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Plane Quartic Twists of $X(5,3)$ |
Canad. Math. Bull. 50(2007), 196-205
Published:2007-06-01
Printed: Jun 2007
Printed: Jun 2007
- Julio Fernández
- Josep González
- Joan-C. Lario
Abstract
Given an odd surjective Galois representation $\varrho\from \G_\Q\to\PGL_2(\F_3)$ and a
positive integer~$N$, there exists a twisted modular curve $X(N,3)_\varrho$
defined over $\Q$ whose rational points classify the quadratic $\Q$-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 $N=5$.
| MSC Classifications: |
11F03 - Modular and automorphic functions 11F80 - Galois representations 14G05 - Rational points |