tokens: 2003 ) and have been called “GRB-SNe” (see Hjorth Bloom 2012 ; Woosley Bloom 2006 ; Cano et al. 2017 , and references therein). While most GRB-SNe are Type Ic-BL, not all SNe Ic-BL are associated with GRBs. The most luminous SNe Ic are Type Ic superluminous supernovae (SLSNe; Quimby et al. 2011 ; Gal-Yam 2012 ); their peak luminosities are erg s −1 (Gal-Yam 2012 ), tens of times greater than those of ordinary SNe. In this paper, we study a very luminous SN Ic, SN 2011kl, which is associated with an ultralong ( s) GRB 111209A (see, e.g., Golenetskii et al. 2011 ; Palmer et al. 2011 ; Gendre et al. 2013 ; Stratta et al. 2013 ; Gompertz Fruchter 2017 ) at redshift z = 0.677 (Vreeswijk et al. 2011 ). By using WMAP ΛCDM cosmology (Spergel et al. 2003 ) and adopting km s −1 Mpc −1 , , and , Kann et al. ( 2016 ) derived a luminosity distance ( D L ) of 4076.5 Mpc for GRB 111209A/SN 2011kl. With a peak luminosity erg s −1 (Kann et al. 2016 ), 8 8 Greiner et al. ( 2015 ) found a slightly lower peak luminosity ( erg s −1 ) since they ignored the near-infrared contribution. SN 2011kl is the most luminous GRB-SN yet detected and is significantly more luminous than all other GRB-SNe, whose average peak luminosity is erg s −1 with a standard deviation of erg s −1 (Cano et al. 2017 ). The time of peak brightness of SN 2011kl is ∼14 days, slightly larger than the average (13.0 days with a standard deviation of 2.7 days; Cano et al. 2017 ) of other GRB-SNe. The peak luminosity of SN 2011kl is comparable to that of some not-quite-superluminous “SLSNe” (e.g., PTF11rks, PTF10hgi, iPTF15esb, iPTF16bad, and PS15br) and commensurate with the SN-SLSN gap transients observed by Arcavi et al. ( 2016 ); moreover, Liu et al. ( 2017c ) pointed out that the spectrum of SN 2011kl is very different from those of GRB-SNe, but consistent with that of SLSNe. So, the energy sources powering its LC might be similar to those powering the SLSN LCs instead of the ordinary SNe Ic. The most popular prevailing models for explaining SLSNe are the magnetar model (Maeda et al. 2007 ; Kasen Bildsten 2010 ; Woosley 2010 ; Chatzopoulos et al. 2012 , 2013 ; Inserra et al. 2013 ; Chen et al. 2015 ; Wang et al. 2015a , 2016b ; Dai et al. 2016 ; Moriya et al. 2017 ) and the ejecta plus circumstellar medium (CSM) interaction model (Chevalier 1982 ; Chevalier Fransson 1994 ; Chugai Danziger 1994 ; Chatzopoulos et al. 2012 , 2013 ; Liu et al. 2017a ). 9 9 Almost all SLSNe (except maybe pair-instability SLSNe—e.g., SN 2007bi Gal-Yam et al. 2009 ; but see Dessart et al. 2012 and Nicholl et al. 2013 ) cannot be explained by the radioactive heating model (Quimby et al. 2011 ; Inserra et al. 2013 ; Nicholl et al. 2013 , 2014 ). Some SLSNe I exhibiting late-time rebrightening and H α emission lines (Yan et al. 2015 , 2017 ) might be powered by a hybrid model containing contributions from magnetars and ejecta-CSM interaction (Wang et al. 2016c ). There have been several papers modeling the LCs of SN
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