This article describes a determination of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ from the decay $B^0to D^{*-}ell^+ u_ell$ using 711 fb$^{-1}$ of Belle data collected near the $Upsilon(4S)$ resonance. We simultaneously measure the product of the form factor normalization $mathcal{F}(1)$ and the matrix element $|V_{cb}|$ as well as the three parameters $rho^2$, $R_1(1)$ and $R_2(1)$, which determine the form factors of this decay in the framework of the Heavy Quark Effective Theory. The results, based on about 120,000 reconstructed $B^0to D^{*-}ell^+ u_ell$ decays, are $rho^2=1.214pm 0.034pm 0.009$, $R_1(1)=1.401pm 0.034pm 0.018$, $R_2(1)=0.864pm 0.024pm 0.008$ and $mathcal{F}(1)|V_{cb}|=(34.6pm 0.2pm 1.0)times 10^{-3}$. The branching fraction of $B^0to D^{*-}ell^+ u_ell$ is measured at the same time; we obtain a value of $mathcal{B}(B^0 to D^{*-}ell^+ u_ell) = (4.58 pm 0.03 pm 0.26) %$. The errors correspond to the statistical and systematic uncertainties. These results give the most precise determination of the form factor parameters and $mathcal{F}(1)|V_{cb}|$ to date. In addition, a direct, model-independent determination of the form factor shapes has been carried out.
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