For the specific state E_1 , we have chosen all spins up. The energy of this configuration becomes then \begin{equation*} E_1=E_{\uparrow\uparrow}=-J. \end{equation*} The other configurations give \begin{equation*} E_2=E_{\uparrow\downarrow}=+J, \end{equation*} \begin{equation*} E_3=E_{\downarrow\uparrow}=+J, \end{equation*} and \begin{equation*} E_4=E_{\downarrow\downarrow}=-J. \end{equation*}