Small rational points on elliptic curves over number fields
Abstract
Description
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
11 pages. In this revision, an irritating LaTeX error has been corrected