| Let E/Q be an elliptic curve without complex multiplication. For a prime p (of good reduction), let p + 1 - a_p be the number of points of E modulo p. In 1976, S. Lang and H. Trotter formulated a conjecture regarding the number of primes p < x for which the ``Frobenius fields'' Q(sqrt{a_p^2 - 4p}) are isomorphic to a fixed imaginary quadratic field. The conjecture is still open and can be related to the classical open question about primes of the form n^2 + 1. I will discuss recent results of myself and Chantal David (Concordia University, Montreal) towards this Lang-Trotter Conjecture. |