  This article proposes a model including thermal effects for closed
supercoiled DNA. Existing models include an elastic rod. Euler's elastica,
ideal elastic rods on a plane, have only two kinds of closed shapes, the circle
and a figure-eight, realized as minima of the Euler-Bernoulli energy. Even
considering three dimensional effects, this elastica model provides much
simpler shapes than observed via Atomic-Force Microscope (AFM), since the
minimal points of the energy are expressed by elliptic functions. In this
paper, by a generalization of elastica, we obtain shapes determined by data of
hyperelliptic curves, which partially reproduce the shapes and properties of
the DNA.
