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

Andrej Dujella; Mirela Jukić Bokun

doi:10.3792/pjaa.86.93

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June 2010 On the rank of elliptic curves over $\mathbf{Q}(i)$ with torsion group $\mathbf{Z}/4\mathbf{Z} \times \mathbf{Z}/4\mathbf{Z}$

Andrej Dujella, Mirela Jukić Bokun

Proc. Japan Acad. Ser. A Math. Sci. 86(6): 93-96 (June 2010). DOI: 10.3792/pjaa.86.93

Abstract

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 $\ge 2$.

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Andrej Dujella. Mirela Jukić Bokun. "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. 86 (6) 93 - 96, June 2010. https://doi.org/10.3792/pjaa.86.93