Optical and radio astrometry of the galaxy associated with FRB 150418

A fading radio source, coincident in time and position with the fast radio burst FRB 150418, has been associated with the galaxy WISE J071634.59-190039.2. Subsequent observations of this galaxy have revealed that it contains a persistent, but variable, radio source. We present e-Multi-Element Radio Linked Interferometer Network, Very Long Baseline Array, and Australia Telescope Compact Array radio observations and Subaru optical observations of WISE J071634.59-190039.2 and find that the persistent radio source is unresolved and must be compact (<0.01 kpc), and that its location is consistent with the optical centre of the galaxy. We conclude that it is likely that WISE J071634.59-190039.2 contains a weak radio active galactic nucleus.