curve #1226

y² + xy = x³ − x² − 1407918189274x + 648619542235505344

a-invariants: [1, -1, 0, -1407918189274, 648619542235505344]
rank (lower bound): ≥ 15
torsion subgroup: trivial
conductor (N): 1566351503089209175204588574733288574
discriminant (Δ): -3132703006178418350409177149466577148
Faltings height: 5.8213
naive height: 95.5504
primes of bad reduction: 2, 197, 70560241303, 56342089479098806741957
regulator: 287819533962.00687462824307972247339816657476502373911403736675878177
submitted by: Michael Rubinstein
submitted at: 2026-09-24 14:35:40 UTC
last updated: 2026-09-24 14:35:40 UTC

(701256, 78120580)
(341518, 455485742)
(595038, -147061580)
(1227790, -878591698)
(2056000, 2537658312)
(740875, 110041937)
(548729, -203444262)
(-1255762, -659954780)
(669157, -78629242)
(1823826, 2035626070)
(726368, 95510640)
(186495, 626433832)
(10621477/16, 5150482685/64)
(550173, 201102142)
(-75050, -868214212)

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

last edited by Michael Rubinstein at 2026-09-24 14:35:40 UTC · history