curve #936

y² + xy + y = x³ + x² − 84x + 261

a-invariants: [1, 1, 1, -84, 261]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 42
discriminant (Δ): 63504
Faltings height: -0.1575
naive height: 24.9068
primes of bad reduction: 2, 3, 7
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:03:35 UTC
last updated: 2026-09-23 15:03:35 UTC

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Commentary

Cremona 42a2 = LMFDB 42.a4: https://www.lmfdb.org/EllipticCurve/Q/42/a/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 42, minimal discriminant 63504, torsion ℤ/2ℤ × ℤ/4ℤ.

last edited by David Renshaw at 2026-09-23 15:03:35 UTC · history