I am working on the proof of the main Theorem of complex multiplication states in "Advanced topics in the arithemtics of elliptic curves" of J.Silverman.

We have the following situation: $K$ is a quadratic imaginary field with ring of intgers $R_K$, $E/C$ an elliptic curve with End$(E) \cong R_K$. We fix an integer $m \geq 3$ and let $L/K$ a finite Galois extension satisfying $j(E) \in L$ und $E[m] \subset E(L)$. Then we define a Prime ideal $\mathcal{P}$ which does not divide $m$. Now it says that we can use a proposition (VII, 3.1 in Arithmetic of elliptic curves from J.Silverman) which has as condition that the reduced curve is non-singular because of $\mathcal{P} \nmid m$.

Q: How can I conclude that $E$ has good reduction on $\mathcal{P}$ because of $\mathcal{P} \nmid m$?