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On the rank of elliptic curves over \(\mathbb Q(i)\) with torsion group \(\mathbb Z/4\mathbb Z\times \mathbb Z/4\mathbb Z\). (English) Zbl 1217.11058

Summary: We construct an elliptic curve over \(\mathbb Q(i)\) with torsion group \(\mathbb Z/4\mathbb Z \times\mathbb Z/4\mathbb Z\) and rank equal to 7 and a family of elliptic curves with the same torsion group and rank \(\geq 2\).

MSC:

11G05 Elliptic curves over global fields
11Y50 Computer solution of Diophantine equations

Software:

PARI/GP; APECS; ecdata
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Full Text: DOI

References:

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