The near-Earth asteroid ( 196256 ) 2003 EH1 has been suggested to have a dynamical association with the Quadrantid meteoroid stream . We present photometric observations taken to investigate the physical character of this body and to explore its possible relation to the stream . We find no evidence for on-going mass-loss . A model fitted to the point-like surface brightness profile at 2.1 AU limits the fractional contribution to the integrated brightness by near-nucleus coma to \leq 2.5 % . Assuming an albedo equal to those typical of cometary nuclei ( \it p _ { R } =0.04 ) , we find that the effective nucleus radius is r _ { e } = 2.0 \pm 0.2 km . Time-resolved { \it R } -band photometry can be fitted by a two-peaked lightcurve having a rotational period of 12.650 \pm 0.033 hr . The range of the lightcurve , \Delta m _ { R } = 0.44 \pm 0.01 mag , is indicative of an elongated shape having an axis ratio \sim 1.5 projected into the plane of the sky . The asteroid shows colors slightly redder than the Sun , being comparable with those of C-type asteroids . The limit to the mass loss rate set by the absence of resolved coma is \lesssim 2.5 \times 10 ^ { -2 } kg { s ^ { -1 } } , corresponding to an upper limit on the fraction of the surface that could be sublimating water ice f _ { A } \lesssim 10 ^ { -4 } . Even if sustained over the 200-500 yr dynamical age of the Quadrantid stream , the total mass loss from 2003 EH1 would be too small to supply the reported stream mass ( 10 ^ { 13 } kg ) , implying either that the stream has another parent or that mass loss from 2003 EH1 is episodic .