Even elliptic functions are rational in the Weierstrass function
= Even elliptic functions are rational in the Weierstrass function
{title2=$f(-z)=f(z)\Longrightarrow f=Q(\wp)$}
The <Weierstrass elliptic function> is the quotient map from the complex torus by $z\mapsto-z$. An even <elliptic function> descends through this map; its even Laurent series at each branch point makes the descended function meromorphic there. A <meromorphic function> on the <Riemann sphere> is rational, so $f=Q(\wp)$.