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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
Torsion of rational elliptic curves over quadratic fields II
(Springer, 2016-03)
Let E be an elliptic curve defined over Q and let G=E(Q)_tors be the associated torsion group. In a previous paper, the authors studied, for a given G, which possible groups G\leq H could appear such that H=E(K)_tors, for ...
Artículo
Markoff-Rosenberger triples in arithmetic progression
(Elsevier, 2013-06)
We study the solutions of the Rosenberg–Markoff equation ax2 + by2 + cz2 = dxyz (a generalization of the well–known Markoff equation). We specifically focus on looking for solutions in arithmetic progression that lie in ...
Artículo
Torsion of rational elliptic curves over cubic fields
(Rocky Mountain Mathematics Consortium, 2016)
Let E be an elliptic curve defined over Q. We study the relationship between the torsion subgroup E(Q)tors and the torsion subgroup E(K)tors, where K is a cubic number field. In particular, we study the number of cubic ...
Artículo
On the ubiquity of trivial torsion on elliptic curves
(Springer, 2010-08)
The purpose of this paper is to give a down-to-earth proof of the well–known fact that a randomly chosen elliptic curve over the rationals is most likely to have trivial torsion.
Artículo
Torsion of rational elliptic curves over quadratic fields
(Springer, 2014-09)
Let E be an elliptic curve defined over Q. We study the relationship between the torsion subgroup E(Q)tors and the torsion subgroup E(K)tors, where K is a quadratic number field.