On Fri, Oct 28, 2011 at 12:01 AM, Andrei Jorza <[email protected]> wrote: > Hello, > > I noticed something I find odd in sha().an() > > sage: E=EllipticCurve([0,0,0,-3,1]) > sage: E.is_minimal() > True > sage: E.rank() > 1 > sage: E.lseries().deriv_at1(1000)[0] > 2.61683934093655 > sage: E.sha().an() * E.period_lattice().basis()[0] * E.regulator() * > E.tamagawa_product_bsd()/(E.torsion_order()**2) > 1.30841967046636 > > so the two quantities differ by a factor of 2, whereas they should be > equal, at least in my understanding of what sha().an() is supposed to > be > doing. > > Am I doing anything wrong? > > Thanks, > Andrei Jorza
The period lattice is rectangular, so the Omega in the BSD is twice the least real period. sage: E=EllipticCurve([0,0,0,-3,1]) sage: E.global_minimal_model() Elliptic Curve defined by y^2 = x^3 - 3*x + 1 over Rational Field sage: s = E.sha().an() sage: s 1 sage: E.period_lattice().basis() (2.17755142623757, 1.88697504100100*I) sage: E.period_lattice().omega() 4.35510285247513 > > PS. I am running Sage Version 4.7, Release Date: 2011-05-23 on Ubuntu > 11.04. The CPU is an Intel i7-960. > > -- > To post to this group, send email to [email protected] > To unsubscribe from this group, send email to > [email protected] > For more options, visit this group at > http://groups.google.com/group/sage-support > URL: http://www.sagemath.org > -- William Stein Professor of Mathematics University of Washington http://wstein.org -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
