  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.
