curve #4613

y² + xy + y = x³ + 1480361870444871550162634921271192x + 124343164943544456786374111107788444051173036216422

a-invariants: [1, 0, 1, 1480361870444871550162634921271192, 124343164943544456786374111107788444051173036216422]
c-invariants: [-71057369781353834407806476221017239, -107432494511222410556841177325098464048503788959462965]
rank (lower bound): ≥ 16
torsion subgroup: ℤ/2ℤ
conductor (N): 259955327597572535406995941385230425410717342343794896566
discriminant (Δ): -6886875104942838067919739663568819289092737050278520832178866966976154723419029064540447623322535630448
Faltings height: 18.4132
naive height: 244.2174
primes of bad reduction: 2, 3, 7, 11, 13, 17, 43, 53, 71, 109, 149, 173, 233, 241, 263, 487, 691, 773, 1019, 1459, 2579, 5659, 8689, 15877
regulator: 293540929150798381.4410219109512617384447646325899970062830896224628555
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:24:37 UTC
last updated: 2026-10-19 03:24:37 UTC

(34586706482146133, 14728136911097138276749011)
(38235374813499866, 15389715000995362831925070)
(96399958821196373, 34101175654060857016978131)
(-38814179154994054, 2899827787344985917563895)
(-9637739104618984639/256, 15996764285267595708457219833/4096)
(-889560766169973331/25, 644896341772703529401414043/125)
(-19398975882246959, -9398161138717733927183305)
(-39794513236978066, -1553757701428659464811882)
(420139890392265386, 273693910746317743441001070)
(-183429520837552354035682991/6308330625, 3773244063509912288429390417133068191927/501039159890625)
(-24654691471135029742645606/712623025, -107133743095753664137205547349927350462/19023471652375)
(-7674841480464347650756111/267159025, 33286765395032747475740370644559742647/4366714263625)
(41770258230306775448377/1225449, 19863669586901173314293512538673533/1356572043)
(-33464818090572678022/22801, 38054700802530455895556714502946/3442951)
(-6965679338502030762760291/258727225, -33545086297424464679535685961446744293/4161627414125)
(-279094802658273219109807/25573249, -1337032385540665225364779423397912457/129323920193)

X400, T=-2246/1211.

last edited by Andrii Prokhorenkov at 2026-10-19 03:24:37 UTC · history