  The K2 mission of the Kepler Space Telescope allowed the observations of
light curves of small solar system bodies throughout the whole Solar system. In
this paper we present the results of a collection of K2 transneptunian object
observations, between Campaigns C03 (November 2014 -- February 2015) to C19
(August -- September, 2018), which includes 66 targets. Due to the faintness of
our targets the detectability rate of a light curve period is $\sim$56%,
notably lower than in the case of other small body populations, like Hildas or
Jovian trojans. We managed to obtain light curve periods with an acceptable
confidence for 37 targets; the majority of these cases are new identifications.
We were able to give light curve amplitude upper limits for the other 29
targets. Several of the newly detected light curve periods are longer than
$\sim$24 h, in many cases close to $\sim$80 h, i.e., these targets are slow
rotators. This relative abundance of slowly rotating objects is similar to that
observed among Hildas, Jovian trojans and Centaurs in the K2 mission, and also
among main belt asteroids measured with the TESS Space Telescope.
Transneptunian objects show notably higher light curve amplitudes at large (D
$\gtrsim$ 300 km) sizes than that found among large main belt asteroids, in
contrast to the general expectation that due to their lower compressive
strength they reach hydrostatic equlibrium at smaller sizes than their inner
solar system counterparts.
