  The formal group law of an elliptic curve has seen recent applications to
computational algebraic geometry in the work of Couveignes to compute the order
of an elliptic curve over finite fields of small characteristic. The purpose of
this paper is to explain in an elementary way how to associate a formal group
law to an elliptic curve and to expand on some theorems of Couveignes. In
addition, the paper serves as background for [J. Number Theory 70 (1998),
127-145]. We treat curves defined over arbitrary fields, including fields of
characteristic two or three.
