English: This sketch shows the locations of the zeros and poles of the 12 Jacobi elliptic functions ${\displaystyle \mathrm{pq}(u,m)}$ where ${\displaystyle p,q\in \{\mathrm{s},\mathrm{c},\mathrm{n},\mathrm{d}\}}$ with ${\displaystyle \mathrm{p}\ne \mathrm{q}}$. The function ${\displaystyle \mathrm{pq}(u,m)}$ will have a zero at the ${\displaystyle \mathrm{p}}$ corner and a singularity at the ${\displaystyle \mathrm{q}}$ corner. The quarter periods are defined by ${\displaystyle K=K(m)}$ and ${\displaystyle K^{\prime }=K(1-m)}$ where ${\displaystyle K(\cdot )}$ is the elliptic integral of the first kind.