curve #3272

y² = x³ − x² − 941360x + 351859200

a-invariants: [0, -1, 0, -941360, 351859200]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 68880
discriminant (Δ): 127606845542400
Faltings height: 1.9799
naive height: 52.8788
primes of bad reduction: 2, 3, 5, 7, 41
regulator: 9.00194907641696072474973149333779524640078
submitted by: David Renshaw
submitted at: 2026-09-26 20:49:29 UTC
last updated: 2026-09-26 20:49:29 UTC

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

(570, 390)
(562, 58)

Commentary

Cremona 68880br4 = LMFDB 68880.q2: https://www.lmfdb.org/EllipticCurve/Q/68880/q/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 68880, minimal discriminant 127606845542400, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:49:29 UTC · history