  Given a conformally nonflat Einstein spacetime we define a fibration $P$ over
it. The fibres of this fibration are elliptic curves (2-dimensional tori) or
their degenerate counterparts. Their topology depends on the algebraic type of
the Weyl tensor of the Einstein metric. The fibration $P$ is a double branched
cover of the bundle of null direction over the spacetime and is equipped with
six linearly independent 1-forms which satisfy certain relatively simple system
of equations.
