Degrees of parametrizations of elliptic curves by Shimura curves

DOI10.1006/jnth.2000.2614zbMath0997.11043OpenAlexW2024902951MaRDI QIDQ5949912

Shuzo Takahashi

Publication date: 5 December 2001

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

Full work available at URL: https://doi.org/10.1006/jnth.2000.2614

zbMATH Keywords

Néron modelShimura curveEichler orderisogeny class of elliptic curvesmodular curveNéron fibers

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Arithmetic ground fields for curves (14H25) Congruences for modular and (p)-adic modular forms (11F33) Arithmetic aspects of modular and Shimura varieties (11G18) Global ground fields in algebraic geometry (14G25)

Related Items (5)

Shimura curves and the abc conjecture ⋮ On the quantitative variation of congruence ideals and integral periods of modular forms ⋮ On a theorem of Bertolini-Darmon on the rationality of Stark-Heegner points over genus fields of real quadratic fields ⋮ On anticyclotomic μ-invariants of modular forms ⋮ On the \(p\)-adic Birch and Swinnerton-Dyer conjecture for elliptic curves over number fields

Uses Software

• ecdata

Cites Work

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• Finiteness theorems for abelian varieties over number fields.
• A rigid analytic Gross-Zagier formula and arithmetic applications. (With an appendix by B. Edixhoven)
• Integral models of certain Shimura curves
• On modular representations of \(\text{Gal}(\overline{\mathbb Q}/\mathbb Q)\) arising from modular forms
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• Integral Hodge theory and congruences between modular forms
• \(p\)-adic periods, \(p\)-adic \(L\)-functions, and the \(p\)-adic uniformization of Shimura curves.
• Automorphic forms on GL (2)
• Courbes de Weil semi-stables de discriminant une puissance m-ième.
• Modular Parametrizations of Elliptic Curves
• Parametrizations of elliptic curves by Shimura curves and by classical modular curves
• Les Schémas de Modules de Courbes Elliptiques

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