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On several families of elliptic curves with arbitrary large Selmer groups

✍ Scribed by Fei Li; DeRong Qiu

Book ID
107348268
Publisher
SP Science China Press
Year
2010
Tongue
English
Weight
260 KB
Volume
53
Category
Article
ISSN
1674-7283

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On Elliptic Curves with Large Tate–Shafa
On Elliptic Curves with Large Tate–Shafarevich Groups
✍ Daisuke Atake πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 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.