Small rational points on elliptic curves over number fields
Number Theory
2007-05-23 v2
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.
Cite
@article{arxiv.math/0508160,
title = {Small rational points on elliptic curves over number fields},
author = {Clayton Petsche},
journal= {arXiv preprint arXiv:math/0508160},
year = {2007}
}
Comments
11 pages. In this revision, an irritating LaTeX error has been corrected