curve #881

y² + xy + y = x³ + x² − 135x − 660

a-invariants: [1, 1, 1, -135, -660]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 15 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 0
discriminant (Δ): 164025
Faltings height: -0.0557
naive height: 26.3299
primes of bad reduction: 3, 5
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:55:00 UTC
last updated: 2026-09-23 14:55:00 UTC

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Commentary

Cremona 15a2 = LMFDB 15.a2: https://www.lmfdb.org/EllipticCurve/Q/15/a/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 15, minimal discriminant 164025, torsion ℤ/2ℤ × ℤ/2ℤ.

last edited by David Renshaw at 2026-09-23 14:55:00 UTC · history