  We give a complete classification of all the potentially crystalline 3-adic
representations of the absolute Galois group of $\mathbb{Q}_3$ that are
isomorphic to the Tate module of an elliptic curve defined over $\mathbb{Q}_3$.
These representations are described in terms of their associated filtered
$(\varphi, \mathrm{Gal}(K/\mathbb{Q}_3))$-modules. The most interesting cases
occur when the potential good reduction is wild.
