The distribution of central values of elliptic curve L-functions

We present some numerical results on the distribution of nonzero central values of elliptic curve L  -functions. We compare the family of elliptic curves Ea,b:y2=x3+ax+bEa,b:y2=x3+ax+b with (a,b)(a,b) ranging over a large box, and Cremona's list of all elliptic curves with conductor 340000≤N<350000. We also present a non-rigorous method for calculating central values that is faster than the approximate functional equation by a logarithmic factor.