curve #866

y² + xy + y = x³ + x² − 2160x − 39540

a-invariants: [1, 1, 1, -2160, -39540]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ
conductor (N): 15
discriminant (Δ): 405
Faltings height: 0.2909
naive height: 34.6472
primes of bad reduction: 3, 5
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:40:23 UTC
last updated: 2026-09-23 14:40:23 UTC

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Commentary

LMFDB 15.a1 (Cremona 15a5): https://www.lmfdb.org/EllipticCurve/Q/15/a/1 Mordell–Weil rank exactly 0 per LMFDB. Conductor 15, minimal discriminant 405, 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): #10 by conductor.

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