  Solar active regions (ARs) are the main sources of flares and coronal mass
ejections (CMEs). NOAA AR 12089, which emerged on 2014 June 10, produced two
C-class flares accompanied by CMEs within five hours after its emergence. When
producing the two eruptive flares, the total unsigned magnetic flux
($\Phi_{\text{AR}}$) and magnetic free energy ($E_f$) of the AR are much
smaller than the common CME-producing ARs. Why can this extremely small AR
produce eruptive flares so early? We compare the AR magnetic environment for
the eruptive flares to that for the largest confined flare from the AR. Besides
the $\Phi_{\text{AR}}$ and $E_f$, we calculate the ratio between the mean
characteristic twist parameter ($\alpha_{\text{FPIL}}$) within the flaring
polarity inversion line (FPIL) region and $\Phi_{\text{AR}}$, a parameter
considering both background magnetic field constraint and non-potentiality of
the core region, for the three flares. We find higher
$\alpha_{\text{FPIL}}/{\Phi_{\text{AR}}}$ values during the eruptive flares
than during the confined flare. Furthermore, we compute the decay index along
the polarity inversion line, revealing values of 1.69, 3.45, and 0.98 before
the two eruptive and the confined flares, respectively. Finally, nonlinear
force-free field extrapolation indicates that a flux rope was repeatedly formed
along the FPIL before eruptive flares, which ejected out and produced CMEs. No
flux rope was found before the confined flare. Our research suggests that even
a newly emerged, extremely small AR can produce eruptive flares if it has
sufficiently weak background field constraint and strong non-potentiality in
the core region.
