Small rational points on elliptic curves over number fields

Abstract

Let E/k be an elliptic curve over a number field. We obtain some quantitative refinements of results of Hindry-Silverman, giving an upper bound for the number of k-rational torsion points, and a lower bound for the canonical height of non-torsion k-rational points, in terms of expressions depending explicitly on the degree of k and the Szpiro ratio of E/k. The bounds exhibit only polynomial dependence on both quantities.

11 pages. In this revision, an irritating LaTeX error has been corrected

Cited by in corpus (6)

• The average number of integral points on elliptic curves is bounded
• Explicit Kummer Theory for Elliptic Curves
• Critically separable rational maps in families
• Heights of points on elliptic curves over $\mathbb{Q}$
• Lang's Height Conjecture and Szpiro's Conjecture
• Minoration de la hauteur de Neron-Tate sur les surfaces abeliennes