curve #877

y² + xy + y = x³ − x² − 91x − 310

a-invariants: [1, -1, 1, -91, -310]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ
conductor (N): 17
discriminant (Δ): 17 ☆ record for ℤ/2ℤ torsion, rank ≥ 0
Faltings height: -0.3766
naive height: 25.1359
primes of bad reduction: 17
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:41:29 UTC
last updated: 2026-09-23 14:41:29 UTC

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Commentary

LMFDB 17.a1 (Cremona 17a3): https://www.lmfdb.org/EllipticCurve/Q/17/a/1 Mordell–Weil rank exactly 0 per LMFDB. Conductor 17, minimal discriminant 17, torsion ℤ/2ℤ. 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): #5 by |minimal discriminant|.

last edited by David Renshaw at 2026-09-23 14:41:29 UTC · history