We present a survey on the rotational and physical properties of the dynamically low inclination Cold Classical trans-Neptunian objects . The Cold Classicals are primordial planetesimals and contain relevant information about the early phase of our Solar System and planet formation over the first 100 million years after the formation of the Sun . Our project makes use of the Magellan and the Lowell ’ s Discovery Channel Telescopes for photometric purposes . We obtained partial/complete lightcurves for 42 Cold Classicals . We use statistical tests to derive general properties about the shape and rotational frequency distributions of the Cold Classical population , and infer that the Cold Classicals have slower rotations and are more elongated/deformed than the other trans-Neptunian objects . Based on the available full lightcurves , the mean rotational period of the Cold Classical population is 9.48 \pm 1.53 h whereas the mean period of the rest of the trans-Neptunian objects is 8.45 \pm 0.58 h. About 65 \% of the trans-Neptunian objects ( excluding the Cold Classicals ) have a lightcurve amplitude below 0.2 mag compared to the 36 \% of Cold Classicals with small amplitude . We present the full lightcurve of one new likely contact binary : 2004 VC _ { 131 } with a potential density of 1 g cm ^ { -3 } for a mass ratio of 0.4 . We also have hints that 2004 MU _ { 8 } and 2004 VU _ { 75 } are maybe potential contact binaries based on their sparse lightcurves but more data are needed to confirm such a find . Assuming equal-sized binaries , we find that only \sim 10-25 % of the Cold Classicals could be contact binaries , suggesting that there is a deficit of contact binaries in this population compared to previous estimates and compared to the abundant ( \sim 40-50 \% ) possible contact binaries in the 3:2 resonant ( Plutino ) population . This estimate is a lower limit and will increase if non equal-sized contact binaries are also considered . Finally , we put in context the early results of the New Horizons flyby of ( 486958 ) 2014 MU _ { 69 } .