  The form factor of the electromagnetic excitation of $^{12}$C to its 2$^+_1$
state was measured at extremely low momentum transfers in an electron
scattering experiment at the S-DALINAC. A combined analysis with the world form
factor data results in a reduced transition strength $B(E2; 2^+_1\rightarrow
0^+_1) =7.63(19)$ e$^2$fm$^4$ with an accuracy improved to 2.5\%. In-Medium-No
Core Shell Model results with interactions derived from chiral effective field
theory are capable to reproduce the result. A quadrupole moment $Q(2^+_1) =
5.97(30)$ efm$^2$ can be extracted from the strict correlation with the
$B((E2)$ strength emerging in the calculations.
