Parallel LLL-reduction for bounding the integral solutions of elliptic Diophantine equations
Lajos Hajdu, T. Kovács · Mathematics of Computation · 2008
Stroeker and Tzanakis gave convincing numerical and heuristic evidence for the fact that in their E l l o g \mathcal {E}llog method a certain parameter λ \lambda 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 Mordell-Weil basis of the curve which corresponds to the optimal choice of λ \lambda . In this paper we show that working with more Mordell-Weil bases simultaneously, the final bound for the integral points can be further decreased.