curve #2750

y² + xy + y = x³ − x² − x + 2

a-invariants: [1, -1, 1, -1, 2]
rank (lower bound): ≥ 2
torsion subgroup: trivial
conductor (N): 1873
discriminant (Δ): -1873
Faltings height: -0.6921
naive height: 15.0011
primes of bad reduction: 1873
regulator: 0.530087735621530269181804915821798573401281
submitted by: David Renshaw
submitted at: 2026-09-26 20:20:38 UTC
last updated: 2026-09-26 20:20:38 UTC

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

(0, 1)
(-1, 1)

Commentary

Cremona 1873a1 = LMFDB 1873.a1: https://www.lmfdb.org/EllipticCurve/Q/1873/a/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 1873, minimal discriminant -1873, torsion trivial. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:20:38 UTC · history