curve #900

y² = x³ − x² − 24x − 36

a-invariants: [0, -1, 0, -24, -36]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 24
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 14:57:11 UTC
last updated: 2026-09-23 14:57:11 UTC

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Commentary

Cremona 24a2 = LMFDB 24.a3: https://www.lmfdb.org/EllipticCurve/Q/24/a/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 24, minimal discriminant 82944, torsion ℤ/2ℤ × ℤ/2ℤ.

last edited by David Renshaw at 2026-09-23 14:57:11 UTC · history