Geodesic
Plane Quartic Twists of X(5, 3)
Canadian mathematical bulletin, Tome 50 (2007) no. 2, pp. 196-205

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DOI

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 $N=5$ .
DOI : 10.4153/CMB-2007-021-8
Mots-clés : 11F03, 11F80, 14G05 
Fernández, Julio; González, Josep; Lario, Joan-C. Plane Quartic Twists of X(5, 3). Canadian mathematical bulletin, Tome 50 (2007) no. 2, pp. 196-205. doi: 10.4153/CMB-2007-021-8
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     author = {Fern\'andez, Julio and Gonz\'alez, Josep and Lario, Joan-C.},
     title = {Plane {Quartic} {Twists} of {X(5,} 3)},
     journal = {Canadian mathematical bulletin},
     pages = {196--205},
     year = {2007},
     volume = {50},
     number = {2},
     doi = {10.4153/CMB-2007-021-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-021-8/}
}
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