curve #2676

y² + xy + y = x³ + x² − 5x + 6

a-invariants: [1, 1, 1, -5, 6]
rank (lower bound): ≥ 3
torsion subgroup: trivial
conductor (N): 21443
discriminant (Δ): -21443
Faltings height: -0.4774
naive height: 17.7483
primes of bad reduction: 41, 523
regulator: 1.2451011244899535578268621795574659946742513
submitted by: David Renshaw
submitted at: 2026-09-26 20:17:15 UTC
last updated: 2026-09-26 20:17:15 UTC

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

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

Commentary

Cremona 21443a1 = LMFDB 21443.a1: https://www.lmfdb.org/EllipticCurve/Q/21443/a/1 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 21443, minimal discriminant -21443, torsion trivial. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:17:15 UTC · history