Reduction map on torsion points of an elliptic curve and their valuation Let $K$ be a field of characteristic zero, complete with respect a discrete valuation $v$. Assume that the residue field $k$ is of positive characteristic $p$. 
Now take an elliptic curve $E$ defined over $K$ such that it has a good reduction at $v$ of height 1 (that is Hasse invariant not zero). There is the exact sequence (as abstract group)
$$ 0 \longrightarrow \ker (\pi) \longrightarrow E[p](K) \overset{\pi}{\longrightarrow} \tilde E[p](k) \longrightarrow 0$$
where $\pi$ is the reduction map (described in homogeneus coordinate) $[x:y:z] \mapsto [\tilde x: \tilde y: \tilde z]$ ($\tilde t$ is the image of $t \in \mathcal{O}_K$ in k).
My question is: how describe $\ker(\pi)$ in terms of the valuation $v$? More specific, wich valuation have the coordinates of the points of $\ker(\pi)$? 

The points $[x:y:z] \in \ker(\pi)$ are those mapped in $[0:1:0]$ so they must satisfy $v(x),v(z)>0$ and $v(y)=0$.
