curve #1001

y² + xy = x³ + 15x + 9

a-invariants: [1, 0, 0, 15, 9]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/5ℤ
conductor (N): 186
discriminant (Δ): -241056
Faltings height: -0.2784
naive height: 19.7336
primes of bad reduction: 2, 3, 31
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:13:17 UTC
last updated: 2026-09-23 15:13:17 UTC

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Commentary

Cremona 186b1 = LMFDB 186.c2: https://www.lmfdb.org/EllipticCurve/Q/186/c/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 186, minimal discriminant -241056, torsion ℤ/5ℤ.

last edited by David Renshaw at 2026-09-23 15:13:17 UTC · history