Normalizers of non-split Cartan subgroups, modular curves, and the class number one problem

DOI10.1016/j.jnt.2010.06.005zbMath1236.11094OpenAlexW2025350338MaRDI QIDQ710512

Burcu Baran

Publication date: 19 October 2010

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2010.06.005

zbMATH Keywords

modular curvegenus formulanon-split Cartan subgroup

Mathematics Subject Classification ID

Complex multiplication and moduli of abelian varieties (11G15) Arithmetic aspects of modular and Shimura varieties (11G18) Class numbers, class groups, discriminants (11R29)

Related Items (23)

Congruences of elliptic curves arising from nonsurjective mod 𝑁 Galois representations ⋮ Quadratic points on non-split Cartan modular curves ⋮ Automorphism group of split Cartan modular curves ⋮ On a probabilistic local-global principle for torsion on elliptic curves ⋮ Bounding the $j$-invariant of integral points on $X_{\mathrm {ns}}^{+}(p)$ ⋮ Constraints on the automorphism group of a curve ⋮ Serre’s Constant of Elliptic Curves Over the Rationals ⋮ -adic images of Galois for elliptic curves over (and an appendix with John Voight) ⋮ Automorphisms of Cartan modular curves of prime and composite level ⋮ The automorphism group of the non-split Cartan modular curve of level 11 ⋮ On smooth plane models for modular curves of Shimura type ⋮ ON THE AUTOMORPHISMS OF THE NONSPLIT CARTAN MODULAR CURVES OF PRIME LEVEL ⋮ A MODULI INTERPRETATION FOR THE NON-SPLIT CARTAN MODULAR CURVE ⋮ Elliptic curves over \(\mathbb {Q}\) and 2-adic images of Galois ⋮ A spectral proof of class number one ⋮ Computing integral points on \(X_{\mathrm{ns}}^+(p)\) ⋮ Modular forms invariant under non-split Cartan subgroups ⋮ Double covers of Cartan modular curves ⋮ Computing models for quotients of modular curves ⋮ An exceptional isomorphism between modular curves of level 13 ⋮ A modular curve of level 9 and the class number one problem ⋮ Functions and differentials on the non-split Cartan modular curve of level 11 ⋮ CLASS NUMBER ONE FROM ANALYTIC RANK TWO

Cites Work

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• A modular curve of level 9 and the class number one problem
• On Siegel's modular curve of level 5 and the class number one problem
• On the proof of Stark's theorem
• Galois properties of points of finite order of elliptic curves
• Diophantine analysis and modular forms
• Integral points of a modular curve of level 11
• Some ternary Diophantine equations of signature (n, n, 2)
• A note on the integral points of a modular curve of level 7
• Elliptic curves with nonsplit mod $11$ representations
• On Complex Quadratic Fields with Class Number Equal to One

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