j-invariant

Phase of the j-invariant as a function of the nome q on the unit disk

The fundamental domain of the modular group acting on the upper half plane.

In mathematics, Klein's j-invariant or j function, regarded as a function of a complex variable τ, is a modular function of weight zero for $SL(2, Z)$ defined on the upper half-plane of complex numbers. It is the unique such function which is holomorphic away from a simple pole at the cusp such that

单词	Elliptic modular function
释义	Elliptic modular function 英语百科 j-invariant In mathematics, Klein's j-invariant or j function, regarded as a function of a complex variable τ, is a modular function of weight zero for $SL(2, Z)$ defined on the upper half-plane of complex numbers. It is the unique such function which is holomorphic away from a simple pole at the cusp such that
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Elliptic modular function

j-invariant