  We calculate the forward unpolarised doubly-virtual Compton scattering (VVCS)
off the deuteron in the framework of pionless effective field theory, up to
next-to-next-to-next-to-leading order (N3LO) for the longitudinal and
next-to-leading order (NLO) for the transverse amplitude. The charge elastic
form factor of the deuteron, obtained from the residue of the longitudinal VVCS
amplitude, is used to extract the value of the single unknown two-nucleon
one-photon contact coupling that enters the longitudinal amplitude at N3LO. We
also study the lowest spin-independent generalised polarisabilities of the
deuteron. The calculated unpolarised VVCS amplitude provides a high-precision
model-independent input for a future calculation of the two-photon-exchange
correction to the Lamb shift of muonic deuterium.
