Solar filaments are cold and dense materials situated in magnetic dips, which show distinct radiation characteristics compared to the surrounding coronal plasma. They are associated with coronal sheared and twisted magnetic field lines. However, the exact magnetic configuration supporting a filament material is not easy to be ascertained because of the absence of routine observations of the magnetic field inside filaments. Since many filaments lie above weak-field regions, it is nearly impossible to extrapolate their coronal magnetic structures by applying the traditional methods to noisy photospheric magnetograms, in particular the horizontal components. In this paper, we construct magnetic structures for some filaments with the regularized Biot--Savart laws and calculate their magnetic twists. Moreover, we make a parameter survey for the flux ropes of the Titov-Demoulin-modified model to explore the factors affecting the twist of a force-free magnetic flux rope. It is found that the twist of a force-free flux rope is proportional to its axial length to minor radius ratio, and is basically independent of the overlying background magnetic field strength. Thus, we infer that long quiescent filaments are likely to be supported by more twisted flux ropes than short active-region filaments, which is consistent with observations.
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