curve #2871

y² + xy = x³ + x² − 16x − 20

a-invariants: [1, 1, 0, -16, -20]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 462
discriminant (Δ): 213444
Faltings height: -0.2809
naive height: 20.0275
primes of bad reduction: 2, 3, 7, 11
regulator: 0.5034041158591907496344257770048243993527
submitted by: David Renshaw
submitted at: 2026-09-26 20:26:12 UTC
last updated: 2026-09-26 20:26:12 UTC

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

(7, 13)

Commentary

Cremona 462c2 = LMFDB 462.a3: https://www.lmfdb.org/EllipticCurve/Q/462/a/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 462, minimal discriminant 213444, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:26:12 UTC · history