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December 2021 Elliptic curves with a point of order $13$ defined over cyclic cubic fields
Peter Bruin, Maarten Derickx, Michael Stoll
Funct. Approx. Comment. Math. 65(2): 191-197 (December 2021). DOI: 10.7169/facm/1945

Abstract

We show that there is essentially a unique elliptic curve $E$ defined over a cubic Galois extension $K$ of $\mathbb{Q}$ with a $K$-rational point of order $13$ and such that $E$ is not defined over $\mathbb{Q}$.

Citation

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Peter Bruin. Maarten Derickx. Michael Stoll. "Elliptic curves with a point of order $13$ defined over cyclic cubic fields." Funct. Approx. Comment. Math. 65 (2) 191 - 197, December 2021. https://doi.org/10.7169/facm/1945

Information

Published: December 2021
First available in Project Euclid: 13 October 2021

Digital Object Identifier: 10.7169/facm/1945

Subjects:
Primary: 11G05 , 14G05 , 14G25 , 14H52

Keywords: cyclic cubic fields , Elliptic curves , torsion points

Rights: Copyright © 2021 Adam Mickiewicz University

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Vol.65 • No. 2 • December 2021
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