curve #2810

y² + xy = x³ + x² − 88x + 268

a-invariants: [1, 1, 0, -88, 268]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
conductor (N): 141870
discriminant (Δ): 4256100
Faltings height: 0.0272
naive height: 25.0633
primes of bad reduction: 2, 3, 5, 4729
regulator: 1.9526127387992785966930193950928491255628022
submitted by: David Renshaw
submitted at: 2026-09-26 20:23:25 UTC
last updated: 2026-09-26 20:23:25 UTC

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

(7, 4)
(6, -2)
(9, 13)

Commentary

Cremona 141870i1 = LMFDB 141870.a1: https://www.lmfdb.org/EllipticCurve/Q/141870/a/1 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 141870, minimal discriminant 4256100, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:23:25 UTC · history