curve #677

y² + y = x³ − 301x + 2052

a-invariants: [0, 0, 1, -301, 2052]
rank (lower bound): ≥ 5
torsion subgroup: trivial
conductor (N): 74129723
discriminant (Δ): -74129723
Faltings height: 0.2952
naive height: 28.7765
primes of bad reduction: 74129723
regulator: 22.6019169540370965767879839625999406415438901463
submitted by: David Renshaw
submitted at: 2026-09-08 19:27:12 UTC
last updated: 2026-09-08 19:27:12 UTC

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

(10, 6)
(9, 8)
(8, 12)
(11, 8)
(19, 56)

Commentary

LMFDB 74129723.a1. Curve data, generators (10, 6), (9, 8), (8, 12), (11, 8), (19, 56) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/74129723/a/1

last edited by David Renshaw at 2026-09-08 19:27:12 UTC · history