From: rgep@pmms.cam.ac.uk (Richard Pinch)
Newsgroups: sci.math
Subject: Re: Elliptic curves over finite fields
Date: 3 May 1995 16:28:22 GMT

In article <3o367v$122@sunserver.lrz-muenchen.de>, ug142el@lrz.muenchen.de (Matthias Rehm) writes:
|> Does anybody know where to find a proof of the following theorem about
|> elliptic curves over finite fields? Let E be an elliptic curve.
|> 
|> Theorem: The group E(Z/pZ) is either cyclic or the product of two
|> cyclic groups of order m_{1} and m_{2} that satisfy
|> 
|> m_{1} | m_{2 };  m_{1} | gcd(m,p-1),
|> 
|> where m=#E(Z/pZ).

It follows from the analysis of the endomorphism ring in
Silverman, The Arithmetic of Elliptic Curves, Springer GTM 106
in Chapter V.2

Richard Pinch;	Queens' College, Cambridge