  The goal of this paper is to show there is a single orbit of the c.e. sets
with inclusion, $\mathcal{E}$, such that the question of membership in this
orbit is $\Sigma^1_1$-complete. This result and proof have a number of nice
corollaries: The Scott rank of $\mathcal{E}$ is $\omega^{CK}_1+1; Not all
orbits are elementarily definable; There is no arithmetic description of all
orbits of $\mathcal{E}$; For all finite $\alpha \geq 9$, there is a properly
$\Delta^0_\alpha$ orbit (from the proof).
  April 6, 2007, minor changes
  Nov 20, 2007, minor changes
