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Long-duration gamma-ray bursts (GRBs) have been found to be associated withbroad-lined type-Ic supernovae (SNe), but only a handful of cases have beenstudied in detail. Prompted by the discovery of the exceptionally bright,nearby GRB130427A (redshift z=0.3399), we aim at characterising the propertiesof its associated SN2013cq. This is the first opportunity to test directly theprogenitors of high-luminosity GRBs. We monitored the field of the Swift longduration GRB130427A using the 3.6-m TNG and the 8.2-m VLT during the timeinterval between 3.6 and 51.6 days after the burst. Photometric andspectroscopic observations revealed the presence of the type Ic SN2013cq.Spectroscopic analysis suggests that SN2013cq resembles two previous GRB-SNe,SN1998bw and SN2010bh associated with GRB980425 and XRF100316D, respectively.The bolometric light curve of SN2013cq, which is significantly affected by thehost galaxy contribution, is systematically more luminous than that of SN2010bh($\sim$ 2 mag at peak), but is consistent with SN1998bw. The comparison withthe light curve model of another GRB-connected SN2003dh, indicates thatSN2013cq is consistent with the model when brightened by 20%. This suggests asynthesised radioactive $^{56}$Ni mass of $\sim 0.4 M_\odot$.GRB130427A/SN2013cq is the first case of low-z GRB-SN connection where the GRBenergetics are extreme ($E_{\rm \gamma, iso} \sim 10^{54}$ erg). We show thatthe maximum luminosities attained by SNe associated with GRBs span a verynarrow range, but those associated with XRFs are significantly less luminous.On the other hand the isotropic energies of the accompanying GRBs span 6 ordersof magnitude (10$^{48}$ erg $< E_{\rm \gamma, iso} <$ 10$^{54}$ erg), althoughthis range is reduced when corrected for jet collimation. The GRB totalradiated energy is in fact a small fraction of the SN energy budget.

Diversity of GRB energetics vs. SN homogeneity: supernova 2013cq associated with the gamma-ray burst 130427A