We report the first measurement of the azimuthal anisotropy of J$/\psi$ at forward rapidity ($1.2<|\eta|<2.2$) in Au$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV at the Relativistic Heavy Ion Collider. The data were collected by the PHENIX experiment in 2014 and 2016 with integrated luminosity of 14.5~nb$^{-1}$. The second Fourier coefficient ($v_2$) of the azimuthal distribution of $J/\psi$ is determined as a function of the transverse momentum ($p_T$) using the event-plane method. The measurements were performed for several selections of collision centrality: 0%--50%, 10%--60%, and 10%-40%. We find that in all cases the values of $v_2(p_T)$, which quantify the elliptic flow of J$/\psi$, are consistent with zero. The results are consistent with measurements at midrapidity, indicating no significant elliptic flow of the J$/\psi$ within the quark-gluon-plasma medium at collision energies of $\sqrt{s_{_{NN}}}=200$ GeV.
JPSI v2 in Au+Au collisions as a function of pT (GeV/c) for 10%--60% centrality with pT binned by [0, 1], [1, 2], [2, 3], and [3, 5] GeV/c.
JPSI v2 in Au+Au collisions as a function of pT (GeV/c) for 10%--60% centrality with pT binned by [0, 0.5], [0.5, 1], [1, 5], and [0, 5] GeV/c.
JPSI v2 in Au+Au collisions as a function of pT (GeV/c) for 10%--40% centrality with pT binned by [0, 2], [2, 5], and [5, 10] GeV/c.
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