Lang's conjecture and sharp height estimates for the elliptic curves $y^{2}=x^{3}+b$

preprint2016arXivOpen access

For $E_{b}: y^{2}=x^{3}+b$ , we establish Lang's conjecture on a lower bound for the canonical height of non-torsion points along with upper and lower bounds for the difference between the canonical and logarithmic height. In many cases, our results are actually best-possible.

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Lang's conjecture and sharp height estimates for the elliptic curves $y^{2}=x^{3}+b$

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Lang's conjecture and sharp height estimates for the elliptic curves y2=x3+by^{2}=x^{3}+by2=x3+b

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Lang's conjecture and sharp height estimates for the elliptic curves $y^{2}=x^{3}+b$