Parallel LLL-reduction for bounding the integral solutions of elliptic Diophantine equations

Stroeker and Tzanakis gave convincing numerical and heuristic evidence for the fact that in their Ellog method a certain parameter λ plays a decisive role in the size of the final bound for the integral points on elliptic curves. Furthermore, they provided an algorithm to determine the MordellWeil basis of the curve which corresponds to the optimal choice of λ. In this paper we show that working with more Mordell-Weil bases simultaneously, the final bound for the integral points can be further decreased.