curve #937

y² + xy + y = x³ + x² − 104x + 101

a-invariants: [1, 1, 1, -104, 101]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 42
discriminant (Δ): 63011844
Faltings height: 0.1891
naive height: 25.5474
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 42a3 = LMFDB 42.a3: https://www.lmfdb.org/EllipticCurve/Q/42/a/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 42, minimal discriminant 63011844, torsion ℤ/2ℤ × ℤ/2ℤ.

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