Direct sum decomposition of elliptic curve cohomology

Question

I am reading Kolyvagin's work on modular elliptic cruves. At (5.1) there is the following statement: Since $p$ is odd, there is a direct sum decomposition into eigenspaces for complex conjugation $\tau$: $$H^1(\text{Gal}(K/\mathbb{Q}),E(K_n)_p)=H^1(\text{Gal}(K/\mathbb{Q}),E(K_n)_p)^+\oplus H^1(\text{Gal}(K/\mathbb{Q}),E(K_n)_p)^-,$$ where $K_n$ is the ring class field of conductor $n$ and $(\cdot)_p$ is the set of $p$-torsion points. My question is why is this true? Many thanks in advance!