Galois representations of octahedral type and 2-coverings of elliptic curves

DOI10.1007/BF02571397zbMath0712.11035OpenAlexW1969407705MaRDI QIDQ1812965

Pilar Bayer, Gerhard Frey

Publication date: 25 June 1992

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174278

zbMATH Keywords

Galois representationsArtin L-series2- coverings of elliptic curvesalgorithm due to Birch and Swinnerton-Dyerconstruction of cusp forms of weight 1 and type \(S_ 4\)octahedral type

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Coverings of curves, fundamental group (14H30) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items

A Note on Regular Crossed Products and Galois Representations ⋮ Formes primitives et représentations galoisiennes de type octaédral ⋮ Construction of a cuspform of weight 3/2 ⋮ On modular mod \(\ell\) Galois representations with exceptional images ⋮ On the embedding problem for $2^+S_4$ representations ⋮ \(S_4\) and \(\widetilde{S}_4\) extensions of \(\mathbb{Q}\) ramified at only one prime ⋮ Exceptional congruences for the coefficients of certain eta-product newforms.

Cites Work

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• Explicit construction of \(2S_ n\) Galois extensions
• The Witt invariant of the form \(\text{Tr}(x^ 2)\)
• Modular functions of one variable. IV. Proceedings of the international summer school, University of Antwerp, RUCA, July 17 -- August 3, 1972
• Artin’s conjecture for representations of octahedral type
• Formes modulaires de poids $1$
• Diophantine Equations with Special Reference To Elliptic Curves
• Notes on elliptic curves. I.