Bielliptic quotient modular curves with N square-free

Francesc Bars; Josep González; Mohamed Kamel

doi:10.1016/j.jnt.2020.03.010

Bielliptic quotient modular curves with N square-free

Francesc Bars^*, Josep González, Mohamed Kamel

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

6 Citations (Scopus)

Abstract

Let N≥1 be an square free integer and let W_N be a non-trivial subgroup of the group of the Atkin-Lehner involutions of X₀(N) such that the modular curve X₀(N)/W_N has genus at least two. We determine all pairs (N,W_N) such that X₀(N)/W_N is a bielliptic curve and the pairs (N,W_N) such that X₀(N)/W_N has an infinite number of quadratic points over Q.

Original language	English
Pages (from-to)	380-402
Number of pages	23
Journal	Journal of Number Theory
Volume	216
DOIs	https://doi.org/10.1016/j.jnt.2020.03.010
Publication status	Published - Nov 2020

Keywords

Atkin-Lehner involutions
Bielliptic curves
Modular curves
Quadratic points

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10.1016/j.jnt.2020.03.010

https://ddd.uab.cat/record/240665

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title = "Bielliptic quotient modular curves with N square-free",

abstract = "Let N≥1 be an square free integer and let WN be a non-trivial subgroup of the group of the Atkin-Lehner involutions of X0(N) such that the modular curve X0(N)/WN has genus at least two. We determine all pairs (N,WN) such that X0(N)/WN is a bielliptic curve and the pairs (N,WN) such that X0(N)/WN has an infinite number of quadratic points over Q.",

keywords = "Atkin-Lehner involutions, Bielliptic curves, Modular curves, Quadratic points",

author = "Francesc Bars and Josep Gonz{\'a}lez and Mohamed Kamel",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2020",

month = nov,

doi = "10.1016/j.jnt.2020.03.010",

language = "English",

volume = "216",

pages = "380--402",

journal = "Journal of Number Theory",

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TY - JOUR

T1 - Bielliptic quotient modular curves with N square-free

AU - Bars, Francesc

AU - González, Josep

AU - Kamel, Mohamed

PY - 2020/11

Y1 - 2020/11

N2 - Let N≥1 be an square free integer and let WN be a non-trivial subgroup of the group of the Atkin-Lehner involutions of X0(N) such that the modular curve X0(N)/WN has genus at least two. We determine all pairs (N,WN) such that X0(N)/WN is a bielliptic curve and the pairs (N,WN) such that X0(N)/WN has an infinite number of quadratic points over Q.

AB - Let N≥1 be an square free integer and let WN be a non-trivial subgroup of the group of the Atkin-Lehner involutions of X0(N) such that the modular curve X0(N)/WN has genus at least two. We determine all pairs (N,WN) such that X0(N)/WN is a bielliptic curve and the pairs (N,WN) such that X0(N)/WN has an infinite number of quadratic points over Q.

KW - Atkin-Lehner involutions

KW - Bielliptic curves

KW - Modular curves

KW - Quadratic points

UR - https://www.scopus.com/pages/publications/85084504462

U2 - 10.1016/j.jnt.2020.03.010

DO - 10.1016/j.jnt.2020.03.010

M3 - Article

AN - SCOPUS:85084504462

SN - 0022-314X

VL - 216

SP - 380

EP - 402

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Bielliptic quotient modular curves with N square-free

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Keywords

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