What is the right dual isogeny?

Question

I have a question regarding dual isogenies. I read an example in Silverman's book about elliptic curves and am wondering something about this example. We have $\zeta$ as a primitive cube root of unity. Then the elliptic curve $C: y^2=x^3+1$ has complex multiplication: \begin{align*} \phi(x,y)=(\zeta x, -y) \end{align*} Now it is clear to me that we have $\phi^3(P)=-P$ and $\phi^6(P)=P$. But what is now the dual isogeny of $\phi$? Since we could take $\hat{\phi}=\phi^2$ and have $\phi \phi^2= [-1]$ or we could take $\hat{\phi}=\phi^5$ and get $\phi \phi^5 = [1]$. How do I know which is the right one?