curve #1009

y² + xy + y = x³ + x² − 70x − 205

a-invariants: [1, 1, 1, -70, -205]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 210
discriminant (Δ): 8643600
Faltings height: 0.0436
naive height: 24.3600
primes of bad reduction: 2, 3, 5, 7
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:14:22 UTC
last updated: 2026-09-23 15:14:22 UTC

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

Commentary

Cremona 210c2 = LMFDB 210.c5: https://www.lmfdb.org/EllipticCurve/Q/210/c/5 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 210, minimal discriminant 8643600, torsion ℤ/2ℤ × ℤ/4ℤ.

last edited by David Renshaw at 2026-09-23 15:14:22 UTC · history