curve #588

y² + y = x³ − 1129201567x + 23953648602246

a-invariants: [0, 0, 1, -1129201567, 23953648602246]
rank (lower bound): ≥ 13
torsion subgroup: trivial
conductor (N): 155721986935837682842530035243
discriminant (Δ): -155721986935837682842530035243
Faltings height: 4.2975
naive height: 75.1374 ★ record for rank ≥ 13
primes of bad reduction: 401, 137507, 4811267, 586977288977347
regulator: 1683637618.841578093468805445545313455367883895927339218701409161
submitted by: Michael Rubinstein
submitted at: 2026-09-05 22:13:53 UTC
last updated: 2026-09-05 22:13:53 UTC

(-41321, 246731)
(-31532, 5311158)
(-18067, 6201416)
(-2305, 5152107)
(86, 4884315)
(847, 4795604)
(3304, 4500981)
(19999, 3060971)
(21377, 3095720)
(28464, 3856626)
(30009, 4134216)
(38281, 6068360)
(50563, 9804491)

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

last edited by Michael Rubinstein at 2026-09-05 22:13:53 UTC · history