Title of article
On Elliptic Curves with Large Tate–Shafarevich Groups Original Research Article
Author/Authors
Daisuke Atake، نويسنده ,
Issue Information
روزنامه با شماره پیاپی سال 2001
Pages
19
From page
282
To page
300
Abstract
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.
Keywords
Tate Shafarevich group , Elliptic Curve , quadratic field , quadratic residuesymbol.
Journal title
Journal of Number Theory
Serial Year
2001
Journal title
Journal of Number Theory
Record number
715180
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