Template-Type: ReDIF-Paper 1.0
Author-Name: Stroeker, R.J.
Author-Name-Last: Stroeker
Author-Name-First: Roel
Author-Name: Tzanakis, N.
Author-Name-Last: Tzanakis
Author-Name-First: Nikos
Title: Computing all integer solutions of a genus 1 equation
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.
Creation-Date: 2001-12-31
File-URL: https://repub.eur.nl/pub/592/feweco20020115120646.pdf
File-Format: application/pdf
Series: RePEc:ems:eureir
Number: EI 2001-44
Keywords: Dophantine equation, Elliptic curve, Elliptic logarithm
Handle: RePEc:ems:eureir:592