The amount and distribution of heavy elements in Jupiter gives indications on the process of its formation and evolution . Core mass and metallicity predictions however depend on the equations of state used , and on model assumptions . We present an improved ab initio hydrogen equation of state , H-REOS.2 and compute the internal structure and thermal evolution of Jupiter within the standard three-layer approach . The advance over our previous Jupiter models with H-REOS.1 by Nettelmann et al . ( 2008 ) is that the new models are also consistent with the observed \gtrsim 2 times solar heavy element abundances in Jupiter ’ s atmosphere . Such models have a rock core mass M _ { c } = 0 – 8 \ > M _ { \oplus } , total mass of heavy elements M _ { Z } = 28 – 32 \ > M _ { \oplus } , a deep internal layer boundary at \geq 4 Mbar , and a cooling time of 4.4–5.0 Gyrs when assuming homogeneous evolution . We also calculate two-layer models in the manner of Militzer et al . ( 2008 ) and find a comparable large core of 16-21 \ > M _ { \oplus } , out of which \sim 11 \ > M _ { \oplus } is helium , but a significantly higher envelope metallicity of 4.5 \times solar . According to our preferred three-layer models , neither the characteristic frequency ( \nu _ { 0 } \sim 156 \mu Hz ) nor the normalized moment of inertia ( \lambda \sim 0.276 ) are sensitive to the core mass but accurate measurements could well help to rule out some classes of models .