curve #3244

y² = x³ + x² − 519x + 4381

a-invariants: [0, 1, 0, -519, 4381]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
conductor (N): 345856
discriminant (Δ): 4841984
Faltings height: 0.2587
naive height: 30.3712
primes of bad reduction: 2, 7, 193
regulator: 5.6801193798719366044970201315169729320769389
submitted by: David Renshaw
submitted at: 2026-09-26 20:44:54 UTC
last updated: 2026-09-26 20:44:54 UTC

Witness: 3 independent points log in to add more points →

(12, 5)
(15, 14)
(5, 44)

Commentary

Cremona 345856c1 = LMFDB 345856.c2: https://www.lmfdb.org/EllipticCurve/Q/345856/c/2 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 345856, minimal discriminant 4841984, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:44:54 UTC · history