Lang's Conjecture and Sharp Height Estimates for the elliptic curves $y^{2}=x^{3}+ax$

Paul Voutier; Minoru Yabuta

doi:10.1142/S1793042113500176

paper

Lang's Conjecture and Sharp Height Estimates for the elliptic curves $y^{2} = x^{3} + a x$

arXiv:1104.4645 · doi:10.1142/S1793042113500176

Abstract

For elliptic curves given by the equation $E_{a} : y^{2} = x^{3} + a x$ , we establish the best-possible version of Lang's conjecture on the lower bound of the canonical height of non-torsion points along with best-possible upper and lower bounds for the difference between the canonical and logarithmic height.

published version. Lemmas 5.1 and 6.1 now precise (with resultant refinement to Theorem 1.2). Small corrections too

Lang's Conjecture and Sharp Height Estimates for the elliptic curves y2=x3+ax

Abstract

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Lang's Conjecture and Sharp Height Estimates for the elliptic curves $y^{2} = x^{3} + a x$