We analyze magnetic and axial two-nucleon contact terms in a combined large-$N_c$ and pionless effective field theory expansion. These terms play important roles in correctly describing, e.g., the low-energy cross section of radiative neutron capture and the deuteron magnetic moment. We show that the large-$N_c$ expansion hints towards a hierarchy between the two leading-order magnetic terms that matches that found in phenomenological fits. We also comment on the issue of naturalness in different Lagrangian bases.
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