curve #3152

y² + xy = x³ − x² − 6183x + 178605

a-invariants: [1, -1, 0, -6183, 178605]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 5382
discriminant (Δ): 1586058134544
Faltings height: 1.0933
naive height: 37.8024
primes of bad reduction: 2, 3, 13, 23
regulator: 0.973591903612835960313969206897904279068373
submitted by: David Renshaw
submitted at: 2026-09-26 20:39:49 UTC
last updated: 2026-09-26 20:39:49 UTC

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

(66, 201)
(118, 981)

Commentary

Cremona 5382g2 = LMFDB 5382.b3: https://www.lmfdb.org/EllipticCurve/Q/5382/b/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 5382, minimal discriminant 1586058134544, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:39:49 UTC · history