In early sixties Manin proved that every formal group of finite height defined
over a field of finite characteristic is a summand in the formal
completion of the Jacobian of a certain curve.
It turns out
that a universal lift of a formal group of height $p-1$ over
an algebraically closed field of characteristic $p$
comes as a summand in the formal completion of the Jacobian
of a certain curve with $p$ marked points, defined over the
Lubin-Tate deformation space.
These curves generalize the Legendre
family of elliptic curves.
As an immediate application,
we will describe the representation which is crucial for calculating
the initial term of the spectral sequence, converging to the homotopy
groups of the higher real $K$-theories, introduced recently by Hopkins and
Miller.