A Modulus such that

where is a complete Elliptic Integral of the First Kind, and . The Elliptic Lambda Function gives the value of .

Abel (quoted in Whittaker and Watson 1990, p. 525) proved that if is an
Integer, or more generally whenever

where , , , , and are Integers, then the Modulus is the Root of an algebraic equation with Integer Coefficients.

**References**

Whittaker, E. T. and Watson, G. N. *A Course in Modern Analysis, 4th ed.* Cambridge, England: Cambridge
University Press, pp. 524-528, 1990.

© 1996-9

1999-05-26