curve #659

y² + xy = x³ − x² − 16x + 28

a-invariants: [1, -1, 0, -16, 28]
rank (lower bound): ≥ 3
torsion subgroup: trivial
conductor (N): 11642
discriminant (Δ): 23284
Faltings height: -0.4030
naive height: 19.9663
primes of bad reduction: 2, 5821
regulator: 0.42196553018652073206166803847027733176833008
submitted by: David Renshaw
submitted at: 2026-09-08 19:17:14 UTC
last updated: 2026-09-08 19:17:14 UTC

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

(2, 0)
(3, -1)
(4, 2)

Commentary

Cremona 11642a1 = LMFDB 11642.a1. Curve data, generators (2, 0), (3, -1), (4, 2) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/11642/a/1

last edited by David Renshaw at 2026-09-08 19:17:15 UTC · history