Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms
Roelof J. Stroeker, Nikos Tzanakis · Acta Arithmetica · 1994
In order to compute all integer points on a Weierstra equation for an elliptic curve E=Q, one may translate the linear relation between rational points on E into a linear form of elliptic logarithms. An upper bound for this linear form can be obtained by employing the N'eron-Tate height function and a lower bound is provided by a recent theorem of S. David. Combining these two bounds allows for the estimation of the integral coefficients in the group relation, once the group structure of E(Q) is fully known. Reducing the large bound for the coefficients so obtained to a manageable size is achieved by applying a reduction process due to de Weger. In the final section two examples of elliptic curves of rank 2 and 3 are worked out in detail. 1.