The ordinary component of l-isogeny graph of elliptic curves

Abstract

In this thesis, our aim is to understand `-volcanoes which are ordinary compo nents of `-isogeny graphs of elliptic curves over finite fields under certain conditions. In 1996, the structure of isogeny graphs of elliptic curves described by David Kohel in his PhD thesis [1]. Later, in 2002 Mireille Fouquet and Francois Morain extended Kohel’s work by defining isogeny volcanoes [2]. Firstly, we give some basic definitions and tools as used throughout this thesis. Then we study the Kohel’s theorem and give a 3-volcano of depth 2 over F409 as an example.