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

Francesc Bars; Aristides Kontogeorgis; Xavier Xarles

Acta Arithmetica (2013)

- Volume: 161, Issue: 3, page 283-299
- ISSN: 0065-1036

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topFrancesc 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 -

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