I'm currently studying Gross' paper about modular elliptic curves. Lemma 4.3 is quite difficult for me to understand. It states that an elliptic $E$ has no $p$-torsion rational over $K_n$, the ring class field of order $n$. The only thing I seem to know by now is that there is a well defined representation $\rho:\text{Gal}(\mathbb{Q}(E_p)/\mathbb{Q})\to \text{GL}_2(\mathbb{Z}/p\mathbb{Z})$.
Any insights on this, or references recommended? Thanks in advance.