Functiones et Approximatio Commentarii Mathematici

Points of order $13$ on elliptic curves

Sheldon Kamienny and Burton Newman

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Abstract

We study elliptically parametrized families of elliptic curves with a point of order $13$ that do not arise from rational parametrizations. We also show that no elliptic curve over $\mathbb{Q}(\zeta_{13})^+$ can possess a rational point of order $13$.

Article information

Source
Funct. Approx. Comment. Math., Volume 58, Number 1 (2018), 121-129.

Dates
First available in Project Euclid: 2 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.facm/1512183758

Digital Object Identifier
doi:10.7169/facm/1666

Mathematical Reviews number (MathSciNet)
MR3780039

Zentralblatt MATH identifier
06924921

Subjects
Primary: 11G05: Elliptic curves over global fields [See also 14H52] 11G10: Abelian varieties of dimension > 1 [See also 14Kxx] 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35]

Keywords
elliptic curves torsion subgroups modular curves

Citation

Kamienny, Sheldon; Newman, Burton. Points of order $13$ on elliptic curves. Funct. Approx. Comment. Math. 58 (2018), no. 1, 121--129. doi:10.7169/facm/1666. https://projecteuclid.org/euclid.facm/1512183758


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