Proving modularity for a given elliptic curve over an imaginary quadratic field

DOI10.1090/S0025-5718-09-02291-1zbMath1227.11073arXiv0804.2302OpenAlexW1971372964MaRDI QIDQ3584823

Lucio Guerberoff, Ariel Pacetti, Luis V. Dieulefait

Publication date: 30 August 2010

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.2302

zbMATH Keywords

elliptic curvemodularity

Mathematics Subject Classification ID

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

Related Items

Computing systems of Hecke eigenvalues associated to Hilbert modular forms ⋮ Black box Galois representations ⋮ Theta lifts of Bianchi modular forms and applications to paramodularity ⋮ Uniformization of modular elliptic curves via \(p\)-adic periods ⋮ On the effective version of Serre's open image theorem ⋮ On elliptic curves of prime power conductor over imaginary quadratic fields with class number 1 ⋮ Faltings-Serre method on three dimensional selfdual representations ⋮ The \(L\)-functions and Modular Forms Database project ⋮ Modular elliptic curves over the field of twelfth roots of unity ⋮ Hilbert modularity of some double octic Calabi-Yau threefolds ⋮ Cohomology with twisted one-dimensional coefficients for congruence subgroups of \(\operatorname{SL}_4(\mathbb{Z})\) and Galois representations ⋮ On the paramodularity of typical abelian surfaces ⋮ Examples of genuine QM abelian surfaces which are modular ⋮ Arithmetic Aspects of Bianchi Groups ⋮ On an elliptic curve defined over $\mathbb {Q}(\sqrt {-23})$

Uses Software

• PARI/GP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(l\)-adic representations associated to modular forms over imaginary quadratic fields. I: Lifting to \(GSp_ 4(\mathbb{Q})\)
• \(l\)-adic representations associated to modular forms over imaginary quadratic fields. II
• On the Modularity of Three Calabi–Yau Threefolds With Bad Reduction at 11
• Abelian Varieties with Extra Twist, Cusp Forms, and Elliptic Curves Over Imaginary Quadratic Fields
• Periods of Cusp Forms and Elliptic Curves Over Imaginary Quadratic Fields
• Advanced Topics in Computional Number Theory
• ℓ-adic Representations Associated to Modular Forms over Imaginary Quadratic Fields