curve #3011

y² + y = x³ − x² + 2450x + 328882

a-invariants: [0, -1, 1, 2450, 328882]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/5ℤ
conductor (N): 153083
discriminant (Δ): -47899781072843
Faltings height: 1.3051
naive height: 38.9350
primes of bad reduction: 7, 19, 1151
regulator: 7.71579698196041020166206462589596667597667
submitted by: David Renshaw
submitted at: 2026-09-26 20:33:11 UTC
last updated: 2026-09-26 20:33:11 UTC

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

(25, 636)
(38, 689)

Commentary

Cremona 153083b1 = LMFDB 153083.b2: https://www.lmfdb.org/EllipticCurve/Q/153083/b/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 153083, minimal discriminant -47899781072843, torsion ℤ/5ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:33:11 UTC · history