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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 Z[u, v] is irreducible over 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... (Update)
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3.1: Computing All Integer Solutions of a General Elliptic Equation - Stroeker, Tzanakis (2000) (Correct)
1.8: Solving Elliptic Diophantine Equations: The General Cubic Case - Stroeker, de Weger (1999) (Correct)
0.5: On Sums of Consecutive Squares - Bremner, Stroeker, Tzanakis (1997) (Correct)
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BibTeX entry: (Update)
@misc{ stroeker-computing,
author = "R.J. Stroeker and N. Tzanakis",
title = "Computing All Integer Solutions of a Genus 1 Equation",
url = "citeseer.ist.psu.edu/506575.html" }
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3 On sums of consecutive squares - Bremner, Stroeker et al. - 1997
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3 the complexity of rational Puiseux expansions (context) - Walsh - 1999
3 Elliptic Binomial Diophantine Equations (context) - Stroeker, de Weger - 1999
2 Computing parametrizations of rational algebraic curves - van Hoeij
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1 A quantitative version of Runge's theorem on diophantine equ.. (context) - Walsh - 1992
1 Irreducibility testing over local fields (context) - Walsh - 2000
1 Computing all integer solutions of a general elliptic equati.. - Stroeker, Tzanakis - 2000
1 erence of the Weil height and the Neron-Tate height (context) - Zimmer, di - 1976
1 An algorithm for computing an integral basis in an algebraic.. (context) - van Hoeij - 1994
1 A polynomial-time complexity bound for the computation of th.. (context) - Walsh - 2000
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