curve #3308

y² + xy + y = x³ + x² − 12285x + 1096051

a-invariants: [1, 1, 1, -12285, 1096051]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/5ℤ
conductor (N): 369278
discriminant (Δ): -405171591170528
Faltings height: 1.4924
naive height: 41.3469
primes of bad reduction: 2, 7, 13, 2029
regulator: 5.87324294708823381569041058299318265095927
submitted by: David Renshaw
submitted at: 2026-09-26 20:55:19 UTC
last updated: 2026-09-26 20:55:19 UTC

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

(37, 814)
(331, 5616)

Commentary

Cremona 369278a1 = LMFDB 369278.a2: https://www.lmfdb.org/EllipticCurve/Q/369278/a/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 369278, minimal discriminant -405171591170528, torsion ℤ/5ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:55:19 UTC · history