curve #593

y² + xy = x³ − x² − 47306953864x + 4103869699271524

a-invariants: [1, -1, 0, -47306953864, 4103869699271524]
rank (lower bound): ≥ 14
torsion subgroup: trivial
conductor (N): 249940365173246666568907372690714
discriminant (Δ): -499880730346493333137814745381428
Faltings height: 5.0404
naive height: 85.4246
primes of bad reduction: 2, 1871, 7872773437, 8484082116786312991
regulator: 1207731896067365.34047681040774313390176960254100802985517338878438
submitted by: Michael Rubinstein
submitted at: 2026-09-05 23:00:38 UTC
last updated: 2026-09-05 23:00:38 UTC

(-2143, 64848883)
(620819/4, 178307465/8)
(-9169999241/241081, 9054520800491998/118370771)
(-383014029/8836, 64745147598095/830584)
(-30429449/121, 13208082270/1331)
(-2099/16, 4103036051/64)
(293150498/169, 4979685567316/2197)
(353764175/1369, 4834685758779/50653)
(933315266/121, 28496631261150/1331)
(1468670998/9409, 20795972041220/912673)
(2526679593/32041, 168331069766545/5735339)
(3484461968/36481, 148581714279362/6967871)
(12329516690/380689, 11986140221031546/234885113)
(29123760128/380689, 7163663225597574/234885113)

From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-05 23:00:38 UTC · history