Periodica Mathematica Hungarica

, Volume 68, Issue 2, pp 222–230 | Cite as

High rank elliptic curves with prescribed torsion group over quadratic fields

  • Julián Aguirre
  • Andrej Dujella
  • Mirela Jukić Bokun
  • Juan Carlos Peral


There are 26 possibilities for the torsion groups of elliptic curves defined over quadratic number fields. We present examples of high rank elliptic curves with a given torsion group which set the current rank records for most of the torsion groups. In particular, we show that for each possible torsion group, except maybe for \(\mathbb {Z}/15\mathbb {Z}\), there exists an elliptic curve over some quadratic field with this torsion group and with rank \(\ge 2\).


Quadratic fields Elliptic curves Rank Torsion group 

Mathematics Subject Classification

11G05 14H52 11R11 



The authors would like to thank Filip Najman and the referee for very useful comments on the previous version of this paper.


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2014

Authors and Affiliations

  • Julián Aguirre
    • 1
  • Andrej Dujella
    • 2
  • Mirela Jukić Bokun
    • 3
  • Juan Carlos Peral
    • 1
  1. 1.Departamento de MatemáticasUniversidad del País VascoBilbaoSpain
  2. 2.Department of MathematicsUniversity of ZagrebZagrebCroatia
  3. 3.Department of MathematicsUniversity of OsijekOsijekCroatia

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