Abstract
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.
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Zimmer, H.G. Torsion points on elliptic curves over a global field. Manuscripta Math 29, 119–145 (1979). https://doi.org/10.1007/BF01303623
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DOI: https://doi.org/10.1007/BF01303623