  We report the discovery of a Neptune-like planet (LP 714-47 b, P = 4.05204 d,
m_b = 30.8 +/- 1.5 M_earth , R_b = 4.7 +/- 0.3 R_earth ) located in the 'hot
Neptune desert'. Confirmation of the TESS Object of Interest (TOI 442.01) was
achieved with radial-velocity follow-up using CARMENES, ESPRESSO, HIRES,
iSHELL, and PFS, as well as from photometric data using TESS, Spitzer, and
ground-based photometry from MuSCAT2, TRAPPIST- South, MONET-South, the George
Mason University telescope, the Las Cumbres Observatory Global Telescope
network, the El Sauce telescope, the TUBITAK National Observatory, the
University of Louisville Manner Telescope, and WASP-South. We also present
high-spatial resolution adaptive optics imaging with the Gemini Near-Infrared
Imager. The low uncertainties in the mass and radius determination place LP
714-47 b among physically well-characterised planets, allowing for a meaningful
comparison with planet structure models. The host star LP 714-47 is a slowly
rotating early M dwarf (T_eff = 3950 +/- 51 K) with a mass of 0.59 +/- 0.02
M_sun and a radius of 0.58 +/- 0.02 R_sun. From long-term photometric
monitoring and spectroscopic activity indicators, we determine a stellar
rotation period of about 33 d. The stellar activity is also manifested as
correlated noise in the radial-velocity data. In the power spectrum of the
radial-velocity data, we detect a second signal with a period of 16 days in
addition to the four-day signal of the planet. This could be shown to be a
harmonic of the stellar rotation period or the signal of a second planet. It
may be possible to tell the difference once more TESS data and radial-velocity
data are obtained.
