curve #1159

y² + xy = x³ + 11356x + 399513

a-invariants: [1, 0, 0, 11356, 399513]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/4ℤ
conductor (N): 486291
discriminant (Δ): -162350158069593
Faltings height: 1.4136 ☆ record for ℤ/4ℤ torsion, rank ≥ 3
naive height: 39.6261 ☆ record for ℤ/4ℤ torsion, rank ≥ 3
primes of bad reduction: 3, 13, 37, 337
regulator: 19.454061799222117132136301154622099065375743
submitted by: David Renshaw
submitted at: 2026-09-23 21:37:55 UTC
last updated: 2026-09-23 21:37:55 UTC

Witness: 3 independent points log in to add more points →

(-29, 229)
(-3, 606)
(231, 3804)

Commentary

Cremona 486291b3, rank exactly 3 according to Cremona's tables. Witness generators from https://github.com/JohnCremona/ecdata/blob/master/allgens/allgens.480000-489999 . Found by screening the local allgens tables for missing torsion size records; torsion and independence independently verified by the site.

last edited by David Renshaw at 2026-09-23 21:37:56 UTC · history