  We describe the analytic calculation of the master integrals required to
compute the two-mass three-loop corrections to the $\rho$ parameter. In
particular, we present the calculation of the master integrals for which the
corresponding differential equations do not factorize to first order. The
homogeneous solutions to these differential equations are obtained in terms of
hypergeometric functions at rational argument. These hypergeometric functions
can further be mapped to complete elliptic integrals, and the inhomogeneous
solutions are expressed in terms of a new class of integrals of combined
iterative non-iterative nature.
