BIELLIPTIC QUOTIENT MODULAR CURVES OF X0(N)

Francesc Bars; Mohamed Kamel; Andreas Schweizer

doi:10.1090/mcom/3800

BIELLIPTIC QUOTIENT MODULAR CURVES OF X0(N)

Francesc Bars^*, Mohamed Kamel, Andreas Schweizer

^*Autor corresponent d’aquest treball

Departament de Matemàtiques

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Abstract. Let N ≥ 1 be a non-square free integer and let WN be a nontrivial 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.

Idioma original	Anglès
Pàgines (de-a)	895-929
Nombre de pàgines	35
Revista	Mathematics of Computation
Volum	92
Número	340
DOIs	https://doi.org/10.1090/mcom/3800
Estat de la publicació	Publicada - de març 2023

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10.1090/mcom/3800

https://ddd.uab.cat/record/270703

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abstract = "Abstract. Let N ≥ 1 be a non-square free integer and let WN be a nontrivial 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.",

author = "Francesc Bars and Mohamed Kamel and Andreas Schweizer",

note = "Publisher Copyright: {\textcopyright} 2022 American Mathematical Society",

year = "2023",

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AU - Kamel, Mohamed

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N2 - Abstract. Let N ≥ 1 be a non-square free integer and let WN be a nontrivial 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 - Abstract. Let N ≥ 1 be a non-square free integer and let WN be a nontrivial 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.

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U2 - 10.1090/mcom/3800

DO - 10.1090/mcom/3800

M3 - Article

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JO - Mathematics of Computation

JF - Mathematics of Computation

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ER -

BIELLIPTIC QUOTIENT MODULAR CURVES OF X0(N)

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