Abstract
On the basis of the general Weierstrass model of the cubic curve with parameters µ = (µ1, µ2, µ3, µ4, µ6), the explicit form of the formal group that corresponds to the Tate uniformization of this curve is described. This formal group is called the general elliptic formal group. The differential equation for its exponential is introduced and studied. As a consequence, results on the elliptic Hirzebruch genus with values in ℤ[µ] are obtained.
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