The function field of $V_\alpha$ is $\mathbb C(t)[W]/(W^2-h_\alpha)$, with $t=X/Y$ and $W\mapsto t(t^m+1)Y$

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The function field of $V_\alpha$ is $\mathbb C(t)[W]/(W^2-h_\alpha)$, with $t=X/Y$ and $W\mapsto t(t^m+1)Y$ · Prove2Me