  The elliptic flow of prompt and non-prompt $J/\psi$ was measured in the
dimuon decay channel in Pb+Pb collisions at $\sqrt{s_{_\text{NN}}}=5.02$ TeV
with an integrated luminosity of $0.42~\mathrm{nb}^{-1}$ with the ATLAS
detector at the LHC. The prompt and non-prompt signals are separated using a
two-dimensional simultaneous fit of the invariant mass and pseudo-proper decay
time of the dimuon system from the $J/\psi$ decay. The measurement is performed
in the kinematic range of dimuon transverse momentum and rapidity
$9<p_\mathrm{T}<30$ GeV, $|y|<2$, and 0-60% collision centrality. The elliptic
flow coefficient, $v_2$, is evaluated relative to the event plane and the
results are presented as a function of transverse momentum, rapidity and
centrality. It is found that prompt and non-prompt $J/\psi$ mesons have
non-zero elliptic flow. Prompt $J/\psi$ $v_2$ decreases as a function of
$p_\mathrm{T}$, while non-prompt $J/\psi$ it is, with limited statistical
significance, consistent with a flat behaviour over the studied kinematic
region. There is no observed dependence on rapidity or centrality.
