### Computing all S-integral points on elliptic curves, by Attila Pethö , Horst G. Zimmer, Josef Gebel and Emanuel Herrmann

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.

Attila Pethö , Horst G. Zimmer, Josef Gebel and Emanuel Herrmann <pethoe@math.klte.hu>