  Mazur's theorem states that there are exactly 15 possibilities for the
torsion subgroup of an elliptic curve over the rational numbers. We determine
how often each of these groups actually occurs. Precisely, if $G$ is one of
these 15 groups, we show that the number of elliptic curves up to height $X$
whose torsion subgroup is isomorphic to $G$ is on the order of $X^{1/d}$, for
some number $d=d(G)$ which we compute.
