J-invariant

Common card · No. 345890

In mathematics, the j-invariant or j function is a modular function of weight zero for the special linear group SL ⁡ ( 2 , Z ) {\displaystyle \operatorname {SL} (2,\mathbb {Z} )} defined on the upper half-plane of complex numbers. It is the unique such function that is holomorphic away from a simple pole at the cusp such that j ( e 2 π i / 3 ) = 0 , j ( i ) = 1728 = 12 3 . {\displaystyle j{\big (}e^{2\pi i/3}{\big )}=0,\quad j(i)=1728=12^{3}.}...

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