curve #2974

y² + xy + y = x³ + x² − 4925125x + 4204962242

a-invariants: [1, 1, 1, -4925125, 4204962242]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 19065
discriminant (Δ): 218311706390625
Faltings height: 2.2954
naive height: 57.8432
primes of bad reduction: 3, 5, 31, 41
regulator: 7.20502898543919713669139430746307905350130
submitted by: David Renshaw
submitted at: 2026-09-26 20:31:15 UTC
last updated: 2026-09-26 20:31:15 UTC

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

(1277, -399)
(1112, 9681)

Commentary

Cremona 19065g2 = LMFDB 19065.c4: https://www.lmfdb.org/EllipticCurve/Q/19065/c/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 19065, minimal discriminant 218311706390625, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:31:15 UTC · history