curve #2936

y² + xy = x³ − x² − 88x − 276

a-invariants: [1, -1, 0, -88, -276]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
conductor (N): 162418
discriminant (Δ): 5522212
Faltings height: 0.0400
naive height: 25.0520
primes of bad reduction: 2, 17, 281
regulator: 6.8267305833990556842818380793931336674775554
submitted by: David Renshaw
submitted at: 2026-09-26 20:29:08 UTC
last updated: 2026-09-26 20:29:08 UTC

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

(-6, 6)
(-5, 7)
(-25/4, 31/8)

Commentary

Cremona 162418c1 = LMFDB 162418.b1: https://www.lmfdb.org/EllipticCurve/Q/162418/b/1 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 162418, minimal discriminant 5522212, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:29:09 UTC · history