On 8 November 2013 16:11, Georgi Guninski <gunin...@guninski.com> wrote: > I am not an expert, but is it normal to get negative canonical > height of a point on elliptic curve over number field?
No, this is certainly an error. There is at least one outstanding patch relating to heights over number fields (#13951) but also there was a numerical instability problem fixed at #12509 which was not done perfectly (I know, I did it) and that might be the issue here too. Heights are supposed to be independent of the base field. Your curve and point are defined over Q where the height is computed as 0.0324132522964454 -- this uses a completely different implementation (in the pari library) which is more reliable, unfortunately. John Cremona > > sage: Z1.<Z>=ZZ[];Nf.<v>=NumberField(Z**16-2);E=EllipticCurve(Nf,[-87, 504, > -40320, 0, 0]);P=E(0,0) > sage: P.height() #not very fast > -0.150688795814905 > sage: P.height(precision=2000) > -0.15068879581490624...<snip> > > Works on cloud.sagemath too. > > -- > 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/groups/opt_out. -- 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/groups/opt_out.
