  We aim to investigate the presence of signatures of magnetic cycles and
rotation on a sample of 71 early M-dwarfs from the HADES RV programme using
high-resolution time-series spectroscopy of the Ca II H & K and Halpha
chromospheric activity indicators, the radial velocity series, the parameters
of the cross correlation function and the V-band photometry. We used mainly
HARPS-N spectra, acquired over four years, and add HARPS spectra from the
public ESO database and ASAS photometry light-curves as support data, extending
the baseline of the observations of some stars up to 12 years. We provide
log(R'hk) measurements for all the stars in the sample, cycle length
measurements for 13 stars, rotation periods for 33 stars and we are able to
measure the semi-amplitude of the radial velocity signal induced by rotation in
16 stars. We complement our work with previous results and confirm and refine
the previously reported relationships between the mean level of chromospheric
emission, measured by the log(R'hk), with the rotation period, and with the
measured semi-amplitude of the activity induced radial velocity signal for
early M-dwarfs. We searched for a possible relation between the measured
rotation periods and the lengths of the magnetic cycle, finding a weak
correlation between both quantities. Using previous v sin i measurements we
estimated the inclinations of the star's poles to the line of sight for all the
stars in the sample, and estimate the range of masses of the planets GJ 3998 b
and c (2.5 - 4.9 Mearth and 6.3 - 12.5 Mearth), GJ 625 b (2.82 Mearth), GJ 3942
b (7.1 - 10.0 Mearth) and GJ 15A b (3.1 - 3.3 Mearth), assuming their orbits
are coplanar with the stellar rotation.
