  Scattering amplitudes at loop level can be reduced to a basis of linearly
independent Feynman integrals. The integral coefficients are extracted from
generalized unitarity cuts which define algebraic varieties. The topology of an
algebraic variety characterizes the difficulty of applying maximal cuts. In
this work, we analyze a novel class of integrals whose maximal cuts give rise
to an algebraic variety with irrational irreducible components. As a
phenomenologically relevant example we examine the two-loop planar double-box
contribution with internal massive lines. We derive unique projectors for all
four master integrals in terms of multivariate residues along with Weierstrass'
elliptic functions. We also show how to generate the leading-topology part of
otherwise infeasible integration-by-parts identities analytically from exact
meromorphic differential forms.
