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The Weierstrass elliptic function is a doubly periodic meromorphic function on the complex numbers (with the periods typically normalized to and satisfying , so that and ) that exhibits an explicit parametrization of the form
where is the set of solutions to the cubic Weierstrass equation, and is the lattice . In other words, we have a cubic relation of type
for some constants , providing an explicit parametrization of an elliptic curve (a nonsingular projective cubic curve considered over ) by a complex torus .
See at elliptic curve and at Möbius transformation for more.
Named after Karl Weierstrass.
Lecture notes:
See also
Last revised on July 28, 2020 at 16:36:47. See the history of this page for a list of all contributions to it.