On 9 June 2014 16:03, Shalec <christopher.sch...@gmail.com> wrote:
> Hi,
> I would like to set up an elliptic curve over a Field F_{p^n} for any prime
> p. Is there a way to do so? My suggestion is to setup an verifying algorithm
> for "Elliptic Curves" by Washington and the Theorem of Hasse. Therefor I
> would like to calc the Order of any elliptic curve over finite fields.
>
> I just used those:
> http://www.sagemath.org/de/html/tutorial/tour_advanced.html
>
> Its not possible to use "GF(5^2)" and creating an elliptic curve over
> GF(5^2). Could someone tell me, how to realize this?It *is* possible, and reading the documentation will show you many similar examples: sage: F.<a> = GF(5^2) sage: E = EllipticCurve(F,[0,1,a,a,1]) sage: E.cardinality() 20 sage: E.abelian_group() Additive abelian group isomorphic to Z/2 + Z/10 embedded in Abelian group of points on Elliptic Curve defined by y^2 + a*y = x^3 + x^2 + a*x + 1 over Finite Field in a of size 5^2 sage: E.cardinality(extension_degree=100) 62230152778611417071440640537801242405902521687211671331011166147896987511823444765142947526679666797869844792692444767708438246773316672000 John Cremona > > Thank you, > Shalec > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To post to this group, send email to sage-support@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
