curve #1005

y² + xy = x³ + x² + 2x

a-invariants: [1, 1, 0, 2, 0]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ
conductor (N): 206
discriminant (Δ): -412
Faltings height: -0.8119
naive height: 12.7880
primes of bad reduction: 2, 103
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:13:19 UTC
last updated: 2026-09-23 15:13:19 UTC

Witness: no points (rank ≥ 0 needs none) log in to add more points →

Commentary

Cremona 206a1 = LMFDB 206.a2: https://www.lmfdb.org/EllipticCurve/Q/206/a/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 206, minimal discriminant -412, torsion ℤ/2ℤ.

last edited by David Renshaw at 2026-09-23 15:13:19 UTC · history