We have theory that tells us that for curves of analytic rank 0 or 1, Sha is finite and while BSD is not completely proved for such curves, the formula it claims for #Sha is certainly rational -- and Sage does compute this exactly. But for analytic rank >1 the "analytic Sha" is just the value predicted by BSD which is not known theoretically to be rational and can only be computed as a floating point approximation, for which it is most honest to leave as such.
John Cremona On 16 October 2013 10:39, Georgi Guninski <gunin...@guninski.com> wrote: > Why E.sha().an() = 0 and E.sha().an_numerical() = 1.0 ? > > On 5.11 on linux and on cloud.sagemath.com: > > sage: E=EllipticCurve(QQ,[0, 0, 1, -79, > 342]);E.sha().an(),E.sha().an_numerical() > (0, 1.00000000000000) > #^ why different and 0 is integer ? > sage: E.sha().bound() > (0, 0) > > sage: type(E.sha().an()) > <type 'sage.rings.integer.Integer'> > sage: E.rank(),E.analytic_rank() > (5, 5) > > sage: E.conductor() > 19047851 > > E.sha().an_padic(3) # stopped this at about 7G of RAM > > -- > 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.
