curve #878

y² + y = x³ + x² − 769x − 8470

a-invariants: [0, 1, 1, -769, -8470]
rank (lower bound): ≥ 0
torsion subgroup: trivial
conductor (N): 19
discriminant (Δ): -19
Faltings height: 0.0334
naive height: 31.5502
primes of bad reduction: 19
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:41:30 UTC
last updated: 2026-09-23 14:41:30 UTC

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Commentary

LMFDB 19.a1 (Cremona 19a2): https://www.lmfdb.org/EllipticCurve/Q/19/a/1 Mordell–Weil rank exactly 0 per LMFDB. Conductor 19, minimal discriminant -19, torsion trivial. 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): #7 by |minimal discriminant|.

last edited by David Renshaw at 2026-09-23 14:41:30 UTC · history