Abstract: I shall prove that the Hausdorff dimension of the Julia set of any non-constant elliptic function $f$ is strictly larger than one. In fact I will show that it is larger than $2q/(q+1)$ where $q\ge 2$ is the maximal order of all poles of $f$. As consequence of this result, it follows that the maximum of Hausdorff dimensions of Julia sets of all elliptic functions periodic with respect to a given lattice in the complex plane, is equal to $2$. Hausdorff and packing measures of such Julia sets also will be discussed.

This is joint work with Janina Kotus.