curve #661

y² + xy + y = x³ − 23x + 42

a-invariants: [1, 0, 1, -23, 42]
rank (lower bound): ≥ 3
torsion subgroup: trivial
conductor (N): 13766
discriminant (Δ): -110128
Faltings height: -0.2884
naive height: 21.0973
primes of bad reduction: 2, 6883
regulator: 0.55430295368319518143351210453405619056042241
submitted by: David Renshaw
submitted at: 2026-09-08 19:17:27 UTC
last updated: 2026-09-08 19:17:27 UTC

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

(3, 0)
(-1, 8)
(2, 1)

Commentary

Cremona 13766a1 = LMFDB 13766.a1. Curve data, generators (3, 0), (-1, 8), (2, 1) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/13766/a/1

last edited by David Renshaw at 2026-09-08 19:17:27 UTC · history