Rational torsion in complex-multiplication elliptic curves

DOI10.1016/0022-314X(89)90012-7zbMath0703.14023MaRDI QIDQ915806

James L. Parish

Publication date: 1989

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

zbMATH Keywords

fields of rationalitytorsion group on an elliptic curve with complex multiplication

Mathematics Subject Classification ID

Elliptic curves (14H52) Complex multiplication and abelian varieties (14K22)

Related Items (14)

Torsion for CM elliptic curves defined over number fields of degree 2𝑝 ⋮ Galois representations attached to elliptic curves with complex multiplication ⋮ Six unlikely intersection problems in search of effectivity ⋮ The least degree of a CM point on a modular curve ⋮ Odd degree isolated points on \(X_1(N)\) with rational \(j\)-invariant ⋮ Torsion points on CM elliptic curves over real number fields ⋮ Torsion points and isogenies on CM elliptic curves ⋮ A simple proof of a theorem of Parish ⋮ Erratum to: ``The number of twists with large torsion of an elliptic curve ⋮ TORSION POINTS ON ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION (WITH AN APPENDIX BY ALEX RICE) ⋮ On torsion points of certain CM elliptic curves ⋮ On \(\lambda\)-invariants of \(\mathbb{Z}_\ell\)-extensions over real abelian number fields of prime power conductors ⋮ Torsion points and Galois representations on CM elliptic curves ⋮ Fine Selmer Groups and Isogeny Invariance

Cites Work

• Unnamed Item
• Arithmetic on elliptic curves with complex multiplication. With an appendix by B. Mazur
• The arithmetic of elliptic curves
• The Field of Definition of a Variety
• A Family of Abelian Varieties Rationally Isogenous to No Jacobian

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