curve #3251

y² + y = x³ + 342

a-invariants: [0, 0, 1, 0, 342]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/3ℤ
conductor (N): 36963
discriminant (Δ): -50602347
Faltings height: 0.1572
naive height: 25.1942
primes of bad reduction: 3, 37
regulator: 12.8827588595277393316032493740640654898495
submitted by: David Renshaw
submitted at: 2026-09-26 20:46:04 UTC
last updated: 2026-09-26 20:46:04 UTC

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

(12, 45)
(1110, 36981)

Commentary

Cremona 36963f1 = LMFDB 36963.g2: https://www.lmfdb.org/EllipticCurve/Q/36963/g/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 36963, minimal discriminant -50602347, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:46:04 UTC · history