A sample of 65210 → (K) decay candidates with 1% background contamination has been collected in 2003-2004 by the NA48/2 collaboration at the CERN SPS. A study of the differential rate provides the first measurement of the hadronic form factor variation in the plane ( , ) and brings evidence for a cusp-like structure in the distribution of the squared invariant mass around . Exploiting a model independent description of this form factor, the branching ratio, inclusive of radiative decays, is obtained using the → decay mode as normalization. It is measured to be BR(K) = (2.552 ± 0.010 ± 0.010 ± 0.032) × 10, which improves the current world average precision by an order of magnitude while the 1.4% relative precision is dominated by the external uncertainty from the normalization mode. A comparison with the properties of the corresponding mode involving a pair (K) is also presented.