On the rank of elliptic curves over \(\mathbb Q(\sqrt{-3})\) with torsion groups \(\mathbb Z/3\mathbb Z\times\mathbb Z/3\mathbb Z\) and \(\mathbb Z/3\mathbb Z\times \mathbb Z/6\mathbb Z\). (English) Zbl 1281.11056

Jukić Bokun, Mirela

Proc. Japan Acad., Ser. A 87, No. 5, 61-64 (2011).

The author constructs elliptic curves over the field \(\mathbb Q(\sqrt{-3})\) with torsion group \(\mathbb Z/3\mathbb Z\times\mathbb Z/3\mathbb Z\) and ranks equal to 7 and an elliptic curve over the same field with torsion group \(\mathbb Z/3\mathbb Z\times \mathbb Z/6\mathbb Z\) and rank equal to 6. This is an improvement of results of F. P. Rabarison [Acta Arith. 144, No. 1, 17–52 (2010; Zbl 1228.11085)] who constructed elliptic curves with these torsion groups and ranks \(\geq 2\), \(\geq 3\), respectively.

Reviewer: Olaf Ninnemann (Berlin)

MSC:

11G05	Elliptic curves over global fields
14H52	Elliptic curves
11R11	Quadratic extensions

Keywords:

elliptic curve; torsion group; rank

Citations:

Zbl 1228.11085

Software:

APECS; PARI/GP; ecdata

References:

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