the modular invariants of the elliptic curve in Weierstrass form: Note that the j-invariant is an isomorphism from the Riemann surface
It has two linearly independent solutions, called the periods of elliptic functions.
However, the ratio of two solutions of the hypergeometric equation is also known as a Schwarz triangle map.
As a partial fraction, it reveals the geometry of the fundamental domain: where (Sƒ)(x) is the Schwarzian derivative of ƒ with respect to x.
In algebraic geometry, this equation has been shown to be a very special case of a general phenomenon, the Gauss–Manin connection.