Mathematics

The local study of elliptic curves modulo primes is one of the most powerful tools, both conjecturally and actually, for proving global results. The trace of the Frobenius morphism is a measure of how far an elliptic curve departs from its expected local behavior, and Lang and Trotter have a well-known conjecture regarding the distribution of these traces for a given curve. In this talk we will discuss some results related to this conjecture for certain families of elliptic curves.