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We present the master integrals relevant for computing the complete set ofleading-colour analytic helicity amplitudes for top-quark pair production viagluon fusion at two-loops in QCD. We include corrections due to massive fermionloops which give rise to integrals involving elliptic curves. We also elaborateon the structure of singularities that play an important role in the numericalevaluation of the iterated integrals and their analytic continuation.

Master integrals contributing to two-loop leading colour QCD helicity amplitudes for top-quark pair production in the gluon fusion channel