In Kolyvagin's work on modular elliptic curves, proposition 5.3, there is the following statement: let $\tau\in\text{Gal}(K/\mathbb{Q})$ be complex conjugation, then $$\tau y_n=\epsilon \sigma'y_n+\text{ (torsion) in }E(K_n), \text{for some }\sigma'\in\text{Gal}(K_n/K)$$ where $E$ is a modular elliptic curve, $K_n$ is the ring class field of conductor $n$, $y_n$ is the Heegner point, and $\epsilon=\pm 1$ is the eigenvalue of the Atkin-Lehner operator on the eigenform associated to the modular curve $E$.
The proof starts with the known identity $\tau x_n=w_N(\sigma'x_n)$. But I don't understand how to come up with it in the citation they give in this paper. Also, I'm confused with the rest of the proof. Can someone help me clarify this? Thanks in advance!