The only known classically known algebraic curve of curve genus that has an explicit parametrization in terms of standard special functions (Burnside 1893, Brezhnev 2001). This equation is given by
(1)
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The closed portion of the curve has area
(2)
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(3)
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where is a gamma function.
The closed portion of this curve has a parametrization in terms of the Weierstrass elliptic function given by
(4)
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(5)
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where
(6)
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the half-periods are given by and ranges over complex values (Brezhnev 2001).