Computing all S-integral points on elliptic curves

In this note we combine the advantages of the methods of Siegel-Baker-Coates and of Lang-Zagier for the computation of S-integral points on elliptic curves in Weierstrass normal form over the rationals. In this way we are able to overcome the absence of an explicit lower bound for linear forms in q-adic elliptic logarithms. We present an efficient algorithm for determining all S-integral points on such curves.