Elliptic Double Box and Symbology Beyond Polylogarithms

We study the elliptic double-box integral, which contributes to generic massless QFTs and is the only contribution to a particular 10-point scattering amplitude in N =4 SYM theory. Based on a Feynman parametrization, we express this integral in terms of elliptic polylogarithms. We then study its symbol, finding a rich structure and remarkable similarity with the nonelliptic case. In particular, the first entry of the symbol is expressible in terms of logarithms of dual-conformal cross ratios, and elliptic letters only occur in the last two entries.