Let $E/ \Bbb{Q}_p$ be an elliptic curve over $ \Bbb{Q}_p$. $\hat{E}$ denote the corresponding formal group of $E$.
I want to know what 
$\Bbb{Q}_p(\hat{E}[p])/\Bbb{Q}_p$ is .

At first I tried to prove  $\hat{E}$ is Lubin Tate formal group, but it wasn't.
I might be missing some basic approach to this problem. 


P.S
 At first I wrote it is degree $p-1$ extension, but Chris Wuthrich pointed out that it does not hold in general(when $E$ is super singular, it is true), and I edited.