Kusner's projective plane with $2n+1$ ends

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$n=1$

Weierstrass Data (Double Cover of the Surface)

\[ M=(\mathbb{C}\cup\{\infty\}\setminus\{z\in\mathbb{C}\;;\;nz^{4n+2}+\sqrt{4n+1}z^{2n+1}-n=0\}, \] where $n$ is a positive integer. \[ g=z^{2n}\frac{z^{2n+1}-\sqrt{4n+1}}{\sqrt{4n+1}z^{2n+1}+1},\qquad \eta = i\frac{(\sqrt{4n+1}z^{2n+1}+1)^2}{(nz^{4n+2}+\sqrt{4n+1}z^{2n+1}-n)^2}dz. \]