We present a detailed analysis of the characteristics of electroconvection patterns in a homeotropic nematic liquid crystal under the influence of a variable magnetic field. An unambiguous observation of low frequency "reentrant" normal rolls and a nonmonotonic magnetic field dependence of the threshold voltages is reported. The effect of the magnetic field on the normal roll-abnormal roll transition is determined, which is in good agreement with theoretical predictions of the weakly nonlinear analysis.