curve #4695

y² = x³ + 402599774387690701016910427272483x

a-invariants: [0, 0, 0, 402599774387690701016910427272483, 0]
c-invariants: [-19324789170609153648811700509079184, 0]
rank (lower bound): ≥ 14
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 576307834087180278659283541515639524426406638619391775412369725472 ☆ record for quartic twists, rank ≥ 14
discriminant (Δ): -4176385271664434364317054505800445497901317365790392719866723077530502652055412286723274656096165568 ☆ record for quartic twists, rank ≥ 14
Faltings height: 17.8049 ☆ record for quartic twists, rank ≥ 14
naive height: 236.8401 ☆ record for quartic twists, rank ≥ 14
primes of bad reduction: 2, 3, 7, 11, 17, 19, 23, 37, 59, 71, 73, 97, 127, 139, 151, 263, 313, 443, 733
regulator: 1916970694428080.90781887425825054764395717739715473152742246491348
submitted by: dujella
submitted at: 2026-10-20 20:47:42 UTC
last updated: 2026-10-20 20:47:42 UTC

(17715373576525779, 3562569314711466369088086)
(2626434695669379, 1037072601415883504491614)
(2569230493256067, 1025344316293086716196318)
(235538747268099, 307962520197557881526046)
(72777729441003372, 20366017444893924849237282)
(208383733118864688, 95565185470960061947766676)
(36178079522739, 120686925577870348570566)
(103189419061250643, 33768487838255557704513174)
(1751414347117072176, 2317991574180462284959749972)
(306104494367228425/4, 175082211930567255911081155/8)
(54693351931994304/25, 118007688830447299097189592/125)
(2696555916804876, 1051304226981395145047478)
(2842774711299072, 1080497092155012281695968)
(46439279877409015377/1681, 391130341466321391183789029622/68921)

Watkins (2002)

last edited by dujella at 2026-10-20 20:47:42 UTC · history