  We present equations for the gravitational lensing flexion expected for an
elliptical lens mass distribution. These can be reduced to one-dimensional
finite integrals, thus saving significant computing time over a full
two-dimensional calculation. We estimate constraints on galaxy halo
ellipticities for a range of potential future surveys, finding that the
constraints from the two different types of flexion are comparable and are up
to two orders of magnitude tighter than those from shear. Flexion therefore
appears to be a very promising potential tool for constraining the shapes of
galaxy haloes from future surveys.
