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2018 Torsion of elliptic curves over imaginary quadratic fields of class number 1
Naba Kanta Sarma, Anupam Saikia
Rocky Mountain J. Math. 48(8): 2689-2703 (2018). DOI: 10.1216/RMJ-2018-48-8-2689

Abstract

Filip Najman examined the possibilities for the group of torsion points on elliptic curves over the number fields $\mathbb {Q}(\sqrt {-1})$ and $\mathbb {Q}(\sqrt {-3})$ in Najman (2011, 2010). In this article, we study the possible torsion structures of elliptic curves over the remaining imaginary quadratic fields of class numbers $1$, i.e., over the fields $\mathbb {Q}(\sqrt {-2})$, $\mathbb {Q}(\sqrt {-7})$, $\mathbb {Q}(\sqrt {-11})$, $\mathbb {Q}(\sqrt {-19})$, $\mathbb {Q}(\sqrt {-43})$, $\mathbb {Q}(\sqrt {-67})$ and $\mathbb {Q}(\sqrt {-163})$.

Citation

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Naba Kanta Sarma. Anupam Saikia. "Torsion of elliptic curves over imaginary quadratic fields of class number 1." Rocky Mountain J. Math. 48 (8) 2689 - 2703, 2018. https://doi.org/10.1216/RMJ-2018-48-8-2689

Information

Published: 2018
First available in Project Euclid: 30 December 2018

zbMATH: 06999280
MathSciNet: MR3894999
Digital Object Identifier: 10.1216/RMJ-2018-48-8-2689

Subjects:
Primary: 11G05
Secondary: 11G18

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 8 • 2018
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