curve #2852

y² + xy = x³ − 487459x + 130953890

a-invariants: [1, 0, 0, -487459, 130953890]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/8ℤ
conductor (N): 6279
discriminant (Δ): 74465610327927
Faltings height: 1.8519
naive height: 50.9045
primes of bad reduction: 3, 7, 13, 23
regulator: 4.425147104430700252296842528635894503574
submitted by: David Renshaw
submitted at: 2026-09-26 20:25:21 UTC
last updated: 2026-09-26 20:25:21 UTC

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

(6413, 507440)

Commentary

Cremona 6279i4 = LMFDB 6279.f2: https://www.lmfdb.org/EllipticCurve/Q/6279/f/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 6279, minimal discriminant 74465610327927, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:25:21 UTC · history