curve #1

y² + y = x³ − 6349808647x + 193146346911036

a-invariants: [0, 0, 1, -6349808647, 193146346911036]
c-invariants: [304790815056, -166878443731135320]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 269601712590130409544942497797
discriminant (Δ): 269601712590130409544942497797
Faltings height: 4.4677
naive height: 79.3287
primes of bad reduction: 60259, 550469, 11241887, 722983930261
regulator: 37541965361.758320665649129943760568697141050295736574648657389
submitted by: David Renshaw
submitted at: 2026-05-27 21:57:08 UTC
last updated: 2026-07-01 22:46:38 UTC

(49421, 200114)
(49493, 333458)
(49513, 362258)
(49632, 502899)
(49667, 538049)
(49797, 654674)
(49899, 735713)
(50012, 818375)
(50165, 921837)
(50215, 954017)
(51108, 1454591)
(-3659, 14708205)

Found by Mestre (1982). A historical rank ≥ 12 record, via Dujella's elliptic-curve rank-records tables.

last edited by David Renshaw at 2026-05-27 22:31:34 UTC · history