The Hopf-Galois Structures of the 3 and 6-Division Points of the Lemniscate Curve

We study the number field generated by the coordinates of a real three (or six) division point of the lemniscate. This extension is not Galois but it admits six different Hopf Galois structures. We provide explicit descriptions of these structures, compute the Hopf algebra associated with one of them and analyze and compute the lattice of the intermediate fields of this extension.