Nonexistence of elliptic curves with good reduction everywhere over real quadratic fields

DOI10.1006/jnth.1997.2177zbMath0895.11023OpenAlexW1982044767MaRDI QIDQ1372588

Masanari Kida, Takaaki Kagawa

Publication date: 18 November 1997

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

Full work available at URL: https://doi.org/10.1006/jnth.1997.2177

zbMATH Keywords

elliptic curvesgood reductionreal quadratic fields

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves (14H52)

Related Items (7)

Reduction of elliptic curves over certain real quadratic number fields ⋮ On the existence of abelian surfaces with everywhere good reduction ⋮ Elliptic curves with everywhere good reduction ⋮ Quadratic fields admitting elliptic curves with rational \(j\)-invariant and good reduction everywhere ⋮ The nonexistence of certain representations of the absolute Galois group of quadratic fields ⋮ Elliptic curves over real quadratic fields with everywhere good reduction and a non-trivial 3-division point ⋮ Elliptic curves with good reduction everywhere over cubic fields

Cites Work

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• Elliptic curves with trivial conductor over quadratic fields
• There are no abelian varieties over \(\mathbb Z\).
• Elliptic curves with good reduction everywhere over quadratic fields and having rational \(j\)-invariant
• Reduction of elliptic curves over imaginary quadratic number fields
• Elliptic curves over complex quadratic fields
• Galois properties of points of finite order of elliptic curves
• On a characterization of Shimura's elliptic curve over ℚ(√37)
• Modular symbols for ₁(N) and elliptic curves with everywhere good reduction

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