curve #940

y² = x³ + x² − 24x + 36

a-invariants: [0, 1, 0, -24, 36]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 48
discriminant (Δ): 82944
Faltings height: -0.2988
naive height: 21.1891
primes of bad reduction: 2, 3
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:03:37 UTC
last updated: 2026-09-23 15:03:37 UTC

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Commentary

Cremona 48a3 = LMFDB 48.a3: https://www.lmfdb.org/EllipticCurve/Q/48/a/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 48, minimal discriminant 82944, torsion ℤ/2ℤ × ℤ/4ℤ.

last edited by David Renshaw at 2026-09-23 15:03:37 UTC · history