  Let $S$ be a finite set of primes. For sufficiently large $n$ and $d$,
Lawrence and Venkatesh proved that in the moduli space of hypersurfaces of
degree $d$ in $\P^n$, the locus of points with good reduction outside $S$ is
not Zariski dense. We make this result effective by computing explicit values
of $n$ and $d$ for which this statement holds. We accomplish this by giving a
more precise computation and analysis of the Hodge numbers of these
hypersurfaces and check that they satisfy certain bounds.
