On Sat, 1 Dec 2018 at 08:42, Steven Craighead <steven.craigh...@gmail.com> wrote:
> E = EllipticCurve('14a1') > K.<b> = E.division_field(p); K for p = 2 and 3 finishes quickly. When I > use p = 5 or p = 7, the command never finishes. > The docstring warns (do E.division_field? to see it) that "This takes a very long time when the degree of the division field is large (e.g. when p is large or when the Galois representation is surjective)." Now for this curve sage: G=E.galois_representation() sage: G.image_type(5) 'The image is all of GL_2(F_5).' sage: GL(2,GF(5)).order() 480 so you are constructing a field of degree 480 over Q. This is done in two steps, first to form the splitting field of the 5-division polynomial : sage: E.division_polynomial(5) 5*x^12 + 5*x^11 + 280*x^10 - 2095*x^9 - 3765*x^8 - 8550*x^7 - 40320*x^6 + 66490*x^5 - 341085*x^4 + 292705*x^3 - 182920*x^2 + 867445*x - 386051 which will have degree 240, and then there's an additional quadratic extension on top. So it is not surprising that this takes a lot longer than the 2- or 3-division fields which are (for this curve) only of degree 2. > > I use Sagemath 8.4 on a linux mint 19. This is a toshiba AMD Turion II > Dual Core Process M500 with 4GB ram. This is a Pentium 64-bit. > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at https://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.