On Elliptic Curves with Large Tate–Shafa
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Daisuke Atake
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Article
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2001
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Elsevier Science
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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.