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

Francesc Bars; Aristides Kontogeorgis; Xavier Xarles

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

Number Theory 2013-05-08 v2 Algebraic Geometry

Authors: Francesc Bars , Aristides Kontogeorgis , Xavier Xarles

Abstract

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 $\operatorname{PSL}_2(\mathbb{R})$ .

Keywords

modular curves hyperelliptic curves bielliptic curves automorphism group normalizer congruence subgroup

Cite

@article{arxiv.1207.2273,
  title  = {Bielliptic and Hyperelliptic modular curves X(N) and the group Aut(X(N))},
  author = {Francesc Bars and Aristides Kontogeorgis and Xavier Xarles},
  journal= {arXiv preprint arXiv:1207.2273},
  year   = {2013}
}

Comments

Corrected typos. Reorganized the whole paper. Main results unchanged

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

Abstract

Keywords

Cite

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