  Let $K$ be a $p$-adic field and $E$ an elliptic curve over $K$ with potential
good reduction. For some large Galois extensions $L$ of $K$ containing all
$p$-power roots of unity, we show the vanishing of certain Galois cohomology
groups of $L$ with values in the $p$-adic representation associated with $E$.
This generalizes some results of Coates, Sujatha and Wintenberger.
