curve #3317

y² + xy = x³ − x² − 3852x + 92988

a-invariants: [1, -1, 0, -3852, 92988]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/6ℤ
conductor (N): 342
discriminant (Δ): 60002532
Faltings height: 0.6548
naive height: 36.3828
primes of bad reduction: 2, 3, 19
regulator: 1.064851355853503832181074157703996386015
submitted by: David Renshaw
submitted at: 2026-09-26 20:56:47 UTC
last updated: 2026-09-26 20:56:47 UTC

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

(42, 42)

Commentary

Cremona 342c3 = LMFDB 342.c1: https://www.lmfdb.org/EllipticCurve/Q/342/c/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 342, minimal discriminant 60002532, torsion ℤ/6ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:56:47 UTC · history