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Plane quartic twists of X(5,3)

Julio Fernandez·Josep Gonzalez·Joan-C. Lario
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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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Julio Fernandez, Josep Gonzalez, Joan-C. Lario. 2005-01-28. Plane quartic twists of X(5,3). https://arxiv.org/abs/math/0501520

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