This is from J.S.Milne's Elliptic Curves book.

We have $H^1(\mathbb{Q}, E_2) \cong (\mathbb{Q}^× / \mathbb{Q}^{×2})^2$ because $Gal(\mathbb{Q}^{al} / \mathbb{Q})$ acts trivially on $E_2(\mathbb{Q}^{al})$, so

$$ H^1(\mathbb{Q}, E_2) \cong H^1(\mathbb{Q}, \mu_2)^2 \cong (\mathbb{Q}^× / \mathbb{Q}^{×2})^2$$

Here, $ \mu_n(L) = \{x \in L | x^n =1\}, E_n(L)=$ the set of points of order $n$ in the Elliptic Curve $E(L)$ and $H^1(G,M)$ is the first cohomological group

My question is, how can I prove a similar isomorphism: $H^1(K, E_2) \cong (K^×/ K^{×2})^2$? ($K$ is a number field) Especially since I don't know how $E_2(K)$ looks like, which I know for $K = \mathbb{Q}$

Thanks!