= Degree-two even elliptic function
{title2=$f=(a\wp+b)/(c\wp+d)$}
An even <elliptic function> descends through the degree-two quotient map $\wp$ to a <rational function> $R$ on the <Riemann sphere>. If the original function also has degree two, composition of map degrees gives $2=2\deg R$, so $R$ has degree one. Consequently it is a <Möbius transformation> with $ad-bc\ne0$. The shift $\operatorname{sn}(z+K,k)$ is even and has degree two, providing an example for the common <period lattice> of the <Jacobi elliptic sine> and $\wp$.
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