curve #2743

y² + y = x³ + x² + 2x + 2

a-invariants: [0, 1, 1, 2, 2]
rank (lower bound): ≥ 2
torsion subgroup: trivial
conductor (N): 1483
discriminant (Δ): -1483
Faltings height: -0.7081
naive height: 14.5337
primes of bad reduction: 1483
regulator: 0.395288186152922788838107840821414308901883
submitted by: David Renshaw
submitted at: 2026-09-26 20:20:19 UTC
last updated: 2026-09-26 20:20:19 UTC

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

(-1, 0)
(0, 1)

Commentary

Cremona 1483a1 = LMFDB 1483.a1: https://www.lmfdb.org/EllipticCurve/Q/1483/a/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 1483, minimal discriminant -1483, torsion trivial. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:20:19 UTC · history