Computing all integer solutions of a genus 1 equation
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- by R. J. Stroeker and N. Tzanakis PDF
- Math. Comp. 72 (2003), 1917-1933 Request permission
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 $f(u,v)=0$, where $f\in \mathbb {Z}[u,v]$ is irreducible over $\overline {\mathbb {Q}}$, defines a curve of genus $1$, 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 $9$.References
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Additional Information
- R. J. Stroeker
- Affiliation: Econometric Institute, Erasmus University, P. O. Box 1738, 3000 DR Rotterdam, The Netherlands
- Email: stroeker@few.eur.nl
- N. Tzanakis
- Affiliation: Department of Mathematics, University of Crete, Iraklion, Greece
- Email: tzanakis@math.uch.gr
- Received by editor(s): January 28, 2002
- Published electronically: January 8, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Math. Comp. 72 (2003), 1917-1933
- MSC (2000): Primary 11D41, 11G05
- DOI: https://doi.org/10.1090/S0025-5718-03-01497-2
- MathSciNet review: 1986812