= Four totally ramified Weierstrass values
{title2=$e_1,e_2,e_3,\infty$}
The <Weierstrass elliptic function> has degree two on its period torus. Its three distinct half-period values $e_j$ have double local preimages, and its <pole> is double, so these four values are totally ramified. This also follows from $\wp'^2=4\prod_j(\wp-e_j)$ and the principal part at the <pole>. A <Möbius transformation> with <pole> away from these values moves all four to finite values without changing local degrees.
Back to article page
