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Archiv der Mathematik

, Volume 73, Issue 1, pp 25–32 | Cite as

Determination of elliptic curves with everywhere good reduction over real quadratic fields

  • Takaaki Kagawa
Article

Abstract.

All elliptic curves having everywhere good reduction over \(\Bbb Q(\sqrt {29})\) are determined by studying the fields of 2- and 3-division points. As a byproduct of the argument, the elliptic curves over some real quadratic fields are determined. Though part of the result are already obtained in [2], [4], [5], [10], the proof given in the present paper is simpler.

Keywords

Elliptic Curve Elliptic Curf Good Reduction Quadratic Field Real Quadratic Field 

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Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • Takaaki Kagawa
    • 1
  1. 1.Department of Mathematics, Ritsumeikan University, Kusatsu, Shiga, 525-8599, JapanJapan

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