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1999 On the elliptic logarithm method for elliptic diophantine equations: reflections and an improvement
Roel J. Stroeker, Nikos Tzanakis
Experiment. Math. 8(2): 135-149 (1999).

Abstract

The elliptic logarithm method for the determination of all integral solutions of a given elliptic equation is discussed for equations with associated elliptic curve of moderately large rank. Major attention is given to the question of optimizing the choice of Mordell-Weil basis for the curves in question. A speculative argument suggests that for any curve of rank larger then 8 the calculations involved are unlikely to be feasible. The arguments are illustrated by examples of curves of rank 5, 6, 7, and 8, taken from the literature.

Citation

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Roel J. Stroeker. Nikos Tzanakis. "On the elliptic logarithm method for elliptic diophantine equations: reflections and an improvement." Experiment. Math. 8 (2) 135 - 149, 1999.

Information

Published: 1999
First available in Project Euclid: 12 March 2003

zbMATH: 0979.11060
MathSciNet: MR1700575

Subjects:
Primary: 11D25
Secondary: 11G05 , 11Y50

Keywords: Diophantine equation , Elliptic curve , elliptic logarithm

Rights: Copyright © 1999 A K Peters, Ltd.

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Vol.8 • No. 2 • 1999
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