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Artículo
Galois Theory, discriminants and torsion subgroups of elliptic curves
(Elsevier, 2010-08)
We find a tight relationship between the torsion subgroup and the image of the mod 2 Galois representation associated to an elliptic curve defined over the rationals. This is shown using some characterizations for the ...
Artículo
On simultaneous arithmetic progressions on elliptic curves
(Taylor & Francis, 2006)
In this paper we study elliptic curves which have a number of points whose coordinates are in arithmetic progression. We first motivate this diophantine problem, prove some results, provide a number of interesting examples ...
Artículo
Thue equations and torsion groups of elliptic curves
(Elsevier, 2009-02)
A new characterization of rational torsion subgroups of elliptic curves is found, for points of order greater than 4, through the existence of solution for systems of Thue equations.
Artículo
Searching for simultaneous arithmetic progressions on elliptic curves
(Australian Mathematical Society, 2005-06)
We look for elliptic curves featuring rational points whose coordinates form two arithmetic progressions, one for each coordinate. A constructive method for creating such curves is shown, for lengths up to 5.
Artículo
A complete diophantine characterization of the rational torsion of an elliptic curve
(Springer, 2012-01)
We give a complete characterization for the rational torsion of an elliptic curve in terms of the (non–)existence of integral solutions of a system of diophantine equations.