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, Volume 29, Issue 2–4, pp 119–145 | Cite as

Torsion points on elliptic curves over a global field

  • Horst G. Zimmer


Let C be an elliptic curve defined over a global field K and denote by CK the group of rational points of C over K. The classical Nagell-Lutz-Cassels theorem states, in the case of an algebraic number field K as groud field, a necessary condition for a point in CK to be a torsion point, i.e. a point of finite order. We shall prove here two generalized and strongthened versions of this classical result, one in the case where K is an algebraic number field and another one in the case where K is an algebraic function field. The theorem in the number field case turns out to be particularly useful for actually computing torsion points on given families of elliptic curves.


Number Theory Algebraic Geometry Elliptic Curve Classical Result Topological Group 
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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Horst G. Zimmer
    • 1
  1. 1.Fachbereich 9 MathematikUniversität des SaarlandesSaarbrücken

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