  We find group cochains valued in currents giving explicit representatives for
the $\text{GL}_2$-equivariant polylogarithm class of a torus. Based on the
construction of weight-$2$ Eisenstein series for $\text{GL}_2$ from this
polylogarithm class, we give a geometrically-flavored derivation of the
classical formulas for the associated Dedekind-Rademacher homomorphisms, i.e.
the periods of $E^2_{\alpha,\beta}$ for various nonzero torsion sections
$(\alpha, \beta)$.
