curve #2672

y² + xy + y = x³ − x² + 6x + 2

a-invariants: [1, -1, 1, 6, 2]
rank (lower bound): ≥ 3
torsion subgroup: trivial
conductor (N): 22481
discriminant (Δ): -22481
Faltings height: -0.4771
naive height: 17.1412
primes of bad reduction: 22481
regulator: 2.0213076902871140047205993450570528201056394
submitted by: David Renshaw
submitted at: 2026-09-26 20:17:05 UTC
last updated: 2026-09-26 20:17:05 UTC

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

(0, 1)
(1, 2)
(9, 22)

Commentary

Cremona 22481a1 = LMFDB 22481.b1: https://www.lmfdb.org/EllipticCurve/Q/22481/b/1 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 22481, minimal discriminant -22481, torsion trivial. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:17:05 UTC · history