curve #3292

y² = x³ − x² − 160x + 4180

a-invariants: [0, -1, 0, -160, 4180]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/4ℤ
conductor (N): 14880
discriminant (Δ): -7092641280
Faltings height: 0.5715
naive height: 30.1736
primes of bad reduction: 2, 3, 5, 31
regulator: 10.1112478713959404127211552704934461416905
submitted by: David Renshaw
submitted at: 2026-09-26 20:52:44 UTC
last updated: 2026-09-26 20:52:44 UTC

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

(-3, 68)
(17, 78)

Commentary

Cremona 14880l4 = LMFDB 14880.c4: https://www.lmfdb.org/EllipticCurve/Q/14880/c/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 14880, minimal discriminant -7092641280, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:52:44 UTC · history