curve #2769

y² = x³ − x² − 16x + 16

a-invariants: [0, -1, 0, -16, 16]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 240
discriminant (Δ): 230400
Faltings height: -0.2772
naive height: 19.9932
primes of bad reduction: 2, 3, 5
regulator: 0.4458105698536916058150170973611500783877
submitted by: David Renshaw
submitted at: 2026-09-26 20:21:37 UTC
last updated: 2026-09-26 20:21:37 UTC

Witness: 1 independent point log in to add more points →

(0, 4)

Commentary

Cremona 240c2 = LMFDB 240.a3: https://www.lmfdb.org/EllipticCurve/Q/240/a/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 240, minimal discriminant 230400, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:21:37 UTC · history