curve #6464

y² + xy + y = x³ − 8485660239679577554542559426x + 301281337686062260024731671623012391910248

a-invariants: [1, 0, 1, -8485660239679577554542559426, 301281337686062260024731671623012391910248]
c-invariants: [407311691504619722618042852425, -260307075760758403628905421211866633674733125]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 1951567213378266819201049902637101362278081912988085662191923334650
discriminant (Δ): -107417754972970946227699696691506638535437233066035099693009547250287676967670062500
Faltings height: 14.8301
naive height: 204.5409
primes of bad reduction: 2, 3, 5, 11, 31, 53, 3259, 91110911, 2424416639772934163503305555287170018035496343203
regulator: 89164068673696297663.709248343368423765236157430551727507104134726359983758703726
submitted by: apkorte
submitted at: 2026-11-03 22:26:32 UTC
last updated: 2026-11-03 22:26:32 UTC

(55537630199362, 36190017611940116681)
(-195258092732933/4, 6192572442873903879931/8)
(64849665463003, 153990302818344072749)
(55065788852902, 31376889520972371836)
(53937028117027, 22445615574543016511)
(20851060722277, -365255630936413491289)
(47381434328242, -74765787844927527559)
(8770440736241053/169, 57101314770145613148407/2197)
(52666483292712, -21343834908308008769)
(118358310047143/4, 2206915363537576517953/8)
(53260274788867, -20343722579581073059)
(79352347493851, 357197030242383627767)
(455723080290523/4, 7214873223099347352223/8)
(60968359972261, 102725502512096839571)
(125349691019292, 1098712417579550800816)
(4387102213398928/169, 689500595989723574737907/2197)
(-25692115423499, 708757323402890819231)
(-4288051601149703/256, 2713018851978455048720651/4096)
(57666242317852, -60895520948403658189)
(811054609434997/16, -2385454357489568371651/64)
(138288950819902, -1331323926972129189739)

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