j-Invariant
An invariant of an Elliptic Curve given in the form 
which is closely related to theDiscriminant and defined by
The determination of
as an Algebraic Integer in the Quadratic Field 
is discussed byGreenhill (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 
.See also Discriminant (Elliptic Curve), Elliptic Curve, Frey Curve
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. 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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