  We consider the family of irreducible crystalline representations of
dimension $2$ of ${\rm Gal}(\overline{\bf Q}_p/{\bf Q}_p)$ given by the
$V_{k,a_p}$ for a fixed weight integer $k\geq 2$. We study the locus of the
parameter $a_p$ where these representations have a given reduction modulo $p$.
We give qualitative results on this locus and show that for a fixed $p$ and $k$
it can be computed by determining the reduction modulo $p$ of $V_{k,a_p}$ for a
finite number of values of the parameter $a_p$. We also generalize these
results to other Galois types.
