manuscripta mathematica

, Volume 29, Issue 2, pp 119–145

Torsion points on elliptic curves over a global field

  • Horst G. Zimmer

DOI: 10.1007/BF01303623

Cite this article as:
Zimmer, H.G. Manuscripta Math (1979) 29: 119. doi:10.1007/BF01303623


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.

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

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