curve #973

y² = x³ + x² + 7x

a-invariants: [0, 1, 0, 7, 0]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/6ℤ
conductor (N): 84
discriminant (Δ): -21168
Faltings height: -0.4811
naive height: 17.3050
primes of bad reduction: 2, 3, 7
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:08:58 UTC
last updated: 2026-09-23 15:08:58 UTC

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Commentary

Cremona 84a1 = LMFDB 84.b4: https://www.lmfdb.org/EllipticCurve/Q/84/b/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 84, minimal discriminant -21168, torsion ℤ/6ℤ.

last edited by David Renshaw at 2026-09-23 15:08:58 UTC · history