curve #680

y² + xy = x³ − 575x + 5236

a-invariants: [1, 0, 0, -575, 5236]
rank (lower bound): ≥ 5
torsion subgroup: trivial
conductor (N): 106974317
discriminant (Δ): 106974317
Faltings height: 0.3871
naive height: 30.6768
primes of bad reduction: 106974317
regulator: 29.3580713129526552732270728499713880276791800541
submitted by: David Renshaw
submitted at: 2026-09-08 19:27:46 UTC
last updated: 2026-09-08 19:27:46 UTC

Witness: 5 independent points log in to add more points →

(13, -6)
(15, -1)
(12, 4)
(16, 6)
(11, 11)

Commentary

LMFDB 106974317.a1. Curve data, generators (13, -6), (15, -1), (12, 4), (16, 6), (11, 11) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/106974317/a/1

last edited by David Renshaw at 2026-09-08 19:27:46 UTC · history