curve #3267

y² = x³ − x² − 3300x + 74052

a-invariants: [0, -1, 0, -3300, 74052]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 1320
discriminant (Δ): 1568160000
Faltings height: 0.7288
naive height: 35.9189
primes of bad reduction: 2, 3, 5, 11
regulator: 1.638502367159678767276391974695921979409
submitted by: David Renshaw
submitted at: 2026-09-26 20:48:41 UTC
last updated: 2026-09-26 20:48:41 UTC

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

(32, 14)

Commentary

Cremona 1320h2 = LMFDB 1320.f4: https://www.lmfdb.org/EllipticCurve/Q/1320/f/4 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 1320, minimal discriminant 1568160000, torsion ℤ/2ℤ × ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:48:41 UTC · history