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.

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.

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 prove $\Bbb{Q}_p(\hat{E}[p])/\Bbb{Q}_p$ has degree $p-1$.

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.

But indeed this is totally ramified extension, so I want to find minimal polynomial of element of $\hat{E}[p]$. Thank you for your help.

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.