curve #1030

y² + xy + y = x³ − x² − 197573x + 33848381

a-invariants: [1, -1, 1, -197573, 33848381]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 630
discriminant (Δ): 79042057113600
Faltings height: 1.7050
naive height: 48.1952
primes of bad reduction: 2, 3, 5, 7
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:18:37 UTC
last updated: 2026-09-23 15:18:37 UTC

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

Commentary

Cremona 630i6 = LMFDB 630.h2: https://www.lmfdb.org/EllipticCurve/Q/630/h/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 630, minimal discriminant 79042057113600, torsion ℤ/2ℤ × ℤ/6ℤ.

last edited by David Renshaw at 2026-09-23 15:18:37 UTC · history