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AM CVn binaries are hydrogen deficient compact binaries with an orbital period in the 5-65 min range and are predicted to be strong sources of persistent gravitational wave radiation. Using Gaia Data Release 2, we present the parallaxes and proper motions of 41 out of the 56 known systems. Compared to the parallax determined using the HST Fine Guidance Sensor we find that the archetype star, AM CVn, is significantly closer than previously thought. This resolves the high luminosity and mass accretion rate which models had difficulty in explaining. Using Pan-STARRS1 data we determine the absolute magnitude of the AM CVn stars. There is some evidence that donor stars have a higher mass and radius than expected for white dwarfs or that the donors are not white dwarfs. Using the distances to the known AM CVn stars we find strong evidence that a large population of AM CVn stars have still to be discovered. As this value sets the background to the gravitational wave signal of LISA, this is of wide interest. We determine the mass transfer rate for 15 AM CVn stars and find that the majority have a rate significantly greater than expected from standard models. This is further evidence that the donor star has a greater size than expected., Accepted by A&A in main journal