I'm completely beginner of Tate curve, sorry to ask a basic question. I don't see for what condition, elliptic curves can be regarded as Tate curve or not.
For example, let $E_p:y^2=x^3+17x$ be an elliptic curve over $\Bbb{Q}_p$, for $p=2,17,37$. Here $2,17$ is bad prime of $E$ and $37$ is good prime of $E$.
For which $p$, is $E_p$ a Tate curve ?