  Recently, a braking index for the pulsar PSR J1640-4631 has been measured.
With a braking index of $n = 3.15 \pm 0.03$, this pulsar has the highest
braking index ever measured. As it is well known, a pure magnetic dipole brake
yields $n = 3$, whereas a pure gravitational wave brake yields $n = 5$.
Therefore, each of these mechanisms alone can not account for the braking index
found for PSR J1640-4631. Here we show that such a braking index can be
accounted for if the spindown model combines magnetic dipole and gravitational
wave brakes. Then, we briefly discuss the detectability of this pulsar by aLIGO
and the planned Einstein Telescope. In particular, we show that the amplitude
of the gravitational wave that comes from our model is around a factor four
lower than the amplitude modeled exclusively by gravitational wave energy loss.
Another interesting outcome of our modeling is that we are able to obtain the
ellipticity from the braking index and other pulsar parameters.
