curve #3119

y² = x³ − x² − 30x + 72

a-invariants: [0, -1, 0, -30, 72]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 480
discriminant (Δ): 129600
Faltings height: -0.2543
naive height: 21.8503
primes of bad reduction: 2, 3, 5
regulator: 1.032556939886938476888927065078884086928
submitted by: David Renshaw
submitted at: 2026-09-26 20:38:12 UTC
last updated: 2026-09-26 20:38:12 UTC

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

(2, 4)

Commentary

Cremona 480f1 = LMFDB 480.c3: https://www.lmfdb.org/EllipticCurve/Q/480/c/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 480, minimal discriminant 129600, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:38:12 UTC · history