Plane quartic twists of X(5,3)

2005/01/28 by Julio Fernandez, Fernandez, Julio, Josep Gonzalez +3
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0501520

11 pages, uses xy package

arxiv created 2005/01/28 · arxiv updated 2009/12/01

Abstract

Given an odd representation of the absolute Galois group of Q onto PGL(2,3) and a positive integer N, there exists a twisted modular curve defined over Q whose rational points classify the quadratic Q-curves of degree N realizing the representation. The paper gives a method to provide an explicit plane quartic model for this curve in the genus-three case N=5.

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