Deformations of the Kepler problem and the harmonic oscillator are considered for which additional integrals of motion are the coordinates of the reduced divisor, according to the Riemann-Roch theorem. For this family of non-commutative integrable systems the validity of the Mishchenko-Fomenko hypothesis about the existence of integrals of motion from a single functional class, in this case polynomial integrals of motion, is discussed.