curve #3288

y² = x³ − x² − 480x + 4212

a-invariants: [0, -1, 0, -480, 4212]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/4ℤ
conductor (N): 480
discriminant (Δ): 23040
Faltings height: 0.0923
naive height: 30.1370
primes of bad reduction: 2, 3, 5
regulator: 2.065113879773876953777854130157768173856
submitted by: David Renshaw
submitted at: 2026-09-26 20:52:05 UTC
last updated: 2026-09-26 20:52:05 UTC

Witness: 1 independent point log in to add more points →

(17, 26)

Commentary

Cremona 480f3 = LMFDB 480.c1: https://www.lmfdb.org/EllipticCurve/Q/480/c/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 480, minimal discriminant 23040, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:52:05 UTC · history