Torsion groups of elliptic curves with integral j-invariant over pure cubic fields

DOI10.1016/0022-314X(90)90003-AzbMath0734.14014MaRDI QIDQ810606

Horst G. Zimmer, H. Ströher, Gilbert Fung, Hugh C. Williams

Publication date: 1990

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

zbMATH Keywords

pure cubic number fieldstorsion groups of elliptic curves with integral j-invariant

Mathematics Subject Classification ID

Elliptic curves (14H52) Computational aspects of algebraic curves (14Q05) Cubic and quartic extensions (11R16) Global ground fields in algebraic geometry (14G25)

Related Items (10)

Torsion groups of elliptic curves over ℚ(μp∞) ⋮ Torsion growth over number fields of degree \(pq\) ⋮ On the torsion of rational elliptic curves over quartic fields ⋮ TORSION POINTS ON ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION (WITH AN APPENDIX BY ALEX RICE) ⋮ Explicit characterization of the torsion growth of rational elliptic curves with complex multiplication over quadratic fields ⋮ Complete classification of the torsion structures of rational elliptic curves over quintic number fields ⋮ Elliptic curves in Huff’s model ⋮ On the torsion of rational elliptic curves over sextic fields ⋮ Torsion of elliptic curves with rational 𝑗-invariant defined over number fields of prime degree ⋮ On cubic exceptional units

Cites Work

• Some aspects of the theory of elliptic curves over number fields
• The arithmetic of elliptic curves
• Some remarks concerning points of finite order on elliptic curves over global fields
• Modèles minimaux des variétés abéliennes sur les corps locaux et globaux
• An elementary proof of the Riemann hypothesis for an elliptic curve over a finite field
• Algorithm for determining the type of a singular fiber in an elliptic pencil
• Explicit determination of nontrivial torsion structures of elliptic curves over quadratic number fields
• Calculation of the Regulator of a Pure Cubic Field
• Universal Bounds on the Torsion of Elliptic Curves
• Diophantine Equations with Special Reference To Elliptic Curves
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