  We present a lattice QCD determination of the distribution amplitude (DA) of
the pion and the first few Mellin moments from an analysis of the quasi-DA
matrix element within the leading-twist framework. We perform our study on a
HISQ ensemble with $a=0.076$ fm lattice spacing with the Wilson-Clover valence
quark mass tuned to the physical point. We analyze the ratios of pion quasi-DA
matrix elements at short distances using the leading-twist Mellin operator
product expansion (OPE) at the next-to-leading order and the conformal OPE at
the leading-logarithmic order. We find a robust result for the first
non-vanishing Mellin moment $\langle x^2 \rangle = 0.287(6)(6)$ at a
factorization scale $\mu=2$ GeV. We also present different Ans\"atze-based
reconstructions of the $x$-dependent DA, from which we determine the
perturbative leading-twist expectations for the pion electromagnetic and
gravitational form-factors at large momentum transfers.
