Upper bound for the height of S-integral points on elliptic curves

We establish new upper bounds for the height of the S-integral points of an elliptic curve. This bound is explicitly given in terms of the set $S$ of places of the number field K involved,but also in terms of the degree of K, as well as the rank, the regulator and the height of a basis of the Mordell-Weil groupof the curve. The proof uses the elliptic analogue of Baker's method, based on lower bounds for linear forms in elliptic logarithms.