Solving elliptic Diophantine equations by estimating linear forms in elliptic logarithms

In order to compute all integer points on a Weierstraß 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 Néron-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 co-efficients 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 man-ageable 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.