## Double Enneper of genus $k$

Drag to Rotate, Scroll the Mouse Wheel to Scale, Ctrl+Drag to Translate.
$k=2$, $a=-0.1$, $b\approx 0.288741$.

### Weierstrass Data

$\overline{M}=\big\{(z,w)\in(\mathbb{C}\cup\{\infty\})^2\;;\;w^{k+1}=z^k(z-b)(1-bz)^k\big\},$ where $k$ is positive integer and $a$, $b$ are constant so that $-1 < -a < 0 < b < 1$. $M=\overline{M}\setminus\{(0,0),\,(\infty ,\infty)\},$ $g=\frac{(az-1)w}{(z-a)(z-b)},\qquad \eta = \frac{(z-a)^2(z-b)}{z^2w}dz.$ For given $k$ and $a$, we can choose $b$ so that $f$ is single valued on $M$.