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We derive an analytic representation of the ten-particle, two-loop double-boxintegral as an elliptic integral over weight-three polylogarithms. To obtainthis form, we first derive a four-fold, rational (Feynman-)parametricrepresentation for the integral, expressed directly in terms ofdual-conformally invariant cross-ratios; from this, the desired form is easilyobtained. The essential features of this integral are illustrated by means of asimplified toy model, and we attach the relevant expressions for both integralsin ancillary files. We propose a normalization for such integrals that rendersall of their polylogarithmic degenerations pure, and we discuss the need for anew 'symbology' of iterated elliptic/polylogarithmic integrals in order tobring them to a more canonical form.

The Elliptic Double-Box Integral: Massless Amplitudes Beyond Polylogarithms