Representions of $GL(2,F)$ Associated to Elliptic Curves

In the first part of this talk we will introduce elliptic curves over
non-archimedean local fields, the concept of minimality and the reduction
types. In the second part we will define the Weil group and introduce the
local Langlands correspondence for $GL(2,F)$. Then for $F=Q_p$ the p-adic
field, we will determine the representation $\pi$ for $GL(2,F)$, associated
to an elliptic curve $E/F$, from the Weierstrass equation.