curve #678

y² + y = x³ − 457x + 3786

a-invariants: [0, 0, 1, -457, 3786]
rank (lower bound): ≥ 5
torsion subgroup: trivial
conductor (N): 84602123
discriminant (Δ): -84602123
Faltings height: 0.3490
naive height: 30.0014
primes of bad reduction: 84602123
regulator: 20.6819296999602593936612529930079948298777543702
submitted by: David Renshaw
submitted at: 2026-09-08 19:27:18 UTC
last updated: 2026-09-08 19:27:18 UTC

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

(11, 9)
(14, 11)
(15, 17)
(12, 5)
(13, 6)

Commentary

LMFDB 84602123.a1. Curve data, generators (11, 9), (14, 11), (15, 17), (12, 5), (13, 6) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/84602123/a/1

last edited by David Renshaw at 2026-09-08 19:27:18 UTC · history