curve #672

y² + xy + y = x³ − x² − 147x + 420

a-invariants: [1, -1, 1, -147, 420]
rank (lower bound): ≥ 5
torsion subgroup: trivial
conductor (N): 138437407
discriminant (Δ): 138437407
Faltings height: 0.2605
naive height: 26.5785
primes of bad reduction: 138437407
regulator: 33.0142278000805304906179791731829817779230312017
submitted by: David Renshaw
submitted at: 2026-09-08 19:18:38 UTC
last updated: 2026-09-08 19:18:38 UTC

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

(2, 10)
(11, 1)
(0, 20)
(-6, 35)
(3, -3)

Commentary

LMFDB 138437407.a1. Curve data, generators (2, 10), (11, 1), (0, 20), (-6, 35), (3, -3) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/138437407/a/1

last edited by David Renshaw at 2026-09-08 19:18:38 UTC · history