  By employing the differential equations, we compute analytically the elliptic
sectors of two-loop master integrals appearing in the NNLO QCD corrections to
CP-even heavy quarkonium exclusive production and decays, which turns out to be
the last and toughest part in the relevant calculation. The integrals are found
can be expressed as Goncharov polylogarithms and iterative integrals over
elliptic functions. The master integrals may be applied to some other NNLO QCD
calculations about heavy quarkonium exclusive production, like
$\gamma^*\gamma\rightarrow Q\bar{Q}$, $e^+e^-\rightarrow \gamma+
Q\bar{Q}$,~and~$H/Z^0\rightarrow \gamma+ Q\bar{Q}$, heavy quarkonium exclusive
decays, and also the CP-even heavy quarkonium inclusive production and decays.
