j-Invariant
المؤلف:
Berwick, W. E. H.
المصدر:
"Modular Invariants Expressible in Terms of Quadratic and Cubic Irrationalities." Proc. London Math. Soc. 28
الجزء والصفحة:
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8-7-2020
2366
j-Invariant
An invariant of an elliptic curve given in the form
which is closely related to the elliptic discriminant and defined by
The determination of 
as an algebraic integer in the quadratic field 
is discussed by Greenhill (1891), Weber (1902), Berwick (1928), Watson (1938), Gross and Zaiger (1985), and Dorman (1988). The norm of 
in 
is the cube of an integer in 
.
REFERENCES:
Berwick, W. E. H. "Modular Invariants Expressible in Terms of Quadratic and Cubic Irrationalities." Proc. London Math. Soc. 28, 53-69, 1928.
Dorman, D. R. "Special Values of the Elliptic Modular Function and Factorization Formulae." J. reine angew. Math. 383, 207-220, 1988.
Greenhill, A. G. "Table of Complex Multiplication Moduli." Proc. London Math. Soc. 21, 403-422, 1891.
Gross, B. H. and Zaiger, D. B. "On Singular Moduli." J. reine angew. Math. 355, 191-220, 1985.
Stepanov, S. A. "The 
-Invariant." §7.2 in Codes on Algebraic Curves. New York: Kluwer, pp. 178-180, 1999.
Watson, G. N. "Ramanujans Vermutung über Zerfällungsanzahlen." J. reine angew. Math. 179, 97-128, 1938.
Weber, H. Lehrbuch der Algebra, Vols. I-II. New York: Chelsea, 1979.
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