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Plane Quartic Twists of X(5, 3)
Published online by Cambridge University Press: 20 November 2018
Abstract
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Given an odd surjective Galois representation 
$\varrho :{{\text{G}}_{\mathbb{Q}}}\to \text{PG}{{\text{L}}_{2}}\left( {{\mathbb{F}}_{3}} \right)$ and a positive integer 
$N$, there exists a twisted modular curve 
$X{{\left( N,3 \right)}_{\varrho }}$ defined over 
$\mathbb{Q}$ whose rational points classify the quadratic $\mathbb{Q}$-curves of degree $N$ realizing 
$\varrho$. This 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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- Research Article
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- Copyright © Canadian Mathematical Society 2007
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