On the rank of elliptic curves over $\mathbf{Q}(i)$ with torsion group $\mathbf{Z}/4\mathbf{Z} \times \mathbf{Z}/4\mathbf{Z}$

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Andrej Dujella¹  Mirela Jukić Bokun² 

[1] Department of Mathematics, University of Zagreb;Department of Mathematics, University of Osijek

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

DOI  :  10.3792/pjaa.86.93

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

We construct an elliptic curve over $\mathbf{Q}(i)$ with torsion group $\mathbf{Z}/4\mathbf{Z} \times \mathbf{Z}/4\mathbf{Z}$ and rank equal to 7 and a family of elliptic curves with the same torsion group and rank $\ge 2$.

【 授权许可】

Unknown