curve #3319

y² + xy + y = x³ − 524x + 4566

a-invariants: [1, 0, 1, -524, 4566]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/6ℤ
conductor (N): 2090
discriminant (Δ): 2528900
Faltings height: 0.2387
naive height: 30.3953
primes of bad reduction: 2, 5, 11, 19
regulator: 1.580049917079489213763931396547031660057
submitted by: David Renshaw
submitted at: 2026-09-26 20:57:06 UTC
last updated: 2026-09-26 20:57:06 UTC

Witness: 1 independent point log in to add more points →

(11, 7)

Commentary

Cremona 2090e1 = LMFDB 2090.b2: https://www.lmfdb.org/EllipticCurve/Q/2090/b/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 2090, minimal discriminant 2528900, torsion ℤ/6ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:57:06 UTC · history