We consider a rotating Bose-Einstein condensate in a harmonic trap and investigate the behavior of the wave function which solves the Gross Pitaevskii equation. We give a simplified expression of the Gross-Pitaevskii energy in an asymptotic regime, which only depends on the number and shape of the vortex lines. Following recent experiments, we study in detail the line of a single quantized vortex, which has either a U or S shape.