We present full analytic results for the four-point one-loop amplitude of a
conformally coupled scalar in four-dimensional Anti-de-Sitter space dual to a
primary operator with scaling dimension 1. The computation is based on an
intriguing recent discovery, connecting Witten diagrams and flat-space Feynman
integrals, which led to an expression of the amplitude of interest as a pure
combination of single-valued multiple polylogarithms and an integral which
cannot be reduced to multiple polylogarithms. We explicitly evaluate that
integral in terms of elliptic multiple polylogarithms, finding that it is not
manifestly single-valued unlike the polylogarithmic contributions to the
amplitude. Further we compute the symbol of the integral and observe similar
structures as for (elliptic) flat-space amplitudes. The result presented here
adds to the relatively short list of explicitly known position space
curved-space amplitudes beyond tree level, and constitutes the first
curved-space amplitude evaluated in terms of elliptic multiple polylogarithms
