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Construction of elliptic curves with large Iwasawa({lambda})-invariants and large Tate-Shafarevich groups

✍ Scribed by Kazuo Matsuno


Publisher
Springer
Year
2007
Tongue
English
Weight
199 KB
Volume
122
Category
Article
ISSN
0025-2611

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On Elliptic Curves with Large Tate–Shafa
✍ Daisuke Atake 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 167 KB

Generalizing results of Lemmermeyer, we show that the 2-ranks of the Tate Shafarevich groups of quadratic twists of certain elliptic curves with a rational point of order 2 can be arbitrarily large. We use only quadratic residue symbols in a quadratic field to obtain our results.