Reduction of elliptic curves over imaginary quadratic number fields

DOI10.2140/pjm.1983.108.451zbMath0491.14024OpenAlexW1974328585MaRDI QIDQ1167241

Roelof J. Stroeker

Publication date: 1983

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.pjm/1102720373

zbMATH Keywords

imaginary quadratic number fieldselliptic curve without minimal model

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves (14H52) Cubic and quartic Diophantine equations (11D25) Global ground fields in algebraic geometry (14G25)

Related Items (18)

Curves of genus 2 with good reduction away from 2 with a rational Weierstrass point ⋮ On the existence of abelian surfaces with everywhere good reduction ⋮ Nonexistence of elliptic curves with good reduction everywhere over real quadratic fields ⋮ A survey on the group of points arising from elliptic curves with a Weierstrass model over a ring ⋮ Global Weierstrass equations of hyperelliptic curves ⋮ Elliptic curves with good reduction away from 3 ⋮ Elliptic curves with everywhere good reduction ⋮ 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 ⋮ Elliptic curves over complex quadratic fields ⋮ Elliptic curves over real quadratic fields with everywhere good reduction and a non-trivial 3-division point ⋮ Good reduction of elliptic curves defined over \({\mathbb Q}(^ 3\sqrt{2})\) ⋮ Elliptic curves with good reduction away from 2: II ⋮ Good reduction of elliptic curves over imaginary quadratic fields ⋮ Arithmetic Aspects of Bianchi Groups ⋮ Elliptic curves with good reduction everywhere over cubic fields ⋮ Potential good reduction of elliptic curves. ⋮ Examples of abelian surfaces with everywhere good reduction

Cites Work

• The arithmetic of elliptic curves
• Elliptic curves over complex quadratic fields
• The non-existence of elliptic curves with everywhere good reduction over certain imaginary quadratic fields
• Galois properties of points of finite order of elliptic curves
• The rational solutions of the diophantine equation \(Y^2=X^3-D\)
• Algorithm for determining the type of a singular fiber in an elliptic pencil
• Algebraic Number-Fields with two Independent Units
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