## Functiones et Approximatio Commentarii Mathematici

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

### Points of order $13$ on elliptic curves

Sheldon Kamienny and Burton Newman

#### 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