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We study a K3 surface, which appears in the two-loop mixedelectroweak-quantum chromodynamic virtual corrections to Drell--Yan scattering.A detailed analysis of the geometric Picard lattice is presented, computing itsrank and discriminant in two independent ways: first using explicit divisors onthe surface and then using an explicit elliptic fibration. We also study indetail the elliptic fibrations of the surface and use them to provide anexplicit Shioda--Inose structure. Moreover, we point out the physical relevanceof our results.

Arithmetic and geometry of a K3 surface emerging from virtual corrections to Drell--Yan scattering