curve #1060

y² + xy = x³ − 2096146x + 1124611076

a-invariants: [1, 0, 0, -2096146, 1124611076]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/12ℤ
conductor (N): 6630
discriminant (Δ): 42904970360310988800
Faltings height: 2.5317
naive height: 55.2804
primes of bad reduction: 2, 3, 5, 13, 17
regulator: 1.267004719860632017573282596365937965919
submitted by: David Renshaw
submitted at: 2026-09-23 15:22:55 UTC
last updated: 2026-09-23 15:22:55 UTC

Witness: 1 independent point log in to add more points →

(676, 3742)

Commentary

Cremona 6630w1 = LMFDB 6630.v7: https://www.lmfdb.org/EllipticCurve/Q/6630/v/7 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 6630, minimal discriminant 42904970360310988800, torsion ℤ/12ℤ. The witness is the generator from Cremona's tables.

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