Computing all integer solutions of a genus 1 equation
2001-12-31
Research Paper
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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
Automatically Extracted Terms
- equation
- integer
- point
- elliptic
- genus
- curve
- solution
- integer solutions
- coefficient
- section
- series
- example
- function
- elliptic logarithms
- puiseux
- degree
- value
- puiseux expansions
- number
- polynomial
