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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Xiong, Maosheng 2013. ON SELMER GROUPS OF QUADRATIC TWISTS OF ELLIPTIC CURVES WITH A TWO-TORSION OVER. Mathematika, Vol. 59, Issue. 02, p. 303.


    Feng, Keqin and Xiong, Maosheng 2012. ON SELMER GROUPS AND TATE–SHAFAREVICH GROUPS FOR ELLIPTIC CURVES y 2=x 3−n 3. Mathematika, Vol. 58, Issue. 02, p. 236.


    Shparlinski, Igor E. 2012. Modular hyperbolas. Japanese Journal of Mathematics, Vol. 7, Issue. 2, p. 235.


    ROLEN, LARRY 2011. A GENERALIZATION OF THE CONGRUENT NUMBER PROBLEM. International Journal of Number Theory, Vol. 07, Issue. 08, p. 2237.


    Xiong, Maosheng and Zaharescu, Alexandru 2008. Distribution of Selmer groups of quadratic twists of a family of elliptic curves. Advances in Mathematics, Vol. 219, Issue. 2, p. 523.


    Chang, Sungkon 2006. Note on the rank of quadratic twists of Mordell equations. Journal of Number Theory, Vol. 118, Issue. 1, p. 53.


    Yu, Gang 2005. On the Quadratic Twists of a Family of Elliptic Curves. Mathematika, Vol. 52, Issue. 1-2, p. 139.


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Rank 0 Quadratic Twists of a Family of Elliptic Curves

  • Gang Yu (a1)
  • DOI: http://dx.doi.org/10.1023/A:1022258905572
  • Published online: 01 February 2003
Abstract

In this paper, we consider a family of elliptic curves over ${\open Q}$ with 2-torsion part ${\open Z}_2$. We prove that, for every such elliptic curve, a positive proportion of quadratic twists have Mordell–Weil rank 0.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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