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On Elliptic Curves with Large Tate–Shafarevich Groups

✍ Scribed by Daisuke Atake

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
167 KB
Volume
87
Category
Article
ISSN
0022-314X

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✦ Synopsis

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.

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