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Precise predictions for an $e^+e^-\rightarrow t\bar{t}$ cross-section arepresented in the energy region from 400 GeV to 800 GeV. Cross-sections areestimated including the beam-polarization effects with full$\mathcal{O}(\alpha)$, and also with the effects of the initial-state photonemission. A radiator technique is used for the initial-state photon emission upto two-loop orders. In this investigation, a weak correction is defined as thefull electroweak corrections without the initial-state photonic corrections. Asa result, it is determined that the total cross-section of a top quarkpair-production receives the weak corrections of $+4\%$ over the trivialinitial state corrections at a center of mass energy of 500 GeV. Among theinitial state contributions, a contribution from two-loop diagrams gives lessthan $0.11\%$ correction over the one-loop ones at the center of mass energiesof from $400$ GeV to $800$ GeV. In addition, the effect of a running couplingconstant is also discussed.

ISR effects on loop corrections of a top pair-production at the ILC