Lang’s conjecture and sharp height estimates for the elliptic curves $y^{2}=x^{3}+b$
Volume 173 / 2016
Acta Arithmetica 173 (2016), 197-224
MSC: 11G05, 11G50.
DOI: 10.4064/aa7761-2-2016
Published online: 11 May 2016
Abstract
For $E_{b}: y^{2}=x^{3}+b$, we establish Lang’s conjecture on a lower bound for the canonical height of nontorsion points along with upper and lower bounds for the difference between the canonical and logarithmic heights. These results are either best possible or within a small constant of the best possible lower bounds.
