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The case of the Weierstraß Elliptic Function with invariants 
and 
.
See also Equianharmonic Case, Weierstraß Elliptic Function, Pseudolemniscate Case
References
Abramowitz, M. and Stegun, C. A. (Eds.).  ``Lemniscate Case ( 
, 
).''  §18.14 in
  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
  New York: Dover, pp. 658-662, 1972.