curve #3146

y² + xy = x³ − x² − 3292x − 48384

a-invariants: [1, -1, 0, -3292, -48384]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 4450
discriminant (Δ): 1237656250000
Faltings height: 1.0245
naive height: 35.9115
primes of bad reduction: 2, 5, 89
regulator: 4.95646172863099317361862972489699377417346
submitted by: David Renshaw
submitted at: 2026-09-26 20:39:29 UTC
last updated: 2026-09-26 20:39:29 UTC

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

(109, 883)
(153, 1659)

Commentary

Cremona 4450c2 = LMFDB 4450.d2: https://www.lmfdb.org/EllipticCurve/Q/4450/d/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 4450, minimal discriminant 1237656250000, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:39:29 UTC · history