An exceptional isomorphism between modular curves of level 13

DOI10.1016/j.jnt.2014.05.017zbMath1300.11055OpenAlexW2127251183WikidataQ57534449 ScholiaQ57534449MaRDI QIDQ741683

Burcu Baran

Publication date: 12 September 2014

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2014.05.017

zbMATH Keywords

elliptic curveGalois representationsmodular curvenon-split Cartan group

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (17)

A group theoretic perspective on entanglements of division fields ⋮ Quadratic points on non-split Cartan modular curves ⋮ Semistable reduction of modular curves associated with maximal subgroups in prime level ⋮ Rational points on \(X_0^+(p^r)\) ⋮ Serre’s Constant of Elliptic Curves Over the Rationals ⋮ Automorphisms of Cartan modular curves of prime and composite level ⋮ Odd degree isolated points on \(X_1(N)\) with rational \(j\)-invariant ⋮ Composite images of Galois for elliptic curves over $\mathbf {Q}$ and entanglement fields ⋮ Elliptic curves over \(\mathbb {Q}\) and 2-adic images of Galois ⋮ Computing integral points on \(X_{\mathrm{ns}}^+(p)\) ⋮ GENERALIZED EXPLICIT DESCENT AND ITS APPLICATION TO CURVES OF GENUS 3 ⋮ The generalized Fermat equation with exponents 2, 3, ⋮ Modular forms invariant under non-split Cartan subgroups ⋮ Double covers of Cartan modular curves ⋮ Computing models for quotients of modular curves ⋮ Explicit arithmetic intersection theory and computation of Néron-Tate heights ⋮ Explicit Chabauty-Kim for the split Cartan modular curve of level 13

Cites Work

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• Normalizers of non-split Cartan subgroups, modular curves, and the class number one problem
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• On a result of Imin Chen
• An exceptional isomorphism between level 13 modular curves via Torelli's theorem
• Galois properties of points of finite order of elliptic curves
• Complex Representations of 𝐺𝐿(2,𝐾) for Finite Fields 𝐾
• The Jacobians of Non-Split Cartan Modular Curves

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