curve #4113

y² + xy = x³ − 9655018350892283504325029185999066818191632795080925x + 365148443787861623261740625520247061309392210825901585560606819503182687214257

a-invariants: [1, 0, 0, -9655018350892283504325029185999066818191632795080925, 365148443787861623261740625520247061309392210825901585560606819503182687214257]
c-invariants: [463440880842829608207601400927955207273198374163884401, -315488255432712442498143901144654782235559282464981071316297102960547402998944649]
rank (lower bound): ≥ 20
torsion subgroup: ℤ/2ℤ
conductor (N): 13147875829450866457593374848357371457853900269857543652894501277726603180941592610
discriminant (Δ): 2205621562116731197532756906964663636141959316343209292470515815670177863401400460200213086067579695203952944383511751506469537620365583348853540000000000
Faltings height: 28.5390
naive height: 370.7116
primes of bad reduction: 2, 3, 5, 7, 19, 23, 29, 41, 53, 59, 71, 127, 131, 149, 269, 503, 521, 631, 1181, 1283, 2017, 2153, 2741, 6079, 9829, 93601, 137399, 1553129, 3220558637
regulator: 22127181460055910145686.2985301775773473603167811924310882330021511400504018079
submitted by: wgxli
submitted at: 2026-10-09 15:28:42 UTC
last updated: 2026-10-09 15:28:42 UTC

(56945559967689538964242298, 947067755935233210722611715747955431)
(56060753738774447950228754, 8308379179596818645442612525778212623)
(56219039035558967177855234, 6113943594253279475006957977917261263)
(56241006522659330300028674, 5801313554307956476493198481135933743)
(56461244348668112216573954, 2306476585712953288535733292146514223)
(56464942690648535743684754, 2232513198916520332805013928124676623)
(56996879103597003623018648, 2261058891787305823296996741462848951)
(53455031578659241794163004, 42233870554368383634821672977960392623)
(54233262488389212557191754, 32228974839481496945872897130204322623)
(57766180797667439521741754, 13293034989212621125434922814524035623)
(58124563809021983562155714, 18069678368517007773046901946918387983)
(59773333478627329021964744, 39963108855796150963020046828241615393)
(59895535782538076441410754, 41589617471635223219788663958664984623)
(23163536041386041899346498, 392342273590994124789893881442053210511)
(-20940329940077544643654246, 747091315049430530246755077002430534623)
(-77213657257120912236703246, 806414189571562495433974736543034690623)
(107339676110347881886560854, 752016510890871247730572495778903409923)
(458340982709182328637913298, 9603463298692019060391661103404459558031)
(-1078044594090317368159266091/16, 53919869509088408733103814605975956207437/64)
(192315714200079271467849349004/3481, 3919036301755913941565865596501548439044687/205379)

2-isogenous to curve #4112

last edited by wgxli at 2026-10-09 15:28:42 UTC · history