curve #2798

y² + xy = x³ + x² − 6x

a-invariants: [1, 1, 0, -6, 0]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ
conductor (N): 2454
discriminant (Δ): 14724
Faltings height: -0.5065
naive height: 17.2386
primes of bad reduction: 2, 3, 409
regulator: 0.636859438157772171869315529332126698420365
submitted by: David Renshaw
submitted at: 2026-09-26 20:22:56 UTC
last updated: 2026-09-26 20:22:56 UTC

Witness: 2 independent points log in to add more points →

(2, 0)
(3, 3)

Commentary

Cremona 2454b1 = LMFDB 2454.a1: https://www.lmfdb.org/EllipticCurve/Q/2454/a/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 2454, minimal discriminant 14724, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:22:56 UTC · history