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In [[mathematics]], a '''lemniscatic elliptic function''' is an [[elliptic function]] related to the arc length of a [[lemniscate of Bernoulli]] studied by [[Giulio Carlo de' Toschi di Fagnano]] in 1718. It has a square period lattice and is closely related to the [[Weierstrass elliptic function]] when the Weierstrass invariants satisfy ''g''<sub>2</sub> = 1 and ''g''<sub>3</sub> = 0.
In the lemniscatic case, the minimal half period ω<sub>1</sub> is real and equal to
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