Abstract:

In this note we report on an experiment related to the distribution of the number of rational points on elliptic curves over the field with $p$ elements. In particular, we analyze the symmetry that these numbers exhibit. A simple proof is provided and a more elaborate interpretation of the phenomenon is given in terms of isomorphism classes of curves and field extension.

The distribution of the number of points of elliptic curves on $\ensuremath{\mathbb{Z}}_p$

Javier Fernandez

Date: June 24, 2003

Department of Mathematics
University of Utah
Salt Lake City
UT 84112

jfernand@math.utah.edu