Now showing items 1-6 of 6

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      Galois Theory, discriminants and torsion subgroups of elliptic curves  [Article]

      García Selfa, Irene; González Jiménez, Enrique; Tornero Sánchez, José María (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 ...
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      Markoff-Rosenberger triples in arithmetic progression  [Article]

      González Jiménez, Enrique; Tornero Sánchez, José María (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 ...
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      On the ubiquity of trivial torsion on elliptic curves  [Article]

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

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

      González Jiménez, Enrique; Tornero Sánchez, José María (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 ...