curve #241

y² + xy + y = x³ + x² − 3002323607176717877406x + 63157734310826839052785319777928

a-invariants: [1, 1, 1, -3002323607176717877406, 63157734310826839052785319777928]
rank (lower bound): ≥ 18
conductor (N): 441460637662701293135009928680986049143542764800100521195695
naive height: 159.9746 ★ record for rank ≥ 18
Faltings height: 11.1400 ★ record for rank ≥ 18
discriminant (Δ): 8813761630935831317440473226115886471150831299234006905672050675 ★ record for rank ≥ 18
primes of bad reduction: 3, 5, 11, 419, 8761, 82207, 365239703, 34272807689, 708278198601699094328534873
regulator: 194929077607817370.28368176934892191839151385168214171212759831564579013299
submitted by: David Renshaw
last updated: 2026-07-01 22:31:41

(33335381221, 343488888049604)
(32930342653, -9948457849462)
(58385705146, 9321742787826029)
(19122392728, -3569117322951697)
(1080673626, 7740442886396429)
(36080669712, -1342491525978361)
(30274713901, -108580448018896)
(238891316806, 113926312448608649)
(111597974979/4, 8431760934883077/8)
(29804045256, 388206891435999)
(448581413029/9, -164980061730477752/27)
(68270113006, -13280948025012256)
(28159186454, 971213609060313)
(2240825377969/64, -501690777622691987/512)
(755795085506, 655380411797650869)
(86509789231/36, 1615773273712297909/216)
(2525729586784/25, -3515662795583333912/125)
(10782499297021/400, 10774154028693723721/8000)

Generated by rational Mestre (u,v) discriminant search: u=-1/2, v=7/2, T=429/2; exact abs-discriminant frontier triage.

last edited by David Renshaw at 2026-06-27 20:28:25 · history