Bielliptic quotient modular curves of 𝑋₀(𝑁)

Author:

Bars Francesc,Kamel Mohamed,Schweizer Andreas

Abstract

Let N 1 N\geq 1 be a non-square free integer and let W N W_N be a nontrivial subgroup of the group of the Atkin-Lehner involutions of X 0 ( N ) X_0(N) such that the modular curve X 0 ( N ) / W N X_0(N)/W_N has genus at least two. We determine all pairs ( N , W N ) (N,W_N) such that X 0 ( N ) / W N X_0(N)/W_N is a bielliptic curve and the pairs ( N , W N ) (N,W_N) such that X 0 ( N ) / W N X_0(N)/W_N has an infinite number of quadratic points over Q \mathbb {Q} .

Funder

Ministerio de Ciencia e Innovación

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference24 articles.

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1. Modular curves $$X_0(N)$$ with infinitely many quartic points;Research in Number Theory;2024-04-08

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