jacobi_sn( z , m )

The Jacobi sn function of z and parameter m in SageMath. Defined as the sine of the Jacobi amplitude:

$\operatorname{sn}( u | m ) = \sin [ \operatorname{am}( u | m ) ]$

Note that all Jacobi elliptic functions in SageMath use the parameter rather than the elliptic modulus k, which is related to the parameter by $$m = k^2$$.

Plot on the real axis: