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The exact answer to your question is to use the mehod division_field, for example
sage: E = EllipticCurve([0,-1,1,-10,-20])
sage: E.division_field(5,'a')
Number Field in a with defining polynomial x^4 - x^3 + x^2 - x + 1
so that
sage: len(E.change_ring(K).torsion_points())
25
but as Nils said the degree is in general very large -- I chose an example where the degree of the 5-division field is only 4, which is as small as possible over QQ.
