Elliptic Curves and Class Fields of Real Quadratic Fields: Algorithms and Evidence

DOI10.1080/10586458.2002.10504467zbMath1040.11048OpenAlexW1969445076MaRDI QIDQ4804801

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Publication date: 30 September 2003

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/50803

zbMATH Keywords

algorithmsStark-Heegner pointsanalogue of the Shimura reciprocity lawGross-Zagier conjectures

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items

The rationality of Stark-Heegner points over genus fields of real quadratic fields ⋮ Overconvergent cohomology and quaternionic Darmon points ⋮ Darmon points on elliptic curves over number fields of arbitrary signature ⋮ Stark–Heegner points on modular Jacobians ⋮ Arithmetic twists and Abelian extensions ⋮ Efficient calculation of Stark-Heegner points via overconvergent modular symbols ⋮ Lifting modular symbols of non-critical slope ⋮ Elementary matrix decomposition and the computation of Darmon points with higher conductor

Uses Software

• ecdata

Cites Work

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• On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer
• Heegner points and derivatives of \(L\)-series
• Refined conjectures of the ``Birch and Swinnerton-Dyer type
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• \(p\)-adic periods and modular symbols of elliptic curves of prime conductor
• \(p\)-adic \(L\)-functions and \(p\)-adic periods of modular forms
• Integration on \({\mathcal H_p}\times\mathcal H\) and arithmetic applications.