curve #868

y² + xy + y = x³ − x² − x

a-invariants: [1, -1, 1, -1, 0]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/4ℤ
conductor (N): 17
discriminant (Δ): 17
Faltings height: -1.0698
naive height: 10.4895
primes of bad reduction: 17
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:40:24 UTC
last updated: 2026-09-23 14:40:24 UTC

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Commentary

LMFDB 17.a4 (Cremona 17a4): https://www.lmfdb.org/EllipticCurve/Q/17/a/4 Mordell–Weil rank exactly 0 per LMFDB. Conductor 17, minimal discriminant 17, torsion ℤ/4ℤ. Submitted as one of the ten smallest rank-0 curves in LMFDB (as of 2026-09-23; places in LMFDB sort order, ties broken by label): #3 by Faltings height, #6 by |minimal discriminant|.

last edited by David Renshaw at 2026-09-23 14:40:24 UTC · history