  A class of elliptic curves with associated Lax matrices is considered. A
family of dynamical systems on e(3) parametrized by polynomial a with above Lax
matrices are constructed. Five cases from the family are selected by the
condition of preserving the standard mea- sure. Three of them are Hamiltonian.
It is proved that two other cases are not Hamiltonian in the standard Poisson
structure on e(3). Integra- bility of all five cases is proven. Integration
procedures are performed in all five cases. Separation of variables in Sklyanin
sense is also given. A connection with Hess-Appel'rot system is established. A
sort of sep- aration of variables is suggested for the Hess-Appel'rot system.
