\t {Example: Came up in work on Birch \& Swinnerton-Dyer}
\begin{verbatim}
sage: E = EllipticCurve('225a'); E
Elliptic Curve defined by y^2 + y = x^3 +1 over Rational Field
sage: f = E.division_polynomial(5); f
5*x^12 + 475*x^9 - 375*x^6 - 3125*x^3 - 625
sage: F = f.factor(); F
(5) * (x^4 + 5*x^3 - 10*x - 5) * (x^8 - 5*x^7 + 25*x^6
   - 20*x^5 + 55*x^4 - 50*x^3 + 100*x^2 - 50*x + 25)
sage: F.unit()
5
sage: h = F[1][0]; h
x^8 - 5*x^7 + 25*x^6 - 20*x^5 + 55*x^4 - 50*x^3 + 100*x^2 - 50*x + 25
sage: G = h.galois_group(); G
Transitive group number 2 of degree 8
sage: G.gens()
((1,2,3,8)(4,5,6,7), (1,5)(2,6)(3,7)(4,8))
sage: G.order()
8
\end{verbatim}