curve #6212

y² + xy = x³ + x² − 24531596047918086751018625133487x + 46777217302979654187145803194876621955279167929

a-invariants: [1, 1, 0, -24531596047918086751018625133487, 46777217302979654187145803194876621955279167929]
c-invariants: [1177516610300068164048894006407401, -40415515749774430049068551210884631736066249146101]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 171517969376759420883760042498182848799261463833072797372265764376806743139910
discriminant (Δ): -424601919016039799285526060520752176742517546600696442984476903665098684096268101032331062500
Faltings height: 16.7588
naive height: 228.4466
primes of bad reduction: 2, 3, 5, 7, 13, 23, 43, 47, 499, 2831503456292872772261507, 956610598243898460696196371322507531568693
regulator: 76632579365406129665503.1086390992200326743823268243456795550149235736296645353911069
submitted by: apkorte
submitted at: 2026-10-30 18:53:12 UTC
last updated: 2026-10-30 18:53:12 UTC

(3799623876558883, -91771932109626035104979)
(2967978903340005, 10610534813011727581847)
(3324417301895608, 44323639824703153476421)
(1168847374285558, -140358149079551696895029)
(2715429196716973, 13629879220428880744831)
(3329294778153808, -44798263297562168304779)
(1061701287079153137/289, -387975272853582875879410852/4913)
(2846987975925648, 3444612982380593217781)
(148234687360025863/36, 26960309568588413696747461/216)
(3010451018476183, -14464117451933766209279)
(166342376120281897/9, 65621843635071687416075092/27)
(11456028781565131/4, 26138465634291900099629/8)
(2434274961267976108, 3797987662206652640775115471)
(2665647749008008, 18051532554144724874021)
(2836519267795383, 3880339306365096786721)
(333523840612151368/121, -13359633819476408030386849/1331)
(2724398044870264, -12837695870822779749947)
(45934418388308893/16, 218051557104194592095419/64)
(-4832529467034897, 229065864781779503205496)
(3488500971224278, -60436069010391508058129)
(-977664575062712, 264246874703965574660371)
(-232891620721247, 229080310862823573518371)
(6524215960578598, 405504138617025524593831)

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