2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71856In this article, we examine the arithmetic aspect of the Kummer-surface-type CY 3-folds $\hat{T/G}$, characterized by the crepant resolution of 3-torus-orbifold $T/G$ with only isolated singularities. Up to isomorphisms, there are only two such space $\hat{T/G}$ with $|G|=3, 7$, and both $T$ carrying the structure of triple-product structure of a CM elliptic curve. The (Griffiths) intermediate Jacobians of these $\hat{T/G}$ are identified explicitly as the corresponding elliptic curve appeared in the structure of $T$. We further provide the $\QZ$-structure of $\hat{T/G}$ and verify their modularity property.Latex 13 pages; Typos corrected, New improved and extended version with rational structures of CY spaces completed and their modular property verifiedAlgebraic GeometryNumber Theory11G, 11R, 14H, 14Jtext