  We prove that the heavy symmetric top (Lagrange, 1788) linearizes on a
two-dimensional non-compact algebraic group -- the generalized Jacobian of an
elliptic curve with two points identified. This leads to a transparent
description of its complex and real invariant level sets. We also deduce, by
making use of a Baker-Akhiezer function, simple explicit formulae for the
general solution of Lagrange top.
