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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

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📜 SIMILAR VOLUMES


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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.

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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