 idUS
 Investigación
 Ciencias
 Álgebra
 Browsing Álgebra by Author
Browsing Álgebra by Author "González Jiménez, Enrique"
Now showing items 16 of 6

Galois Theory, discriminants and torsion subgroups of elliptic curves [Article]
García Selfa, Irene; González Jiménez, Enrique; Tornero Sánchez, José María (Elsevier, 201008)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 ...

MarkoffRosenberger triples in arithmetic progression [Article]
González Jiménez, Enrique; Tornero Sánchez, José María (Elsevier, 201306)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 ...

On the ubiquity of trivial torsion on elliptic curves [Article]
González Jiménez, Enrique; Tornero Sánchez, José María (Springer, 201008)The purpose of this paper is to give a downtoearth proof of the well–known fact that a randomly chosen elliptic curve over the rationals is most likely to have trivial torsion.

Torsion of rational elliptic curves over cubic fields [Article]
González Jiménez, Enrique; Najman, Filip; Tornero Sánchez, José María (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 ...

Torsion of rational elliptic curves over quadratic fields [Article]
González Jiménez, Enrique; Tornero Sánchez, José María (Springer, 201409)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.

Torsion of rational elliptic curves over quadratic fields II [Article]
González Jiménez, Enrique; Tornero Sánchez, José María (Springer, 201603)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 ...