We report the discovery of EPIC201702477b, a transiting brown dwarf in a long period (40.73691 +/- 0.00037 day) and eccentric (e=0.2281 +/- 0.0026) orbit. This system was initially reported as a planetary candidate based on two transit events seen in K2 Campaign 1 photometry and later validated as an exoplanet. We confirm the transit and refine the ephemeris with two subsequent ground-based detections of the transit using the LCOGT 1m telescope network. We rule out any transit timing variations above the level of 30s. Using high precision radial velocity measurements from HARPS and SOPHIE we identify the transiting companion as a brown dwarf with a mass, radius, and bulk density of 66.9 +/- 1.7 M$_J$, 0.757 +/- 0.065 R$_J$, and 191+/-51 g.cm$^{-3}$ respectively. EPIC201702477b is the smallest radius brown dwarf yet discovered, with a mass just below the H-burning limit. It has the highest density of any planet, substellar mass object or main-sequence star discovered so far. We find evidence in the set of known transiting brown dwarfs for two populations of objects - high mass brown dwarfs and low mass brown dwarfs. The higher-mass population have radii in very close agreement to theoretical models, and show a lower-mass limit around 60 M$_J$. This may be the signature of mass-dependent ejection of systems during the formation process.
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