curve #967

y² + xy + y = x³ − x² + 2x − 3

a-invariants: [1, -1, 1, 2, -3]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/4ℤ
conductor (N): 70
discriminant (Δ): -2800
Faltings height: -0.6542
naive height: 15.0599
primes of bad reduction: 2, 5, 7
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:07:54 UTC
last updated: 2026-09-23 15:07:54 UTC

Witness: no points (rank ≥ 0 needs none) log in to add more points →

Commentary

Cremona 70a1 = LMFDB 70.a4: https://www.lmfdb.org/EllipticCurve/Q/70/a/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 70, minimal discriminant -2800, torsion ℤ/4ℤ.

last edited by David Renshaw at 2026-09-23 15:07:54 UTC · history