  Constrained mean-field calculations, based on the Gogny-D1M energy density
functional, have been carried out to describe fission in the isotopes
$^{250-260}$No. The even-even isotopes have been considered within the standard
Hartree-Fock-Bogoliobov (HFB) framework while for the odd-mass ones the Equal
Filling Approximation (HFB-EFA) has been employed. Ground state quantum numbers
and deformations, pairing energies, one-neutron separation energies, inner and
outer barrier heights as well as fission isomer excitation energies are given.
Fission paths, collective masses and zero-point quantum vibrational and
rotational corrections are used to compute the systematic of the spontaneous
fission half-lives t$_\mathrm{SF}$ both for even-even and odd-mass nuclei.
Though there exists a strong variance of the predicted fission rates with
respect to the details involved in their computation, it is shown that both the
specialization energy and the pairing quenching effects, taken into account
within the self-consistent HFB-EFA blocking procedure, lead to larger
t$_\mathrm{SF}$ values in odd-mass nuclei as compared with their even-even
neighbors. Alpha decay lifetimes have also been computed using a
parametrization of the Viola-Seaborg formula. The high quality of the Gogny-D1M
functional regarding nuclear masses leads to a very good reproduction of
$Q_{\alpha}$ values and consequently of lifetimes.
