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We determine all modular curves X(N) (with $N\geq 7$) which are hyperellipticor bielliptic. We make available a proof that the automorphism group of X(N)coincides with the normalizer of $\Gamma(N)$ in$\operatorname{PSL}_2(\mathbb{R})$.

Bielliptic and Hyperelliptic modular curves X(N) and the group Aut(X(N))