In this case the energy for E_1 is different, we obtain namely \begin{equation*} E_1=E_{\uparrow\uparrow}=-2J. \end{equation*} The other cases do also differ and we have \begin{equation*} E_2=E_{\uparrow\downarrow}=+2J, \end{equation*} \begin{equation*} E_3=E_{\downarrow\uparrow}=+2J, \end{equation*} and \begin{equation*} E_4=E_{\downarrow\downarrow}=-2J. \end{equation*}