In this paper we present an analysis of Kepler K2 mission Campaign 3 observations of the irregular Neptune satellite, Nereid. We determined a rotation period of P = 11.594±0.017 h and amplitude of ∆m = 0. m 0328±0. m 0018, confirming previous short rotation periods obtained in ground based observations. The similarities of light curve amplitudes between 2001 and 2015 show that Nereid is in a low-amplitude rotation state nowadays and it could have been in a high-amplitude rotation state in the mid 1960's. Another high-amplitude period is expected in about 30 years. Based on the light curve amplitudes observed in the last 15 years we could constrain the shape of Nereid and obtained a maximum a:c axis ratio of 1.3:1. This excludes the previously suggested very elongated shape of a:c ≈ 1.9:1 and clearly shows that Nereid's spin axis cannot be in forced precession due to tidal forces. Thermal emission data from the Spitzer Space Telescope and the Herschel Space Observatory indicate that Nereid's shape is actually close to the a:c axis ratio limit of 1.3:1 we obtained, and it has a very rough, highly cratered surface.

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 trans-Neptunian object observations between campaigns C03 (2014 November–2015 February) and C19 (2018 August–September), which includes 66 targets. Due to the faintness of our targets, the detectability rate of a light-curve period is ∼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 ∼24 hr, in many cases close to ∼80 hr; 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, as well as among main belt asteroids measured with the TESS space telescope. Trans-Neptunian objects show notably higher light-curve amplitudes at large (D ≳ 300 km) sizes than found among large main belt asteroids, in contrast to the general expectation that due to their lower compressive strength, they reach hydrostatic equilibrium at smaller sizes than their inner solar system counterparts.