curve #3296

y² + xy = x³ − x² − 97443x + 11732121

a-invariants: [1, -1, 0, -97443, 11732121]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/4ℤ
conductor (N): 5382
discriminant (Δ): 413720292492
Faltings height: 1.4399
naive height: 46.0747
primes of bad reduction: 2, 3, 13, 23
regulator: 0.973591903612835960313969206897904279068373
submitted by: David Renshaw
submitted at: 2026-09-26 20:53:23 UTC
last updated: 2026-09-26 20:53:23 UTC

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

(183, -33)
(175, 39)

Commentary

Cremona 5382g4 = LMFDB 5382.b1: https://www.lmfdb.org/EllipticCurve/Q/5382/b/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 5382, minimal discriminant 413720292492, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:53:23 UTC · history