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 $\mathbf{Z}/3\mathbf{Z} \times \mathbf{Z}/6\mathbf{Z}$
Jukić Bokun, Mirela
Proc. Japan Acad. Ser. A Math. Sci., Tome 87 (2011) no. 1, p. 61-64 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 2011-05-15
Classification:  Elliptic curve,  torsion group,  rank,  11G05,  14H52,  11R11 
@article{1303825547,
     author = {Juki\'c Bokun, Mirela},
     title = {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 $\mathbf{Z}/3\mathbf{Z} \times \mathbf{Z}/6\mathbf{Z}$},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {87},
     number = {1},
     year = {2011},
     pages = { 61-64},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1303825547}
}

Jukić Bokun, Mirela. 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., Tome 87 (2011) no. 1, pp.  61-64. http://gdmltest.u-ga.fr/item/1303825547/