Every modular system has a modular system basis consisting of a finite number of polynomials.
Stated another way, for every order 
there exists a nonsingular curve with the maximum number of
circuits and the maximum number for any one nest.
Hilbert's Theorem
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References
Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 61, 1959.Referenced on Wolfram|Alpha
Hilbert's TheoremCite this as:
Weisstein, Eric W. "Hilbert's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HilbertsTheorem.html