  We study the intersection of an algebraic variety with the maximal compact
subgroup of a universal vectorial extension of a product of elliptic curves.
For this intersection we show a Manin-Mumford type statement. This answers some
questions posed by Corvaja-Masser-Zannier which arose in connection with their
investigation of the intersection of a curve with real analytic subgroups of
various algebraic groups. They prove finiteness in the situation of a single
elliptic curve. Using Khovanskii's zero-estimates combined with a
stratification result of Gabrielov-Vorobjov and recent work of the authors we
obtain effective bounds for this intersection that only depend on the degree of
the algebraic variety, and the dimension of the group. This seems new even if
restricted to the classical Manin-Mumford statement.
