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

Bosser, Vincent and Surroca, Andrea. (2013) Upper bound for the height of S-integral points on elliptic curves. The Ramanujan journal, Vol. 32, no. 1. pp. 125-141.

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Official URL: http://edoc.unibas.ch/dok/A6165151

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.