  We show that four exceptional Fuchsian equations, each determined by the four
parabolic singularities, known as the Chudnovsky equations, are transformed
into each other by algebraic transformations. We describe equivalence of these
equations and their counterparts on tori. The latter are the Fuchsian equations
on elliptic curves and their equivalence is characterized by transcendental
transformations which are represented explicitly in terms of elliptic and theta
functions.
