An elliptic function with no poles in a fundamental cell is a constant.
Liouville's Elliptic Function Theorem
See also
Elliptic Function, Fundamental Cell, PoleExplore with Wolfram|Alpha
References
Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, p. 431, 1990.Referenced on Wolfram|Alpha
Liouville's Elliptic Function TheoremCite this as:
Weisstein, Eric W. "Liouville's Elliptic Function Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LiouvillesEllipticFunctionTheorem.html