Degree extension

[paladino@mat.unical.it]

Dear All,

I am Laura, a new mwmber of the list of the
users of PARI.
I have a question. I have the roots of
some polynomials of the form y^2=x^3+Ax+B.
For example p:=y^2=x^3+2x+5.
I call a, b and c the roots of p.
I would like to calculate the degree
of the number field

Q(sqrt(a-b),sqrt(a-c),sqrt(b-c),sqrt(-1)).

Is it possible with PARI?

Thank you and best whishes,

Laura