  Large-scale relativistic calculations are performed for the transition energy
and line strength of the $ 1s^{2} 2s 2p$ $^1P_{1} \,-\ 1s^{2} 2s^{2}$ $^1S_{0}
$ transition in Be-like carbon. Based on the multiconfiguration
Dirac-Hartree-Fock~(MCDHF) approach, different correlation models are developed
to account for all major electron-electron correlation contributions. These
correlation models are tested with various sets of the initial and the final
state wave functions. The uncertainty of the predicted line strength due to
missing correlation effects is estimated from the differences between the
results obtained with those models. The finite nuclear mass effect is
accurately calculated taking into account the energy, wave functions as well as
operator contributions. As a result, a reliable theoretical benchmark of the
$E1$ line strength is provided to support high precision lifetime measurement
of the $ 1s^{2} 2s 2p$ $^1P_{1} $ state in Be-like carbon.
