curve #2802

y² + xy + y = x³ − x² − 10x − 8

a-invariants: [1, -1, 1, -10, -8]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ
conductor (N): 2725
discriminant (Δ): 13625
Faltings height: -0.4795
naive height: 18.4261
primes of bad reduction: 5, 109
regulator: 1.80641455631543743874276132028102361313538
submitted by: David Renshaw
submitted at: 2026-09-26 20:23:06 UTC
last updated: 2026-09-26 20:23:06 UTC

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

(4, 0)
(19, 70)

Commentary

Cremona 2725d1 = LMFDB 2725.a1: https://www.lmfdb.org/EllipticCurve/Q/2725/a/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 2725, minimal discriminant 13625, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:23:06 UTC · history