curve #3089

y² + xy = x³ − 44x + 109

a-invariants: [1, 0, 0, -44, 109]
rank (lower bound): ≥ 3
torsion subgroup: trivial
conductor (N): 24301
discriminant (Δ): -24301
Faltings height: -0.2823
naive height: 22.9720
primes of bad reduction: 19, 1279
regulator: 1.0885646024251077131442859489002163266618169
submitted by: David Renshaw
submitted at: 2026-09-26 20:36:45 UTC
last updated: 2026-09-26 20:36:45 UTC

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

(4, -3)
(3, 1)
(7, 9)

Commentary

Cremona 24301a1 = LMFDB 24301.a1: https://www.lmfdb.org/EllipticCurve/Q/24301/a/1 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 24301, minimal discriminant -24301, torsion trivial. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:36:45 UTC · history