curve #3316

y² + xy = x³ − x² − 3762x + 97470

a-invariants: [1, -1, 0, -3762, 97470]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/6ℤ
conductor (N): 342
discriminant (Δ): -617336050482
Faltings height: 1.0014
naive height: 36.4784
primes of bad reduction: 2, 3, 19
regulator: 2.129702711707007664362148315407992772030
submitted by: David Renshaw
submitted at: 2026-09-26 20:56:36 UTC
last updated: 2026-09-26 20:56:36 UTC

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

(39, 75)

Commentary

Cremona 342c4 = LMFDB 342.c2: https://www.lmfdb.org/EllipticCurve/Q/342/c/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 342, minimal discriminant -617336050482, torsion ℤ/6ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:56:36 UTC · history