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 $\mathbf{Z}/3\mathbf{Z} \times \mathbf{Z}/6\mathbf{Z}$

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Mirela Jukić Bokun¹ 

[1] Department of Mathematics, University of Osijek

关键词: Elliptic curve;    torsion group;    rank.;   

DOI  :  10.3792/pjaa.87.61

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

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.

【 授权许可】

Unknown