curve #3253

y² + xy = x³ − x² − 57x + 399

a-invariants: [1, -1, 0, -57, 399]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/3ℤ
conductor (N): 37962
discriminant (Δ): -51969978
Faltings height: 0.1684
naive height: 25.4282
primes of bad reduction: 2, 3, 19, 37
regulator: 11.4793442785780093742759105522523611603272
submitted by: David Renshaw
submitted at: 2026-09-26 20:46:23 UTC
last updated: 2026-09-26 20:46:23 UTC

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

(7, 14)
(-35/9, 686/27)

Commentary

Cremona 37962m1 = LMFDB 37962.h1: https://www.lmfdb.org/EllipticCurve/Q/37962/h/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 37962, minimal discriminant -51969978, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:46:23 UTC · history