curve #3827

y² + xy = x³ − 17541537989091273759944983317036639798113x + 838497186529932364328616041470150317619209633534876815126217

a-invariants: [1, 0, 0, -17541537989091273759944983317036639798113, 838497186529932364328616041470150317619209633534876815126217]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 761102455033066425125507545248104868826590570844046070162466450825140202126660337641284406350
discriminant (Δ): 41718741959042692180975034294110249756410264968954799205943109793428026953531434551816334653003371274753513189735424000000
Faltings height: 22.0844
naive height: 289.6098
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 31, 67, 107, 35437813, 13128258853185419621, 1973169067988633882749402944712642859852717347498346357
regulator: 46987352815524006134450731.70328036943453474832207245930571789744606239435766214791471112
submitted by: 7fff-zip
submitted at: 2026-10-03 05:22:03 UTC
last updated: 2026-10-03 05:22:03 UTC

(96554740521126400912, -211992458789713339543127326781)
(43569252687383503402, 396146584909340171496139671499)
(55784809428459854218, -183153185742748413244196356373)
(2490507591859170536506/25, -35279276727301056070145266558369/125)
(224803907387199849646, -2873318688876860767332034883645)
(2403923513872266195898/49, 106271626776656966444724930212557/343)
(-119313325375883685494, 1110374412510547918398630434539)
(2481543833435669817346/121, 929196579001114390168831266510089/1331)
(2293613199069852992962, 109665526315449732856831633518019)
(-151829940400747724948, 42353774060856304473853435849)
(122075769877259089642, -718563713247276489371696544821)
(285689707297352497978, 4375460753522754568125124509787)
(-12804116382673513598, 1030049467040967066592016250499)
(54423715187119657162, 212182327688171837786385144619)
(120689740577582751402, 692374108011329157014803895499)
(54822478798965492202, 203950438317671334790118420299)
(-22164361611618519062, 1102907855305911441910918022347)
(-86000128542187018838, 1308056901068765902187776884619)
(91620908742200071402, 20670257485144732440971655499)
(94257365507489766442, -150009897999069679994195309621)
(293827964036019893802, -4588235237173918353983188430901)
(646248896385987667402, 16105904476799193568609826989099)
(91692335306263076938, -31216628756620893183450515285)
(124970261788586334442, 773342061904860257068128671179)
(-4790175803594753558, 960424032928844529520481423179)

X1008; T=-566/63; 2-neighbor step: yes (Q has vector q=[1,0,-1,1,0,2,1,1,1,-2,-1,0,-1,1,1,0,0] in source section basis; h(Q)=12; F'=O+Q-F).

last edited by 7fff-zip at 2026-10-03 05:22:04 UTC · history