curve #3283

y² + xy = x³ + x² − 1602x + 24024

a-invariants: [1, 1, 0, -1602, 24024]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/4ℤ
conductor (N): 330
discriminant (Δ): 4392300
Faltings height: 0.4360
naive height: 33.7516
primes of bad reduction: 2, 3, 5, 11
regulator: 0.5216761379606932399799023420757016726328
submitted by: David Renshaw
submitted at: 2026-09-26 20:51:16 UTC
last updated: 2026-09-26 20:51:16 UTC

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

(23, -9)

Commentary

Cremona 330e3 = LMFDB 330.b1: https://www.lmfdb.org/EllipticCurve/Q/330/b/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 330, minimal discriminant 4392300, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:51:16 UTC · history