curve #676

y² + y = x³ + x² − 30x + 390

a-invariants: [0, 1, 1, -30, 390]
rank (lower bound): ≥ 5
torsion subgroup: trivial
conductor (N): 67445803
discriminant (Δ): -67445803
Faltings height: 0.1831
naive height: 25.5077
primes of bad reduction: 67445803
regulator: 26.5142395008090307755820533842619643591720333222
submitted by: David Renshaw
submitted at: 2026-09-08 19:27:06 UTC
last updated: 2026-09-08 19:27:06 UTC

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

(2, 18)
(-9, 3)
(-7, 17)
(-4, 21)
(15, 59)

Commentary

LMFDB 67445803.a1. Curve data, generators (2, 18), (-9, 3), (-7, 17), (-4, 21), (15, 59) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/67445803/a/1

last edited by David Renshaw at 2026-09-08 19:27:06 UTC · history