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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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

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


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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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Math. Comp. 48 (1987), 425-436
  • MSC: Primary 11G05; Secondary 11D25, 11Y50
  • DOI:
  • MathSciNet review: 866125