curve #3209

y² = x³ + x² − 6x + 4

a-invariants: [0, 1, 0, -6, 4]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ
conductor (N): 160
discriminant (Δ): 320
Faltings height: -0.7060
naive height: 17.1511
primes of bad reduction: 2, 5
regulator: 0.3586929039552797259307493823641187479545
submitted by: David Renshaw
submitted at: 2026-09-26 20:42:47 UTC
last updated: 2026-09-26 20:42:47 UTC

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

(0, 2)

Commentary

Cremona 160a1 = LMFDB 160.a1: https://www.lmfdb.org/EllipticCurve/Q/160/a/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 160, minimal discriminant 320, torsion ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:42:47 UTC · history