curve #1059

y² + xy = x³ − 770x + 168900

a-invariants: [1, 0, 0, -770, 168900]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/8ℤ
conductor (N): 6510
discriminant (Δ): -12303900000000
Faltings height: 1.1910
naive height: 37.5980
primes of bad reduction: 2, 3, 5, 7, 31
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:22:55 UTC
last updated: 2026-09-23 15:22:55 UTC

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

Commentary

Cremona 6510z1 = LMFDB 6510.bb5: https://www.lmfdb.org/EllipticCurve/Q/6510/bb/5 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 6510, minimal discriminant -12303900000000, torsion ℤ/8ℤ.

last edited by David Renshaw at 2026-09-23 15:22:55 UTC · history