curve #2896

y² = x³ − x² − 254x + 1584

a-invariants: [0, -1, 0, -254, 1584]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 36192
discriminant (Δ): 81866304
Faltings height: 0.2807
naive height: 28.2295
primes of bad reduction: 2, 3, 13, 29
regulator: 3.19828276400573861070694160566871278007081
submitted by: David Renshaw
submitted at: 2026-09-26 20:27:19 UTC
last updated: 2026-09-26 20:27:19 UTC

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

(-5, 52)
(7, 10)

Commentary

Cremona 36192j1 = LMFDB 36192.c3: https://www.lmfdb.org/EllipticCurve/Q/36192/c/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 36192, minimal discriminant 81866304, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:27:19 UTC · history