curve #2806

y² + xy = x³ + x² − 11x + 9

a-invariants: [1, 1, 0, -11, 9]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ
conductor (N): 2742
discriminant (Δ): 16452
Faltings height: -0.4538
naive height: 18.9461
primes of bad reduction: 2, 3, 457
regulator: 0.611034784270383171759655271923023151497548
submitted by: David Renshaw
submitted at: 2026-09-26 20:23:16 UTC
last updated: 2026-09-26 20:23:16 UTC

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

(0, 3)
(1, 0)

Commentary

Cremona 2742c1 = LMFDB 2742.a2: https://www.lmfdb.org/EllipticCurve/Q/2742/a/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 2742, minimal discriminant 16452, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:23:16 UTC · history