## Missouri Journal of Mathematical Sciences

- Missouri J. Math. Sci.
- Volume 29, Issue 1 (2017), 19-26.

### Real Preimages of Duplication on Elliptic Curves

#### Abstract

Let $E$ be an elliptic curve defined over the real numbers $R$ and let $P \in E(R)$. In this note we give an elementary proof of necessary and sufficient conditions for the preimages of $P$ under duplication to be real-valued.

#### Article information

**Source**

Missouri J. Math. Sci., Volume 29, Issue 1 (2017), 19-26.

**Dates**

First available in Project Euclid: 2 March 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.mjms/1488423698

**Digital Object Identifier**

doi:10.35834/mjms/1488423698

**Mathematical Reviews number (MathSciNet)**

MR3619772

**Zentralblatt MATH identifier**

06759818

**Subjects**

Primary: 11G05: Elliptic curves over global fields [See also 14H52]

**Keywords**

real elliptic curve Mordell-Weil Theorem torsion group quartic equation

#### Citation

Cullinan, John. Real Preimages of Duplication on Elliptic Curves. Missouri J. Math. Sci. 29 (2017), no. 1, 19--26. doi:10.35834/mjms/1488423698. https://projecteuclid.org/euclid.mjms/1488423698