Skip to main content
SpringerLink
Log in

On the Birch-Swinnerton-Dyer Conjecture of Elliptic Curves E D : y 2 = x 3−D 2 x

  • ORIGINAL ARTICLES
  • Published:
Acta Mathematica Sinica Aims and scope Submit manuscript

Abstract

We prove in this paper that the BSD conjecture holds for a certain kind of elliptic curves.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J H Silverman. The Arithmetic of Elliptic Curves. Springer-Verlag, 1986

  2. J Tunell. A classical Diophantine problem and modular form of weight 3=2. Invent Math, 1983, 72:323-334

    Article  MathSciNet  Google Scholar 

  3. C Zhao. For Elliptic curves with second lowest two-power in L(1). Communication

  4. K Rubin. Tate-Shafarevich group and L-function of elliptic curves with complex multiplication. Invent Math, 1987, 89:527-560

    Article  MATH  MathSciNet  Google Scholar 

  5. K Rubin. The main conjecture for imaginary quadratic fields. Invent Math, 1991, 103:25-68

    Article  MATH  MathSciNet  Google Scholar 

  6. K Feng. Noz-congruent numbers, odd graphs and the Birch-Swinnerton-Dyer conjecture. Acta Arithmetic, 1996, XXV 1

  7. J A Bondy, U S R Murty. Graph theory with applications. The Macmillan Press LTD, 1976

  8. W Koblit. Introduction to Elliptic Curves and Modular Forms. Springer-Verlag, 1984

  9. B Birch, H P F Swinnerton-Dyer. Notes on elliptic curves (II). J Reine Angew Math, 1965, 218:79-108

    MATH  MathSciNet  Google Scholar 

  10. J P Serre. A course in Arithmetic. Springer-Verlag, 1973

  11. J W S Cassels. Arithmatic on curves of genus 1, (IV) proof of the Hauptvermutung. J Reine Angew Math, 1962, 211:95-112

    MATH  MathSciNet  Google Scholar 

  12. M J Razar. A relation between the two-component of the Tate-Sâfarevic group and L(1) for certain elliptic curves. American Journal of Math, 1974, 96:127-144

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Sichuan Union University, Chengdu 610064, P. R. China

    Delang Li

  2. Department of Mathematics, Columbia University, New York, NY 10027, USA

    Ye Tian

Authors
  1. Delang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ye Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Delang Li.

Additional information

Project supported by the National Natural Science Foundation of P. R. China

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, D., Tian, Y. On the Birch-Swinnerton-Dyer Conjecture of Elliptic Curves E D : y 2 = x 3−D 2 x . Acta Math Sinica 16, 229–236 (2000). https://doi.org/10.1007/s101140000040

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s101140000040

Keywords

1991 MR Subject Classification

Search

Navigation