  We compute the reductions of irreducible crystalline two-dimensional
representations of $G_{\mathbf{Q}_p}$ of slope 1, for primes $p \geq 5$, and
all weights. We describe the semisimplification of the reductions completely.
In particular, we show that the reduction is often reducible. We also
investigate whether the extension obtained is peu or tr\`es ramifi\'ee, in the
relevant reducible non-semisimple cases. The proof uses the compatibility
between the $p$-adic and mod $p$ Local Langlands Correspondences, and involves
a detailed study of the reductions of both the standard and non-standard
lattices in certain $p$-adic Banach spaces.
