On the rank of elliptic curves over $\mathbf{Q}(i)$ with torsion group $\mathbf{Z}/4\mathbf{Z} \times \mathbf{Z}/4\mathbf{Z}$
Dujella, Andrej ; Jukić Bokun, Mirela
Proc. Japan Acad. Ser. A Math. Sci., Tome 86 (2010) no. 1, p. 93-96 / Harvested from Project Euclid
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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 $\ge 2$.
Publié le : 2010-06-15
Classification:  Elliptic curve,  torsion group,  rank,  11G05,  14H52,  11R11 
@article{1275486092,
     author = {Dujella, Andrej and Juki\'c Bokun, Mirela},
     title = {On the rank of elliptic curves over $\mathbf{Q}(i)$ with torsion group $\mathbf{Z}/4\mathbf{Z} \times \mathbf{Z}/4\mathbf{Z}$},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {86},
     number = {1},
     year = {2010},
     pages = { 93-96},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1275486092}
}

Dujella, Andrej; Jukić Bokun, Mirela. On the rank of elliptic curves over $\mathbf{Q}(i)$ with torsion group $\mathbf{Z}/4\mathbf{Z} \times \mathbf{Z}/4\mathbf{Z}$. Proc. Japan Acad. Ser. A Math. Sci., Tome 86 (2010) no. 1, pp.  93-96. http://gdmltest.u-ga.fr/item/1275486092/