  In complex algebraic geometry, the problem of enumerating plane elliptic
curves of given degree with fixed complex structure has been solved by
R.Pandharipande using Gromov-Witten theory. In this article we treat the
tropical analogue of this problem, the determination of the number of tropical
elliptic plane curves of degree d and fixed ``tropical j-invariant''
interpolating an appropriate number of points in general position. We show that
this number is independent of the position of the points and the value of the
j-invariant and that it coincides with the number of complex elliptic curves.
The result can be used to simplify Mikhalkin's algorithm to count curves via
lattice paths in the case of rational plane curves.
