  We give some heuristics for counting elliptic curves with certain properties.
In particular, we re-derive the Brumer-McGuinness heuristic for the number of
curves with positive/negative discriminant up to $X$, which is an application
of lattice-point counting. We then introduce heuristics (with refinements from
random matrix theory) that allow us to predict how often we expect an elliptic
curve $E$ with even parity to have $L(E,1)=0$. We find that we expect there to
be about $c_1X^{19/24}(\log X)^{3/8}$ curves with $|\Delta|<X$ with even parity
and positive (analytic) rank; since Brumer and McGuinness predict $cX^{5/6}$
total curves, this implies that asymptotically almost all even parity curves
have rank 0. We then derive similar estimates for ordering by conductor, and
conclude by giving various data regarding our heuristics and related questions.
