• 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