Large integral points on elliptic curves

Zagier, Don

doi:10.1090/S0025-5718-1987-0866125-3

Large integral points on elliptic curves
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Math. Comp. 48 (1987), 425-436 Request permission

Addendum: Math. Comp. 51 (1988), 375.

Abstract:

We describe several methods which permit one to search for big integral points on certain elliptic curves, i.e., for integral solutions (x, y) of certain Diophantine equations of the form ${y^2} = {x^3} + ax + b\;(a,b \in {\mathbf {Z}})$ in a large range $|x|,|y| \leqslant B$, in time polynomial in $\log \log B$. We also give a number of individual examples and of parametric families of examples of specific elliptic curves having a relatively large integral point.

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