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May 2011 On the rank of elliptic curves over $\mathbf{Q}(\sqrt{-3})$ with torsion groups $\mathbf{Z}/3\mathbf{Z} \times \mathbf{Z}/3\mathbf{Z}$ and $\mathbf{Z}/3\mathbf{Z} \times \mathbf{Z}/6\mathbf{Z}$
Mirela Jukić Bokun
Proc. Japan Acad. Ser. A Math. Sci. 87(5): 61-64 (May 2011). DOI: 10.3792/pjaa.87.61

Abstract

We construct elliptic curves over the field $\mathbf{Q}(\sqrt{-3})$ with torsion group $\mathbf{Z}/3\mathbf{Z} \times \mathbf{Z}/3\mathbf{Z}$ and ranks equal to 7 and an elliptic curve over the same field with torsion group $\mathbf{Z}/3\mathbf{Z} \times \mathbf{Z}/6\mathbf{Z}$ and rank equal to 6.

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Mirela Jukić Bokun. "On the rank of elliptic curves over $\mathbf{Q}(\sqrt{-3})$ with torsion groups $\mathbf{Z}/3\mathbf{Z} \times \mathbf{Z}/3\mathbf{Z}$ and $\mathbf{Z}/3\mathbf{Z} \times \mathbf{Z}/6\mathbf{Z}$." Proc. Japan Acad. Ser. A Math. Sci. 87 (5) 61 - 64, May 2011. https://doi.org/10.3792/pjaa.87.61

Information

Published: May 2011
First available in Project Euclid: 26 April 2011

zbMATH: 1281.11056
MathSciNet: MR2803891
Digital Object Identifier: 10.3792/pjaa.87.61

Subjects:
Primary: 11G05 , 11R11 , 14H52

Keywords: Elliptic curve , ‎rank‎ , torsion group

Rights: Copyright © 2011 The Japan Academy

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Vol.87 • No. 5 • May 2011
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