Abel’s quadratures for integrable Hamiltonian systems are defined up to a group law of the corresponding Abelian variety A. If A is isogenous to a direct product of Abelian varieties A ≅ A ₁ ×⋯× A _k, the group law can be used to construct various Lax matrices on the factors A ₁, …, A _k. As an example, we discuss two-dimensional reducible Abelian variety A = E ₊ × E ₋, which is a product of one-dimensional varieties E _± obtained by Euler in his study of the two fixed centres problem, and the Lax matrices on the factors E _±