I am reading Silverman's Arithmetic of Elliptic Curves. In Section X.4 (The Selmer and Shafarevich-Tate Groups) Silverman derives a diagram relating the cohomology of the elliptic curve E over the absolute galois group $G(\overline{K}/K)$ to its cohomology over $G_\nu \simeq G(\overline{K_\nu}/K_\nu)$. If it's helpful the diagram is on the top of page 332 in my second edition book, but my question is just that to compute one part: $$ \ker\left( H^1(G_\nu, E[\varphi]) \rightarrow WC(E/K_\nu)[\varphi] \right)$$ Silverman says "the question of whether a curve has a point over a complete local field $K_\nu$ reduces by Hensel's lemma to checking whether the curve has a point in some finite ring $R_\nu / M_\nu^e$ for some easily computable integer $e$."
My question is why do we need to consider $R_\nu / M_\nu^e$ rather than $R_\nu / M_\nu$? Shouldn't solutions exist over $R_\nu / M_\nu^e$ if and only if they exist over $R_\nu / M_\nu$?