2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125319We investigate the elliptic analogs of multi-indexed polylogarithms that appear in the theory of the fundamental group of the projective line minus three points as sections of a universal nilpotent bundle with regular singular connection. We use an analytic uniformisation to derive the fundamental nilpotent De Rham torsor of a single elliptic curve in terms of a double Jacobi form introduced by Kronecker. We then extend this result to any smooth family, relatively to the base, i.e., to the moduli stack $M_{1,2}$ over $M_{1,1}$. Everything relies on explicit formulas that turn out to be algebraic for rational (families of) elliptic curves, and we conclude by providing the corresponding natural $\QM$ structure.Number TheoryAlgebraic Geometry11G55; 14H52; 33E05text