Using elliptic curves to produce quadratic number fields of high three-rank

DOI10.1216/rmjm/1181069870zbMath1107.11045OpenAlexW1977539495MaRDI QIDQ1880823

Matt Delong

Publication date: 1 October 2004

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181069870

zbMATH Keywords

elliptic curveMordell-Weil groupquadratic fieldSpiegelungssatzShanks' polynomialthree-rank

Mathematics Subject Classification ID

Quadratic extensions (11R11) Elliptic curves over global fields (11G05) Class numbers, class groups, discriminants (11R29)

Related Items (1)

Quadratic fields with a class group of large 3-rank

Cites Work

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• Groupes de Selmer et corps cubiques. (Selmer group and cubic fields)
• Some simple elliptic surfaces of genus zero
• On a parameterized family of quadratic and cubic fields
• New types of quadratic fields having three invariants divisible by 3
• Class Groups of Quadratic Fields
• Über die Beziehung der Klassenzahlen quadratischer Körper zueinander.
• A quadratic field of prime discriminant requiring three generators for its class group, and related theory

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