876871302091456952471825x_{1}^{14} + 1934281311383468527058944/2263661516272324910122487925\nu x_{1}^{13} - 743954350532145568546816/174127808944024993086345225x_{1}^{12} - 3967756536172176040001536/290213014906708321810575375\nu x_{1}^{11} + 23806539217050648426053632/870639044720124965431726125x_{1}^{10} + 38090462747435848718876672/1218894662608174951604416575\nu x_{1}^{9} - 423227363877599567675392/27086548057959443368987035x_{1}^{8} - 3096224743817216/1218894662608174951604416575\nu x_{1}^{7} + 6192449487634432/870639044720124965431726125x_{1}^{6} + 4503599627370496/290213014906708321810575375\nu x_{1}^{5} - 4503599627370496/174127808944024993086345225x_{1}^{4} - 72057594037927936/2263661516272324910122487925\nu x_{1}^{3} + 144115188075855872/5281876871302091456952471825x_{1}^{2} + 1152921504606846976/79228153069531371854287077375\nu x_{1} + 287108874291380224/280371170181375x_{2}^{2} - 288230376151711744/79228153069531371854287077375\)

Belyi Map 13 Denominator:

\(-1073741824/281474976710655\nu x_{1}^{15} + 252201529740623872/4722366201394651725825x_{1}^{14} + 288230221532889088/674623743056378817975\nu x_{1}^{13} - 96076648884994048/44974916203758587865x_{1}^{12} - 4611664852828553216/674623743056378817975\nu x_{1}^{11} + 9223215356447817728/674623743056378817975x_{1}^{10} + 29524086229041152/1889702361502461675\nu x_{1}^{9} - 36865188917143404544/4722366201394651725825x_{1}^{8} + 1548112371908608/72651787713763872705\nu x_{1}^{7} - 3096224743817216/51894134081259909075x_{1}^{6} - 2251799813685248/17298044693753303025\nu x_{1}^{5} + 2251799813685248/10378826816251981815x_{1}^{4} + 36028797018963968/134924748611275763595\nu x_{1}^{3} - 72057594037927936/314824413426310115055x_{1}^{2} - 576460752303423488/4722366201394651725825\nu x_{1} - 93826423914496/21845x_{2}^{2} + 144115188075855872/4722366201394651725825\)