curve #3242

y² = x³ + x² − 19846x + 1069524

a-invariants: [0, 1, 0, -19846, 1069524]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
conductor (N): 476320
discriminant (Δ): 952640
Faltings height: 0.8651
naive height: 41.3009
primes of bad reduction: 2, 5, 13, 229
regulator: 17.636018388778680298871058710064403078758388
submitted by: David Renshaw
submitted at: 2026-09-26 20:44:35 UTC
last updated: 2026-09-26 20:44:35 UTC

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

(77, 62)
(72, 138)
(106, 410)

Commentary

Cremona 476320c1 = LMFDB 476320.c1: https://www.lmfdb.org/EllipticCurve/Q/476320/c/1 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 476320, minimal discriminant 952640, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:44:35 UTC · history