We report the detection of a Neptune-mass exoplanet around the M4.0 dwarf GJ 4276 ( G 232-070 ) based on radial velocity ( RV ) observations obtained with the CARMENES spectrograph .
The RV variations of GJ 4276 are best explained by the presence of a planetary companion that has a minimum mass of m _ { b } \sin i \approx 16 M _ { \oplus } on a P _ { b } = 13.35 day orbit .
The analysis of the activity indicators and spectral diagnostics exclude stellar induced RV perturbations and prove the planetary interpretation of the RV signal .
We show that a circular single-planet solution can be excluded by means of a likelihood ratio test .
Instead , we find that the RV variations can be explained either by an eccentric orbit or interpreted as a pair of planets on circular orbits near a period ratio of 2:1 .
Although the eccentric single-planet solution is slightly preferred , our statistical analysis indicates that none of these two scenarios can be rejected with high confidence using the RV time series obtained so far .
Based on the eccentric interpretation , we find that GJ 4276 b is the most eccentric ( e _ { b } = 0.37 ) exoplanet around an M dwarf with such a short orbital period known today .