Plane quartic twists of X(5,3)

Details Plane quartic twists of X(5,3) Plane quartic twists of X(5,3)

2005-01-28

arxiv.org/abs/math/0501520v1

Mathematics

Number Theory

11 pages, uses xy package

Scientific paper

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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