A table of totally complex number fields of small discriminants

  • Henri Cohen
  • Francisco Diaz y Diaz
  • Michel Olivier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1423)


Using the explicit class field theory developed in [3] and tables of number fields in low degree, we construct totally complex number fields having a degree smaller than 80 and a root discriminant near from Odlyzko's bounds. For some degrees, we extend and improve the table of totally complex number fields of small discriminants given by Martinet


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Cohen: A Course in Computational Algebraic Number Theory. GTM 138, (1993) Springer-VerlagGoogle Scholar
  2. 2.
    H. Cohen and F. Diaz y Diaz: A polynomial reduction algorithm. Sém. Th. Nombres Bordeaux (Série 2) 3, (1991) 351–360MATHGoogle Scholar
  3. 3.
    H. Cohen, F. Diaz y Diaz and M. Olivier: Computing ray class groups, conductors and discriminants. Math. Comp. To appearGoogle Scholar
  4. 4.
    M. Daberkow and M. Pohst: Computations with relative extensions of number fields with an application to the construction of Hilbert class fields. Proc. ISAAC '95, ACM Press, (1995) 68–76Google Scholar
  5. 5.
    C. Fieker and M. Pohst: On lattices over number fields. Algorithmic Number Theory Symposium II. Lecture Notes in Computer Science 1122 (1996) Springer-Verlag 133–139Google Scholar
  6. 6.
    A. Leutbecher and G. Niklash: On cliques of exceptional units and Lenstra's construction of Euclidean fields. Journées arithmétiques 1987. Lecture Notes in Math. 1380, (1989) Springer-Verlag 150–178Google Scholar
  7. 7.
    J. Martinet: Petits discriminants des corps de nombres. Journées arithmétiques 1980, London Math. Soc. Lecture Note Ser. 56, (1982) Cambridge Univ. Press 151–193Google Scholar
  8. 8.
    A. Odlyzko: Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions: a survey of recent results. Sém. Th. des Nombres Bordeaux (Série 2) 2, (1990) 119–141MATHMathSciNetGoogle Scholar
  9. 9.
    X. Roblot: Unités de Stark et corps de classes de Hilbert. C. R. Acad. Sci. Paris. 323 (1996) 1165–1168MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Henri Cohen
    • 1
  • Francisco Diaz y Diaz
    • 1
  • Michel Olivier
    • 1
  1. 1.Laboratoire A2XUniversité Bordeaux ITalenceFrance

Personalised recommendations