Functiones et Approximatio Commentarii Mathematici

On torsion points of certain CM elliptic curves

Naoki Murabayashi

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Abstract

Let $E$ be a CM elliptic curve defined over an algebraic number field $F$ with CM by an imaginary quadratic field $K$. We determine the group of $K_{ab}F$-rational torsion points of $E$. In some cases we also determine the group of $F$ or $KF$-rational torsion points of $E$.

Article information

Source
Funct. Approx. Comment. Math., Volume 47, Number 1 (2012), 89-93.

Dates
First available in Project Euclid: 25 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.facm/1348578279

Digital Object Identifier
doi:10.7169/facm/2012.47.1.8

Mathematical Reviews number (MathSciNet)
MR2987113

Zentralblatt MATH identifier
1290.11098

Subjects
Primary: 11G15: Complex multiplication and moduli of abelian varieties [See also 14K22]
Secondary: 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35]

Keywords
modularity CM elliptic curves torsion points.

Citation

Murabayashi, Naoki. On torsion points of certain CM elliptic curves. Funct. Approx. Comment. Math. 47 (2012), no. 1, 89--93. doi:10.7169/facm/2012.47.1.8. https://projecteuclid.org/euclid.facm/1348578279


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References

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