Bielliptic and Hyperelliptic modular curves X(N) and the group Aut(X(N))
  We determine all modular curves X(N) (with $N\geq 7$) which are hyperelliptic or bielliptic. We make available a proof that the automorphism group of X(N) coincides with the normalizer of $\Gamma(N)$ in $\operatorname{PSL}_2(\mathbb{R})$. 
Francesc Bars, Aristides Kontogeorgis and Xavier Xarles
math.NT math.AG