2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/154622In the case of two degree system the pairs of quadratic in momenta Hamiltonians commuting according the standard Poisson bracket are considered. The new many-parametrical families of such pairs are founded. The universal method of constructing the full solution of Hamilton - Jacobi equation in terms of integrals on some algebraic curve is proposed. For some examples this curve is non-hyperelliptic covering over the elliptic curve.14 pages, proof of Theorem 1 addedExactly Solvable and Integrable Systemstext