Milan Journal of Mathematics

, Volume 78, Issue 2, pp 395–416

The Tate-Shafarevich Group for Elliptic Curves with Complex Multiplication II


DOI: 10.1007/s00032-010-0127-2

Cite this article as:
Coates, J., Liang, Z. & Sujatha, R. Milan J. Math. (2010) 78: 395. doi:10.1007/s00032-010-0127-2


Using Iwasawa theory, we establish some numerical results, and one weak theoretical result, about the enigmatic Tate-Shafarevich group of an elliptic curve defined over the rational field, with complex multiplication. These strengthen results of this kind proven in an earlier paper of ours.


Elliptic curveTate-Shafarevich groupIwasawa theory

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Emmanuel CollegeCambridgeEngland
  2. 2.Department of MathematicsPOSTECHPohangKorea
  3. 3.School of Mathematical SciencesCapital Normal UniversityBeijingChina
  4. 4.School of MathematicsTIFRMumbaiIndia