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Ranks of twists of elliptic curves and Hilbert’s tenth problem

✍ Scribed by B. Mazur; K. Rubin


Publisher
Springer-Verlag
Year
2010
Tongue
English
Weight
775 KB
Volume
181
Category
Article
ISSN
0020-9910

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✍ Gwynneth Coogan; Jorge Jimenéz-Urroz 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 146 KB

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