curve #883

y² + xy + y = x³ + x² + 35x − 28

a-invariants: [1, 1, 1, 35, -28]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/8ℤ
conductor (N): 15 ☆ record for ℤ/8ℤ torsion, rank ≥ 0
discriminant (Δ): -3515625
Faltings height: -0.0557
naive height: 22.2779
primes of bad reduction: 3, 5
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:55:01 UTC
last updated: 2026-09-23 14:55:01 UTC

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Commentary

Cremona 15a4 = LMFDB 15.a8: https://www.lmfdb.org/EllipticCurve/Q/15/a/8 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 15, minimal discriminant -3515625, torsion ℤ/8ℤ.

last edited by David Renshaw at 2026-09-23 14:55:01 UTC · history