Arithmetic and intermediate Jacobians of some rigid Calabi-Yau threefolds

We construct Calabi-Yau threefolds defined over \(\mathbb{Q}\) via quotients of abelian threefolds, and re-verify the rigid Calabi-Yau threefolds in this construction are modular by computing their L-series, without \cite{Dieulefait} or \cite{GouveaYui}. We compute the intermediate Jacobians of the rigid Calabi-Yau threefolds as complex tori, then compute a \(\mathbb{Q}\)-model for the 1-torus given a \(\mathbb{Q}\)-structure on the rigid Calabi-Yau threefolds, and find infinitely many examples and counterexamples for a conjecture of Yui about the relation between the \(L\)-series of the rigid Calabi-Yau threefolds and the \(L\)-series of their intermediate Jacobians.