ON MORDELLS EQUATION

In an earlier paper we developed an algorithm for computing all integr al points on elliptic curves over the rationals Q. Here we illustrate our method by applying it to Mordell's Equation y(2) = x(3) + k for 0 not equal k is an element of Z and draw some conclusions from our nume rical findings. In fact we solve Mordell's Equation in Z for all integ ers Ic within the range 0 < \k\ less than or equal to 10 000 and parti ally extend the computations to 0 < \k\ less than or equal to 100 000. For these values of k, the constant in Hall's conjecture turns out to be C = 5. Some other interesting observations are made concerning lar ge integer points, large generators of the Mordell-Weil group and larg e Tate-Shafarevic groups. Three graphs illustrate the distribution of integer points in dependence on the parameter k. One interesting featu re is the occurrence of lines in the graphs.