19 citations · 67 across the 23 of their papers we have counts for
11 papers · 1 filter
Torsion of rational elliptic curves over quadratic fields
Enrique Gonzalez-Jimenez, Jose M. Tornero
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
Enrique Gonzalez-Jimenez, Jose M. Tornero
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…
Torsion of rational elliptic curves over cubic fields
Enrique Gonzalez-Jimenez, Filip Najman, Jose M. Tornero
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…
Markoff-Rosenberger triples in arithmetic progression
Enrique González-Jiménez, José M. Tornero
We study the solutions of the Rosenberg--Markoff equation ax^2+by^2+cz^2 = dxyz (a generalization of the well--known Markoff equation). We specifically focus on looking for solutio…
On the ubiquity of trivial torsion on elliptic curves
Enrique Gonzalez-Jimenez, Jose M. Tornero
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 torsi…
Galois Theory, discriminants and torsion subgroups of elliptic curves
Irene Garcia-Selfa, Enrique Gonzalez-Jimenez, Jose M. Tornero
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…