Computing all integer solutions of a genus 1 equation

Roel Stroeker and Nikos Tzanakis

No EI 2001-44, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: The Elliptic Logarithm Method has been applied with great success to the problem of computing all integer solutions of equations of degree 3 and 4 defining elliptic curves. We extend this method to include any equation f(u,v)=0 that defines a curve of genus 1. Here f is a polynomial with integer coefficients and irreducible over the algebraic closure of the rationals, but is otherwise of arbitrary shape and degree. We give a detailed description of the general features of our approach, and conclude with two rather unusual examples corresponding to equations of degree 5 and degree 9.

Keywords: Dophantine equation; Elliptic curve; Elliptic logarithm (search for similar items in EconPapers)
Date: 2001-12-31
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Persistent link: https://EconPapers.repec.org/RePEc:ems:eureir:592

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