  We study the decay $J/\psi\to\pi^{+}\pi^{-}\pi^{0}$ within the framework of
the Khuri-Treiman equations. We find that the BESIII experimental di-pion mass
distribution in the $\rho(770)$-region is well reproduced with a
once-subtracted $P$-wave amplitude. Furthermore, we show that $F$-wave
contributions to the amplitude improve the description of the data in the
$\pi\pi$ mass region around 1.5 GeV. We also present predictions for the
$J/\psi\to\pi^{0}\gamma^{*}$ transition form factor.
