curve #886

y² + xy + y = x³ − x² − 6x − 4

a-invariants: [1, -1, 1, -6, -4]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 17
discriminant (Δ): 289
Faltings height: -0.7232
naive height: 16.8284
primes of bad reduction: 17
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:55:02 UTC
last updated: 2026-09-23 14:55:02 UTC

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Commentary

Cremona 17a2 = LMFDB 17.a2: https://www.lmfdb.org/EllipticCurve/Q/17/a/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 17, minimal discriminant 289, torsion ℤ/2ℤ × ℤ/2ℤ.

last edited by David Renshaw at 2026-09-23 14:55:02 UTC · history