Bielliptic and hyperelliptic modular curves X(N) and the group Aut(X(N))
Francesc Bars ; Aristides Kontogeorgis ; Xavier Xarles
Acta Arithmetica, Tome 161 (2013), p. 283-299 / Harvested from The Polish Digital Mathematics Library
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We determine all modular curves X(N) (with N ≥ 7) that are hyperelliptic or bielliptic. We also give a proof that the automorphism group of X(N) is PSL₂(ℤ/Nℤ), whence it coincides with the normalizer of Γ(N) in PSL₂(ℝ) modulo ±Γ(N).

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:278915 
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     author = {Francesc Bars and Aristides Kontogeorgis and Xavier Xarles},
     title = {Bielliptic and hyperelliptic modular curves X(N) and the group Aut(X(N))},
     journal = {Acta Arithmetica},
     volume = {161},
     year = {2013},
     pages = {283-299},
     zbl = {1304.11052},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-3-6}
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Francesc Bars; Aristides Kontogeorgis; Xavier Xarles. Bielliptic and hyperelliptic modular curves X(N) and the group Aut(X(N)). Acta Arithmetica, Tome 161 (2013) pp. 283-299. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-3-6/