curve #947

y² + xy + y = x³ − x² − 14x + 29

a-invariants: [1, -1, 1, -14, 29]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/9ℤ
conductor (N): 54 ☆ record for ℤ/9ℤ torsion, rank ≥ 0
discriminant (Δ): -124416 ☆ record for ℤ/9ℤ torsion, rank ≥ 0
Faltings height: -0.3152 ☆ record for ℤ/9ℤ torsion, rank ≥ 0
naive height: 20.0273 ☆ record for ℤ/9ℤ torsion, rank ≥ 0
primes of bad reduction: 2, 3
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:04:40 UTC
last updated: 2026-09-23 15:04:40 UTC

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Commentary

Cremona 54b3 = LMFDB 54.b2: https://www.lmfdb.org/EllipticCurve/Q/54/b/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 54, minimal discriminant -124416, torsion ℤ/9ℤ.

last edited by David Renshaw at 2026-09-23 15:04:40 UTC · history