Determination of the two-class imaginary quadratic fields with an even discriminant by Heegner's method

  • V. A. Abrashkin


In this article all the imaginary quadratic fields of even discriminant with class number 2 are determined by Heegner's method. These fields are obtained from the integral points of certain elliptic curves.


Integral Point Elliptic Curf Class Number Quadratic Field Imaginary Quadratic Field 
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Literature cited

  1. 1.
    A. Baker, “Linear forms in the logarithms of algebraic numbers,” Mathematika,13, 204–216 (1966).Google Scholar
  2. 2.
    H. M. Stark, “A complete determination of the complex quadratic fields of class-number one,” Michigan J. Math.,14, 1–27 (1967).Google Scholar
  3. 3.
    K. Heegner, “Diophantische Analysis und Modul-Funktionen,” Math. Zeit.,56, 227–253 (1952).Google Scholar
  4. 4.
    B. Birch, “Diophantine analysis and modular functions,” Collection of Translations, Matematika,15, No. 3, 173–178 (1971).Google Scholar
  5. 5.
    A. Baker, “Imaginary quadratic fields with class number 2,” Collection of Translations, Matematika,16, No. 5, 3–14 (1972).Google Scholar
  6. 6.
    M. A. Kenku, “Determination of the even discriminants of complex quadratic fields of class-number 2,” Proc. London Math. Soc.,22, 734–746 (1971).Google Scholar
  7. 7.
    B. Birch, “Invariants of Weber classes,” Collection of Translations, Matematika,15, No. 3, 179–192 (1971).Google Scholar
  8. 8.
    Z. I. Borevich and I. R. Shafarevich, Number Theory [in Russian], Moscow (1964).Google Scholar
  9. 9.
    L. J. Mordell, “On Lerch's class-number for binary quadratic forms,” Ark. Math.,5, 97–100 (1963–1965).Google Scholar
  10. 10.
    W. Ljunggren, “New solution of a problem proposed by Lucas,” Saetrtyke av Norsk, Math. Tidsskrift, 65–72 (1952).Google Scholar

Copyright information

© Consultants Bureau 1974

Authors and Affiliations

  • V. A. Abrashkin
    • 1
  1. 1.Moscow State UniversityUSSR

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