  We report the discovery and characterization of TOI-1759~b, a temperate (400
K) sub-Neptune-sized exoplanet orbiting the M~dwarf TOI-1759 (TIC 408636441).
TOI-1759 b was observed by TESS to transit on sectors 16, 17 and 24, with only
one transit observed per sector, creating an ambiguity on the orbital period of
the planet candidate. Ground-based photometric observations, combined with
radial-velocity measurements obtained with the CARMENES spectrograph, confirm
an actual period of $18.85019 \pm 0.00014$ d. A joint analysis of all available
photometry and radial velocities reveal a radius of $3.17 \pm 0.10\,R_\oplus$
and a mass of $10.8 \pm 1.5\,M_\oplus$. Combining this with the stellar
properties derived for TOI-1759 ($R_\star = 0.597 \pm 0.015\,R_\odot$; $M_\star
= 0.606 \pm 0.020\,M_\odot$; $T_{\textrm{eff}} = 4065 \pm 51$ K), we compute a
transmission spectroscopic metric (TSM) value of over 80 for the planet, making
it a good target for transmission spectroscopy studies. TOI-1759 b is among the
top five temperate, small exoplanets ($T_\textrm{eq} < 500$ K, $R_p < 4
\,R_\oplus$) with the highest TSM discovered to date. Two additional signals
with periods of 80 d and $>$ 200 d seem to be present in our radial velocities.
While our data suggest both could arise from stellar activity, the later
signal's source and periodicity are hard to pinpoint given the $\sim 200$ d
baseline of our radial-velocity campaign with CARMENES. Longer baseline
radial-velocity campaigns should be performed in order to unveil the true
nature of this long period signal.
