Tame Galois realizations of \(\text{GL}_2(\mathbb F_{\ell})\) over \(\mathbb Q\)

DOI10.1016/j.jnt.2008.09.020zbMath1193.11106OpenAlexW2067312586MaRDI QIDQ1017389

Sara Arias-de-Reyna, Núria Vila

Publication date: 19 May 2009

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2008.09.020

zbMATH Keywords

Galois extensiontame ramificationsupersingular elliptic curve

Mathematics Subject Classification ID

Galois theory (11R32) Elliptic curves over global fields (11G05) Galois representations (11F80)

Related Items

Tame torsion and the tame inverse Galois problem, Large Galois images for Jacobian varieties of genus 3 curves, On intersective polynomials with non-solvable Galois group, Tame torsion, the tame inverse Galois problem, and endomorphisms, Formal groups, supersingular abelian varieties and tame ramification

Uses Software

• ecdata

Cites Work

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• Legendre elliptic curves over finite fields
• The existence of infinitely many supersingular primes for every elliptic curve over \(\mathbb Q\).
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• Tame \(A_{n}\)-extensions of \({\mathbb Q}\)
• Class numbers of quadratic fields, Hasse invariants of elliptic curves, and the supersingular polynomial
• Galois properties of points of finite order of elliptic curves
• Congruence properties of special elliptic functions
• Images of mod p Galois Representations Associated to Elliptic Curves
• Counting nilpotent Galois extensions