  Previous works focused on exoplanets discovered with the radial velocity (RV)
method reported an anti-correlation between the orbital eccentricities of the
exoplanets and the multiplicity M (i.e., number of planets) of their system. We
further investigate this reported anti-correlation here using a dataset
comprising exoplanets discovered with both the RV and transit methods,
searching for hints of its causes by exploring the connection between the
number of planets and the dynamical state of the exosystems. To examine the
correlation between multiplicity and orbital eccentricity, for every
multiplicity case considered (1<M<7), we computed the weighted average
eccentricities instead of the median eccentricities used previously. The
average eccentricities were calculated using the inverse of the uncertainty on
the eccentricity values as weights. The analysis of the dynamic state of the
exosystems was performed by computing their angular momentum deficit (AMD), a
diagnostic parameter used in the study of solar system and recently applied to
exosystems. Our results confirm the reported multiplicity-eccentricity
anti-correlation and show that the use of the uncertainties on the orbital
eccentricities in the analysis allows for a better agreement between data and
fits. Our best fit reproduces well the behaviour of average eccentricities for
all systems with M>1, including the additional cases of TRAPPIST-1 (M=7) and
solar system (M=8). The AMD analysis, while not conclusive due to the limited
number of exosystems that could be analysed, also suggests the existence of an
anti-correlation between the multiplicity and the AMD of exosystems. This
second anticorrelation, if confirmed by future studies, raises the possibility
that the population of low-multiplicity exosystems is contaminated by former
high-multiplicity systems that became dynamically unstable and lost some of
their planets.
