Small rational points on elliptic curves over number fields

Details Small rational points on elliptic curves over number fields Small rational points on elliptic curves over number fields

2005-08-09

arxiv.org/abs/math/0508160v2

Mathematics

Number Theory

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

Scientific paper

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.

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