  Extending recent work of others, we provide effective bounds on the family of
all elliptic curves and one-parameter families of elliptic curves modulo p (for
p prime tending to infinity) obeying the Sato-Tate Law. We present two methods
of proof. Both use the framework of Murty-Sinha; the first involves only
knowledge of the moments of the Fourier coefficients of the L-functions and
combinatorics, and saves a logarithm, while the second requires a Sato-Tate
law. Our purpose is to illustrate how the caliber of the result depends on the
error terms of the inputs and what combinatorics must be done.
