Computing all integer solutions of a genus 1 equation
AbstractThe Elliptic Logarithm Method has been applied with great successto the problem of computing all integer solutions of equations ofdegree 3 and 4 defining elliptic curves. We extend this methodto include any equation f(u,v)=0 that defines a curve of genus 1.Here f is a polynomial with integer coefficients and irreducible overthe 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 equationsof degree 5 and degree 9.
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Bibliographic InfoPaper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number EI 2001-44.
Date of creation: 31 Dec 2001
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Elliptic curve; Elliptic logarithm; Dophantine equation;
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