On the Mordell–Weil group of the elliptic curve
✍ Scribed by Yasutsugu Fujita; Tadahisa Nara
- Book ID
- 113731091
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 255 KB
- Volume
- 132
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Explicit complex multiplications for some elliptic curves with CM by O=Z[-&10] are given and used to determine the O-module structure of the Mordell Weil groups of the curves over Q(-&10, -5). The Steinitz class of these modules is determined and in particular shown not to be an isogeny invariant.
We construct an elliptic curve defined over Q with Mordell᎐Weil rank G 6 as a generic twist by a certain quadratic extension. Moreover, since they have four independent parameters, they give us rather a large supply of elliptic curves defined over Q with rank G 6. As an application, we find infinite
Motivated by a conjecture of Mazur, Kuwata and Wang proved that for elliptic curves E 1 and E 2 whose j-invariants are not simultaneously 0 or 1728, there exist infinitely many square-free integers d for which the rank of the Mordell-Weil group of the d-quadratic twists of E 1 and E 2 satisfy: rkðE