Modular lambda function

In mathematics, the modular lambda function is a highly symmetric holomorphic function defined on the complex upper half-plane. It is invariant under the fractional linear action of the congruence group Gamma(2) and generates the function field of the corresponding quotient, making it a Hauptmodul for the modular curve X(2); at each point of its domain, its value can be described as a cross ratio of the branch points of a ramified double cover of the projective line by an elliptic curve.