2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98492This paper studies the arithmetic of the extremal elliptic K3 surface with configuration of singular fibres [19,1,1,1,1,1]. We give a model over Q such that the Neron Severi group is generated by divisors over Q, and we describe the local Hasse-Weil zeta-functions in terms of a modular form of weight 3. Furthermore we verify the Tate conjecture for the reduction at 3 and comment on a conjecture of T. Shioda concerning the similarity of the lattice of transcendental cycles and a lattice resulting from supersingular reduction.8 pages, plain textAlgebraic GeometryNumber Theory11G25, 14J27, 14J28text