2013-06-03 10:34:18 +0200 answered a question Lifting matrices to $SL_2(\mathbb{Z})$ Actually, the question asks only for SL_2, while the trac ticket is more general (SL_m). The case of SL_2 is already in Sage (as long as N <= 2147483647). Try sage: lift_to_sl2z? 2013-05-26 19:39:40 +0200 commented answer Computing maximal orders in relative extensions groups.google.com/forum/?fromgroups#!topic/sage-devel/MpPqbjAqol4 2013-05-26 18:59:59 +0200 commented answer Computing maximal orders in relative extensions As Nils already explained in his answer, the first line of the question's Magma code creates a better starting order (OO[sqrt(kappa12)]) than the third line of the question's Sage code (ZZ[sqrt(kappa12)]). But to start out in Sage with the same order that you start out with in Magma, you shouldn't have to use pari directly. In Sage, just use something like the following: OO = Qa12.maximal_order() bas = [L.structure()$1$(b) for b in OO.basis()] subOrderK = L.order(bas + [alpha]) \# Instead of the last line, you can also do subOrderK = L.order(bas + [b*alpha for b in bas]) Unfortunately, for the field I tried this with, it hangs (I don't know your Qa12). And even Ctrl+C does not work. I'm reporting this as a bug.