Context : Although more than 2 000 brown dwarfs have been detected to date , mainly from direct imaging , their characterisation is difficult due to their faintness and model dependent results .
In the case of transiting brown dwarfs it is , however , possible to make direct high precision observations .

Aims : Our aim is to investigate the nature and formation of brown dwarfs by adding a new well-characterised object , in terms of its mass , radius and bulk density , to the currently small sample of less than 20 transiting brown dwarfs .

Methods : One brown dwarf candidate was found by the KESPRINT consortium when searching for exoplanets in the K2 space mission Campaign 16 field .
We combined the K2 photometric data with a series of multi-colour photometric observations , imaging and radial velocity measurements to rule out false positive scenarios and to determine the fundamental properties of the system .

Results : We report the discovery and characterisation of a transiting brown dwarf in a 5.17 day eccentric orbit around the slightly evolved F7 V star EPIC 212036875 .
We find a stellar mass of 1.15 \pm 0.08 M _ { \odot } , a stellar radius of 1.41 \pm 0.05 R _ { \odot } , and an age of 5.1 \pm 0.9 Gyr .
The mass and radius of the companion brown dwarf are 51 \pm 2 M _ { \mathrm { J } } and 0.83 \pm 0.03 R _ { \mathrm { J } } , respectively , corresponding to a mean density of 108 _ { -13 } ^ { +15 } g cm ^ { -3 } .

Conclusions : EPIC 212036875b is a rare object that resides in the brown dwarf desert .
In the mass-density diagram for planets , brown dwarfs and stars , we find that all giant planets and brown dwarfs follow the same trend from \sim 0.3 M _ { \mathrm { J } } to the turn-over to hydrogen burning stars at \sim 73 M _ { \mathrm { J } } .
EPIC 212036875b falls close to the theoretical model for mature H/He dominated objects in this diagram as determined by interior structure models , as well as the empirical fit .
We argue that EPIC 212036875b formed via gravitational disc instabilities in the outer part of the disc , followed by a quick migration .
Orbital tidal circularisation may have started early in its history for a brief period when the brown dwarf ’ s radius was larger .
The lack of spin–orbit synchronisation points to a weak stellar dissipation parameter ( Q ^ { \prime } _ { \star } \gtrsim 10 ^ { 8 } ) which implies a circularisation timescale of \gtrsim 23 Gyr , or suggests an interaction between the magnetic and tidal forces of the star and the brown dwarf .