Missouri Journal of Mathematical Sciences

Real Preimages of Duplication on Elliptic Curves

John Cullinan

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 2 March 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

real elliptic curve Mordell-Weil Theorem torsion group quartic equation


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

Export citation


  • L. E. Dickson, Elementary Theory of Equations, Wiley, New York, 1914.
  • S. Lang, Elliptic Curves Diophantine Analysis, Grundlehren der Mathematischen Wissenschaften 231, Springer-Verlag, Berlin-New York, 1978.
  • J. H. Silverman, The arithmetic of elliptic curves, Graduate Texts in Mathematics, 106. Springer, Berlin-New York, 2009.
  • Y. Zarhin, Division by 2 on elliptic curves, preprint, posted 30 May, 2016, http://arxiv.org/pdf/1605.09279v1.pdf.