Solar cell electrical model from datasheet
After some additional research, and simulating the circuit with the parameters I obtained, it seems they are correct.
The diode has a very low Is due to the fact its forward voltage is about the open-circuit one (7.56V). So, Is will be much lower than the one from a standard 0.7V diode.
For the same reason, when you short-circuit the output, the current through the diode will be negligible: the series resistance is very small (Vdiode &lt;&lt; 7.56V). It is logical Iph ~= Isc.
Finally, I have simulated the model using CircuitLab. The I-V curve resembles one of an ideal solar cell:



Ideal solar cell I-V curve:  



EDIT: If you are really interested in determining the solar cell electrical model parameters from the I-V curve, you should check this paper: http://kdx.xidian.edu.cn/fj/a11.pdf
I could not get it to work with my example, but the authors claim it should.