On the sum of consecutive cubes being a perfect square
R. J. Stroeker (1995)
Compositio Mathematica
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Displaying similar documents to “-integral points on elliptic curves - Notes on a paper of B. M. M. de Weger”
On the sum of consecutive cubes being a perfect square
L-series and their 2-adic valuations at s = 1 attached to CM elliptic curves
Derong Qiu, Xianke Zhang (2002)
Acta Arithmetica
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The polynomial and elliptic curves of conductor 11
Alfred J. Van der Poorten (1976-1977)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
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Universal bounds on the torsion of elliptic curves
Daniel Sion Kubert (1979)
Compositio Mathematica
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Linear forms in logarithms, effectivity and elliptic curves
Alf Van Der Poorten (1980)
Mémoires de la Société Mathématique de France
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-integral solutions to a Weierstrass equation
Benjamin M. M. de Weger (1997)
Journal de théorie des nombres de Bordeaux
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The rational solutions with as denominators powers of to the elliptic diophantine equation are determined. An idea of Yuri Bilu is applied, which avoids Thue and Thue-Mahler equations, and deduces four-term (-) unit equations with special properties, that are solved by linear forms in real and -adic logarithms.
On Manin's conditional algorithm
Horst G. Zimmer (1977)
Mémoires de la Société Mathématique de France
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The canonical height of an algebraic point on an elliptic curve.
Everest, Graham, Ward, Thomas B. (2000)
The New York Journal of Mathematics [electronic only]
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Solving elliptic diophantine equations: the general cubic case
Roelof J. Stroeker, Benjamin M. M. de Weger (1999)
Acta Arithmetica
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On Elkies subgroups of -torsion points in elliptic curves defined over a finite field
Reynald Lercier, Thomas Sirvent (2008)
Journal de Théorie des Nombres de Bordeaux
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As a subproduct of the Schoof-Elkies-Atkin algorithm to count points on elliptic curves defined over finite fields of characteristic , there exists an algorithm that computes, for an Elkies prime, -torsion points in an extension of degree at cost bit operations in the favorable case where . We combine in this work a fast algorithm for computing isogenies due to Bostan, Morain, Salvy and Schost with the -adic approach followed by Joux and Lercier to get an algorithm...