I have a Jacobi Elliptic sn function: \begin{equation} 0.9258200998{\it sn} \left( 0.7559289460\,It-{\it ns} \left( - 1.154700538,- 0.6123724359\,\sqrt {2} \right) ,- 0.6123724359\,\sqrt {2} \right) \end{equation} which is equivalent to \begin{equation} 0.7559289458\,\sqrt {2}{\it dn} \left( 0.7559289458\,t, 0.5 \right) \end{equation} Here, 'I' is $\sqrt{-1}$, sn is Jacobi sine function,ns is inverse Jacobi sine function.
I obtained the equivalency by plotting the two functions for different time intervals. But, I am unable to explicitly convert one function to the other. I have searched a lot but I am unable to find an explicit conversion formula. Can someone help me out?