  A cubic algebraic equation for the effective parametrizations of the standard
gravitational Lagrangian has been obtained without applying any variational
principle.It was suggested that such an equation may find application in
gravity theory, brane, string and Rundall-Sundrum theories. The obtained
algebraic equation was brought by means of a linear-fractional transformation
to a parametrizable form, expressed through the elliptic Weierstrass function,
which was proved to satisfy the standard parametrizable form, but with $g_{2}$
and $g_{3}$ functions of a complex variable instead of the definite complex
numbers (known from the usual arithmetic theory of elliptic functions and
curves). The generally divergent (two) infinite sums of the inverse first and
second powers of the poles in the complex plane were shown to be convergent in
the investigated particular case, and the case of the infinite point of the
linear-fractional transformation was investigated. Some relations were found,
which ensure the parametrization of the cubic equation in its general form with
the Weierstrass function.
