  We investigate the properties of static and axisymmetric vacuum solutions of
Einstein equations which generalize the Schwarzschild spherically symmetric
solution to include a quadrupole parameter. We test all the solutions with
respect to elementary and asymptotic flatness and curvature regularity.
Analyzing their multipole structure, according to the relativistic invariant
Geroch definition, we show that all of them are equivalent up to the level of
the quadrupole. We conclude that the $q-$metric, a variant of the
Zipoy-Voorhees metric, is the simplest generalization of the Schwarzschild
metric, containing a quadrupole parameter.
