Skip to main content
Log in

Singular moduli, modular polynomials, and the index of the closure of ℤ[j(τ)] in ℚ(j(τ))

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

References

  1. Borel, A., Chowla, S., Herz, C.S., Iwasawa, K., Serre, J.-P.: Semmar on Complex Multiplication. (Lecture Notes in Math. Vol. 21). Berlin Heidelberg New York: Springer 1966.

    Google Scholar 

  2. Deuring, M.: Die Typen der Multiplikatorenringe elliptischer Funktionenkörper. Abh. Math. Semin. Hamb.14, 197–272 (1941).

    Google Scholar 

  3. Dorman, D.R.: Global orders in definite guaternion algebras as endomorphism rings for reduced CM elliptic curve. Proceedings of Conférence internationale de theorie des nombres (to appear)

  4. Dorman, D.R.: Special values of the elliptic modular function and factorization formulae. J. Reine Angew. Math.383, 207–220 (1988)

    Google Scholar 

  5. Dummit D.S., Gold, R., Kisilevsky, H.: The field generated by the discriminant of the class invariants of an imaginary quadratic field. Can Math. Bull.26, 280–282 (1983)

    Google Scholar 

  6. Gross, B.H.: Arithmetic on elliptic curves with complex multiplication. (Lectures Notes in Math. Vol. 776). Berlin Heidelberg New York: Springer 1980

    Google Scholar 

  7. Gross, B.H., Zagier, D.B.: Heegner points and derivatives ofL-Series. Invent. Math.84, 225–320 (1986)

    Google Scholar 

  8. Gross, B.H., Zagier, D.B.: On singular moduli. J. Reine Angew. Math.355, 191–220 (1985)

    Google Scholar 

  9. Rohrlich, D.E.: Elliptic curves with good reduction everywhere. J. Lond. Math. Soc.25, 216–222 (1982)

    Google Scholar 

  10. Serre, J.-P.: Local fields. Grad. Texts in Math. 67. Berlin Heidelberg New York: Springer 1979

    Google Scholar 

  11. Serre, J.-P., Tate, J.T.: Good reduction of abelian varities. An. Math.88, 492–517 (1968)

    Google Scholar 

  12. Vignéras, M.-F.: Arithmétique des algèbres de quaternions. (Lecture Notes in Math. Vol. 800). Berlin Heidelberg New York: Springer 1980

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dorman, D.R. Singular moduli, modular polynomials, and the index of the closure of ℤ[j(τ)] in ℚ(j(τ)). Math. Ann. 283, 177–191 (1989). https://doi.org/10.1007/BF01446429

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01446429

Keywords

Navigation