curve #3274

y² + xy + y = x³ + x² − 370485x + 86638290

a-invariants: [1, 1, 1, -370485, 86638290]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 273585
discriminant (Δ): 316235978150625
Faltings height: 1.8470
naive height: 50.0813
primes of bad reduction: 3, 5, 13, 23, 61
regulator: 7.35753460206292335715299226319725785681329
submitted by: David Renshaw
submitted at: 2026-09-26 20:49:49 UTC
last updated: 2026-09-26 20:49:49 UTC

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

(93, 7233)
(348, -102)

Commentary

Cremona 273585c2 = LMFDB 273585.c3: https://www.lmfdb.org/EllipticCurve/Q/273585/c/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 273585, minimal discriminant 316235978150625, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:49:49 UTC · history