On octahedral extensions of and quadratic -curves
Journal de théorie des nombres de Bordeaux (2003)
- Volume: 15, Issue: 1, page 125-131
- ISSN: 1246-7405
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topFernández, Julio. "On octahedral extensions of $\mathbb {Q}$ and quadratic $\mathbb {Q}$-curves." Journal de théorie des nombres de Bordeaux 15.1 (2003): 125-131. <http://eudml.org/doc/249076>.
@article{Fernández2003,
abstract = {We give a necessary condition for a surjective representation Gal$(\overline\{\mathbb \{Q\}\} /\mathbb \{Q\}) \rightarrow \mathrm \{PGL\}_2(\mathbb \{F\}_3)$ to arise from the $3$-torsion of a $\mathbb \{Q\}$-curve. We pay a special attention to the case of quadratic $\mathbb \{Q\}$-curves.},
author = {Fernández, Julio},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {elliptic curve; trace form; discriminant; Witt invariant},
language = {eng},
number = {1},
pages = {125-131},
publisher = {Université Bordeaux I},
title = {On octahedral extensions of $\mathbb \{Q\}$ and quadratic $\mathbb \{Q\}$-curves},
url = {http://eudml.org/doc/249076},
volume = {15},
year = {2003},
}
TY - JOUR
AU - Fernández, Julio
TI - On octahedral extensions of $\mathbb {Q}$ and quadratic $\mathbb {Q}$-curves
JO - Journal de théorie des nombres de Bordeaux
PY - 2003
PB - Université Bordeaux I
VL - 15
IS - 1
SP - 125
EP - 131
AB - We give a necessary condition for a surjective representation Gal$(\overline{\mathbb {Q}} /\mathbb {Q}) \rightarrow \mathrm {PGL}_2(\mathbb {F}_3)$ to arise from the $3$-torsion of a $\mathbb {Q}$-curve. We pay a special attention to the case of quadratic $\mathbb {Q}$-curves.
LA - eng
KW - elliptic curve; trace form; discriminant; Witt invariant
UR - http://eudml.org/doc/249076
ER -
References
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- [8] J.-P. Serre, Modular forms of weight one and Galois representations. Algebraic number fields: L-functions and Galois properties (Proc. Sympos., Univ. Durham, Durham, 1975), Academic Press, London, 1977, pp. 193-268. Zbl0366.10022MR450201
- [9] J.-P. Serre, L'invariant de Witt de la forme Tr(x2). Comment. Math. Helv.59 (1984), no. 4, 651-676. Zbl0565.12014MR780081
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