Klein invariant J

The Klein j-invariant $j(\tau)$ is the modular function which encodes arithmetic information about the singular moduli of imaginary quadratic fields. It is invariant under the full modular group $\mathbf{SL}(2,\mathbb{Z})$.

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Klein's j-Invariant j(τ) under τ→-1/τ in SL(2,R)