  We give an asymptotic formula for the number of elliptic curves over
$\mathbb{Q}$ with bounded Faltings height. Silverman has shown that the
Faltings height for elliptic curves over number fields can be expressed in
terms of modular functions and the minimal discriminant of the elliptic curve.
We use this to recast the problem as one of counting lattice points in a
particular region in $\mathbb{R}^2$.
