  The problem of an elastica knot in three-dimensional space is solved
explicitly by expressing the Frenet-Serret curvature and torsion of the knot in
terms of the Weierstrass and Jacobi elliptic functions. This solution is
obtained by variational methods and is derived by minimizing of the
squared-curvature energy integral. In the present work, an equivalency is
established between pairs of Jacobi elliptic solutions that are described by
the same values for curvature and torsion functionals.
