Let $\mathrm{\wp }(z)$ be a Weierstrauss $\mathrm{\wp }$-function. Then ${\mathrm{\wp }}^{\prime }(z)$ is 1;;elliptic and odd, and $\mathrm{\wp }(z)$ is elliptic.

PROOF:

1. Differentiate $\mathrm{\wp }(z)$ termwise by Weierstrauss.
2. Conclude that $\mathrm{\wp }(z+w_1)-\mathrm{\wp }(z)=c_1$ for some constant, and use evenness of $\mathrm{\wp }$ to show that $c_1$ is 0. Similar for ${\omega }_2$.