Families of non-Galois quartic fields (Q1900882)

\textit{Ph. Cassou-Noguès} and \textit{M. J. Taylor} [Elliptic functions and rings of integers, Prog. Math. 66 (1987; Zbl 0608.12013)] used the Fueter model of an elliptic curve with multiplication \(Y^2= X(4X^2+ tX+ 4)\) to find generators of the rings of integers in abelian extensions of imaginary quadratic fields. The authors use this model in the case of an elliptic curve without complex multiplication to compute a basis of the integers and the group of units of some quadratic extensions of the field of rationals.