Bielliptic and hyperelliptic modular curves $X(N)$
and the group $\mathrm {Aut}(X(N))$
Acta Arithmetica, Tome 161 (2013) no. 3, pp. 283-299
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We determine all modular curves $X(N)$ (with $N\geq 7$) that are hyperelliptic or bielliptic. We also give a proof that the automorphism group of $X(N)$ is $\operatorname {PSL}_2(\mathbb {Z}/N\mathbb {Z})$, whence it coincides with the normalizer of $\varGamma (N)$ in $\operatorname {PSL}_2(\mathbb {R})$ modulo $\pm \varGamma (N)$.
Keywords:
determine modular curves geq hyperelliptic bielliptic proof automorphism group operatorname psl mathbb mathbb whence coincides normalizer vargamma operatorname psl mathbb modulo vargamma
Affiliations des auteurs :
Francesc Bars 1 ; Aristides Kontogeorgis 2 ; Xavier Xarles 1
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author = {Francesc Bars and Aristides Kontogeorgis and Xavier Xarles},
title = {Bielliptic and hyperelliptic modular curves $X(N)$
and the group $\mathrm {Aut}(X(N))$},
journal = {Acta Arithmetica},
pages = {283--299},
publisher = {mathdoc},
volume = {161},
number = {3},
year = {2013},
doi = {10.4064/aa161-3-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa161-3-6/}
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AU - Francesc Bars
AU - Aristides Kontogeorgis
AU - Xavier Xarles
TI - Bielliptic and hyperelliptic modular curves $X(N)$
and the group $\mathrm {Aut}(X(N))$
JO - Acta Arithmetica
PY - 2013
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%A Aristides Kontogeorgis
%A Xavier Xarles
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and the group $\mathrm {Aut}(X(N))$
%J Acta Arithmetica
%D 2013
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Francesc Bars; Aristides Kontogeorgis; Xavier Xarles. Bielliptic and hyperelliptic modular curves $X(N)$
and the group $\mathrm {Aut}(X(N))$. Acta Arithmetica, Tome 161 (2013) no. 3, pp. 283-299. doi: 10.4064/aa161-3-6
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