  We describe an algorithm to compute the reduction modulo $p$ of a crystalline
Galois representation of dimension $2$ of
$\text{Gal}(\overline{\mathbf{Q}}_p/\mathbf{Q}_p)$ with distinct Hodge-Tate
weights via the semi-simple modulo $p$ Langlands correspondence. We give some
examples computed with an implementation of this algorithm in SAGE.

Number Theory