curve #3304

y² + xy + y = x³ − x² − 373297x + 87880144

a-invariants: [1, -1, 1, -373297, 87880144]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/4ℤ
conductor (N): 275665
discriminant (Δ): 17918225
Faltings height: 1.5021
naive height: 50.1040
primes of bad reduction: 5, 13, 4241
regulator: 30.9837404644778331078053405938909747069624
submitted by: David Renshaw
submitted at: 2026-09-26 20:54:40 UTC
last updated: 2026-09-26 20:54:40 UTC

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

(64, 7983)
(4018/9, 79582/27)

Commentary

Cremona 275665c1 = LMFDB 275665.c3: https://www.lmfdb.org/EllipticCurve/Q/275665/c/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 275665, minimal discriminant 17918225, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:54:40 UTC · history