  We construct $SL(2,R)$ invariant in anisotropic medium, with a dual
anisotropic charged black hole geometry in massive gravity. We show how to
obtain $SL(2,R)$ elements in terms of new degrees of freedom for
Electromagnetic configuration, and construct the general expressions for
conductivity with $SL(2,R)$ invariant. The holographic conductivities can be
calculated using horizon data in an external magnetic field, and we show the
numerical results using the linear response theory.
