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The Crab nebula is a supernova remnant exhibiting a highly polarizedsynchrotron radiation at radio and millimeter wavelengths. It is the brightestsource in the microwave sky with an extension of 7 by 5 arcminutes and commonlyused as a standard candle for any experiment which aims at measuring thepolarization of the sky. Though its spectral energy distribution has been wellcharacterized in total intensity, polarization data are still lacking atmillimetre wavelengths. We report in this paper high resolution (18 arcsecFWHM) observations of the Crab nebula in total intensity and linearpolarization at 150 GHz with the NIKA camera. NIKA, operated at the IRAM 30 mtelescope from 2012 to 2015, is a camera made of Lumped Element KineticInductance Detectors (LEKIDs) observing the sky at 150 and 260 GHz. From theseobservations we are able to reconstruct the spatial distribution of thepolarization degree and angle of the Crab nebula, which is found to becompatible with previous observations at lower and higher frequencies.Averaging across the source and using other existing data sets we find that theCrab nebula polarization angle is consistent with being constant over a widerange of frequencies with a value of -87.7$^\circ$ +- 0.3 in Galacticcoordinates. We also present the first estimation of the Crab nebula spectralenergy distribution polarized flux in a wide frequency range: 30-353 GHz.Assuming a single power law emission model we find that the polarizationspectral index $\beta_{pol}$ = - 0.347 +- 0.026 is compatible with theintensity spectral index $\beta$ = - 0.323 +- 0.001.

NIKA 150 GHz polarization observations of the Crab nebula and its spectral energy distribution