curve #2669

y² + xy = x³ + 6x − 5

a-invariants: [1, 0, 0, 6, -5]
rank (lower bound): ≥ 3
torsion subgroup: trivial
conductor (N): 26743
discriminant (Δ): -26743
Faltings height: -0.4641
naive height: 16.9784
primes of bad reduction: 47, 569
regulator: 2.0829721641483903997939166220928417012294659
submitted by: David Renshaw
submitted at: 2026-09-26 20:16:55 UTC
last updated: 2026-09-26 20:16:55 UTC

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

(1, 1)
(2, 3)
(5, 10)

Commentary

Cremona 26743a1 = LMFDB 26743.a1: https://www.lmfdb.org/EllipticCurve/Q/26743/a/1 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 26743, minimal discriminant -26743, torsion trivial. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:16:56 UTC · history