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

Francesc Bars, Aristides Kontogeorgis, and Xavier Xarles. "Bielliptic and hyperelliptic modular curves X(N) and the group Aut(X(N))." Acta Arithmetica 161.3 (2013): 283-299. <http://eudml.org/doc/278915>.

@article{FrancescBars2013,
abstract = {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).},
author = {Francesc Bars, Aristides Kontogeorgis, Xavier Xarles},
journal = {Acta Arithmetica},
keywords = {modular curve; automorphism; bielliptic; hyperelliptic; quadratic points},
language = {eng},
number = {3},
pages = {283-299},
title = {Bielliptic and hyperelliptic modular curves X(N) and the group Aut(X(N))},
url = {http://eudml.org/doc/278915},
volume = {161},
year = {2013},
}

TY - JOUR
AU - Francesc Bars
AU - Aristides Kontogeorgis
AU - Xavier Xarles
TI - Bielliptic and hyperelliptic modular curves X(N) and the group Aut(X(N))
JO - Acta Arithmetica
PY - 2013
VL - 161
IS - 3
SP - 283
EP - 299
AB - 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).
LA - eng
KW - modular curve; automorphism; bielliptic; hyperelliptic; quadratic points
UR - http://eudml.org/doc/278915
ER -