Sawtooth inversion radii and profile peaking factors of a large variety of ohmic and ECH heated L mode plasmas, including elongations up to 2.6 and triangularities between -0.5 and 0.75, have been investigated in the TCV tokamak. In ohmic plasmas, normalized inversion radii and electron temperature profile peaking factors (corrected for sawtoothing effects) depend solely on the parameter ⟨j⟩/q0j0, irrespective of plasma shape. With ECH this parameter remains the main scaling parameter. Density profiles are well described as functions of poloidal flux, in agreement with turbulent equipartition theories. Parameter conversions are also provided that allow the observed scalings to be expressed using the conventional scaling variables q95, δ95 and κ95.