Elliptic curves with good reduction everywhere over cubic fields

DOI10.1142/S1793042115500621zbMath1322.11060MaRDI QIDQ5253877

Nao Takeshi

Publication date: 5 June 2015

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

zbMATH Keywords

elliptic curvesabelian varietygood reductioncyclotomic fieldscubic fieldsunit equations

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Linear Diophantine equations (11D04)

Related Items (4)

A survey on the group of points arising from elliptic curves with a Weierstrass model over a ring ⋮ Quadratic fields admitting elliptic curves with rational \(j\)-invariant and good reduction everywhere ⋮ Elliptic curves over the rational numbers with semi-abelian reduction and two-division points ⋮ Family of elliptic curves with good reduction everywhere over number fields of given degree

Cites Work

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• Elliptic curves over complex quadratic fields
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• The Magma algebra system. I: The user language
• Nonexistence of elliptic curves with good reduction everywhere over real quadratic fields
• Abelian varieties over cyclotomic fields with good reduction everywhere
• On the solution of units and index form equations in algebraic number fields
• Good reduction of elliptic curves defined over \({\mathbb Q}(^ 3\sqrt{2})\)
• Potential good reduction of elliptic curves.
• The Arithmetic of Elliptic Curves
• Advanced Topics in Computional Number Theory
• Nonexistence of elliptic curves having good reduction everywhere over certain quadratic fields

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