Fujimori-Shoda of genus $k$
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$k=2$, $a\approx 1.77968$.
Weierstrass Data
\[ \overline{M}=\left\{(z,w)\in(\mathbb{C}\cup\{\infty\})^2\;;\;w^{k+1}=z^2\left(\frac{z-1}{z-a}\right)^k\right\}, \] where $k$ is positive even integer and $a$ is a constant so that \( a > 1 \). \[ M=\overline{M}\setminus\{(0,0),\,(\infty ,\infty)\}, \] \[ g=a^{(k-2)/(2k+2)}w,\qquad \eta = \frac{dz}{zw}. \] For given $k$, we can choose $a$ so that $f$ is single valued on $M$.
