Copolymers of ethylene with α-olefins which have a molar mass distribution Mw/Ma of from 1 to 8, a density of from 0.85 to 0.94 g/cm3, a molar mass Ma of from 10,000 g/mol to 4 000 000 g/mol and a CDBI of less than 50% and in which the side chain branching of the maxima of the individual peaks of the short chain branching distribution is in each case greater than 5 CH3/1 000 carbon atoms, a process for preparing them, a catalyst suitable for preparing them and fibers, moldings, films or polymer mixtures in which these copolymers are present