curve #880

y² + xy + y = x³ + x² − 10x − 10

a-invariants: [1, 1, 1, -10, -10]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 15 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 0
discriminant (Δ): 50625
Faltings height: -0.4023
naive height: 18.5276
primes of bad reduction: 3, 5
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:54:59 UTC
last updated: 2026-09-23 14:54:59 UTC

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Commentary

Cremona 15a1 = LMFDB 15.a5: https://www.lmfdb.org/EllipticCurve/Q/15/a/5 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 15, minimal discriminant 50625, torsion ℤ/2ℤ × ℤ/4ℤ.

last edited by David Renshaw at 2026-09-23 14:54:59 UTC · history