  Vertical Sato-Tate states that the Frobenius trace of a randomly chosen
elliptic curve over $\mathbb F_p$ tends to a semicircular distribution as
$p\rightarrow \infty$. We go beyond this statement by considering the number of
elliptic curves $N_{t,p}'$ with a given trace $t$ over $\mathbb F_p$ and
characterizing the 2-dimensional distribution of $(t,N_{t,p}')$. In particular,
this gives the distribution of the size of isogeny classes of elliptic curves
over $\mathbb F_p$. Furthermore, we show a notion of stronger convergence for
vertical Sato-Tate which states that the number of elliptic curves with
Frobenius trace in an interval of length $p^\epsilon$ converges to the expected
amount. The key step in the proof is to truncate Gekeler's infinite product
formula, which relies crucially on an effective Chebotarev's density theorem
that was recently developed by Pierce, Turnage-Butterbaugh and Wood.
