curve #669

y² + xy = x³ − 245x + 1366

a-invariants: [1, 0, 0, -245, 1366]
rank (lower bound): ≥ 5
torsion subgroup: trivial
conductor (N): 111061427
discriminant (Δ): 111061427
Faltings height: 0.2922
naive height: 28.1176
primes of bad reduction: 111061427
regulator: 33.4286242684821343246962385880470837953642308152
submitted by: David Renshaw
submitted at: 2026-09-08 19:18:19 UTC
last updated: 2026-09-08 19:18:19 UTC

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

(6, 8)
(5, 14)
(7, -6)
(15, 26)
(13, 14)

Commentary

LMFDB 111061427.a1. Curve data, generators (6, 8), (5, 14), (7, -6), (15, 26), (13, 14) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/111061427/a/1

last edited by David Renshaw at 2026-09-08 19:18:19 UTC · history