curve #3303

y² + xy + y = x³ + x² − 370480x + 86640752

a-invariants: [1, 1, 1, -370480, 86640752]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/4ℤ
conductor (N): 273585
discriminant (Δ): 17783025
Faltings height: 1.5004
naive height: 50.0813
primes of bad reduction: 3, 5, 13, 23, 61
regulator: 29.4301384082516934286119690527890314272531
submitted by: David Renshaw
submitted at: 2026-09-26 20:54:30 UTC
last updated: 2026-09-26 20:54:30 UTC

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

(576, 7759)
(1192, 36016)

Commentary

Cremona 273585c1 = LMFDB 273585.c4: https://www.lmfdb.org/EllipticCurve/Q/273585/c/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 273585, minimal discriminant 17783025, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:54:30 UTC · history