References
- O. Atkin and F. Morain, Elliptic curves and primality proving, Math. Comp. 61 (1993), 29-68. https://doi.org/10.1090/S0025-5718-1993-1199989-X
- R. M. Broker, Constructing elliptic curves of prescribed order, Ph.D. Thesis, Universiteit Leiden, 2006.
- J. H. Bruinier, P. Jenkins, and K. Ono, Hilbert class polynomials and traces of singular moduli, Math. Ann. 334 (2006), 373-393. https://doi.org/10.1007/s00208-005-0723-6
-
H. H. Chan, A. Gee, and V. Tan, Cubic singular moduli, Ramanujan's class invariants
${\lambda}_{n}$ and the explicit Shimura reciprocity law, PaciFic J. Math. 208 (2003), 23-37. https://doi.org/10.2140/pjm.2003.208.23 -
D. Cox, Primes of the form x
$^{2}$ + ny$^{2}$ , John Wiley & Sons, 1989. -
M. Deuring, Die Klassenkorper der komplexen Multiplikation, in 'Enz. Math. Wiss. Band I
$_{2}$ ' Heft 10, Teil II, Stuttgart 1958. - A. Gee, Class invariants by Shimura's reciprocity law, J. Theor. Nombre Bordeaux 11 (1999), 45-72. https://doi.org/10.5802/jtnb.238
- A. Gee, Class Fields by Shimura reciprocity, Ph. D. Thesis, Universiteit van Amsterdam, 2001.
- A. Gee and P. Stevenhagen, Generating class Fields using Shimura reciprocity, Proceedings of the Third International Symposium on Algorithmic Number Theory (Lecture Notes in Computer Sciences 1423 pp. 441-453, Springer-Verlag, 1998).
- W. Hart, Schlafli modular equations for generalized Weber functions, Ramanujan J. 15 (2008), 435-468. https://doi.org/10.1007/s11139-007-9087-8
- F. Hajir and F. R. Villegas , Explicit elliptic units I, Duke Math. J. 90 (1997), no. 3, 495-521. https://doi.org/10.1215/S0012-7094-97-09013-X
- S. Lang, Elliptic Functions, Springer Graduate Texts in Mathematics, vol. 112, 1987.
- G. Shimura, Introduction to the arithmetic theory of automorphic forms, Princeton University Press, 1971.
- J. H. Silverman, Advanced topics in the arithmetic of elliptic curves, Springer Graduate Texts in Mathematics, vol. 151, 1994.
- P. Stevenhagen, Hilbert's 12th problem, complex multiplication and Shimura reciprocity, Class Field theory-its centenary and prospect, ed. K. Miyake, Adv. Studies in pure math. 30 (2001), 161-176.
- H. Weber, Lehrbuch der Algebra, dritter Band, Friedrich Vieweg und Sohn, 1908.