On the explicit models of Shimura's elliptic curves
The author studies the abelian varieties \(B_ N\), rational over the field \({\mathbb{Q}}(\sqrt{N})\), which \textit{G. Shimura} [J. Math. Soc. Japan 25, 523-544 (1973; Zbl 0266.14017)] has considered in relation with Nebentypus cusp forms of level N, in three cases (vis. \(N=29, 37, 41)\) where they have dimension \(1\). He computes their j-invariants by estimating their periods with sufficient accuracy, and deduces from known examples of elliptic curves over \({\mathbb{Q}}(\sqrt{N})\), with good reduction everywhere, explicit Weierstraß equations for the \(B_ N's\).
scientific article; zbMATH DE number 3983366