Thanks for *not* complaining about the "multiplicative" in "Torsion Subgroup isomorphic to Multiplicative Abelian Group..."
I once wrote a patch to fix that but no-one liked it enough. I also tried E.change_ring(QQbar).torsion_subgroup() but that failed for a different reason! For some reason, E.change_ring(Qbar) has this type: sage: type(E.change_ring(QQbar)) <class 'sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic'> while sage: type(EllipticCurve(QQbar, E.a_invariants())) <class 'sage.schemes.elliptic_curves.ell_field.EllipticCurve_field'> which is inconsistent; and neither helps, since EllipticCurve_field objects don't have a torsion subgroup.... Some of this should be easy to fix. Assuming that you could do something useful with the torsion subgroup over QQbar! Wait a minute: in what sense is the torsion subgroup of J_0(11) of structure [5,5] anyway? Over Q it is cyclic of order 5, while over QQbar it is (Q/Z)^2 . So the output is worse than you thought! John On Apr 26, 11:57 pm, "Kenneth A. Ribet" <[email protected]> wrote: > Hi, > Maybe this is a frivolous comment, but I'd like to express my surprise at the > use of "torsion_subgroup" to mean two very different things for an abelian > variety and for an elliptic curve: > sage: E=EllipticCurve('11a') > sage: E.torsion_subgroup() > Torsion Subgroup isomorphic to Multiplicative Abelian Group isomorphic to C5 > associated to the Elliptic Curve defined by y^2 + y = x^3 - x^2 - 10*x - 20 > over Rational Field > sage: A=J0(11) > sage: A.torsion_subgroup() > Traceback (most recent call last): > ... > TypeError: torsion_subgroup() takes exactly 2 arguments (1 given) > sage: A.torsion_subgroup(5) > Finite subgroup with invariants [5, 5] over QQ of Abelian variety J0(11) of > dimension 1 > sage: A.rational_torsion_subgroup() > Torsion subgroup of Abelian variety J0(11) of dimension 1 > sage: A.rational_torsion_subgroup().order() > 5 > sage: A.rational_torsion_subgroup().abelian_group() > Traceback (most recent call last): > ... > AttributeError: 'RationalTorsionSubgroup' object has no attribute > 'abelian_group' > I'm surprised that "torsion_subgroup" for an elliptic curve over Q refers to > *rational* torsion while for an abelian variety over Q it refers to *all* > torsion. Further, it's frustrating to me that the rational torsion subgroup > of an abelian variety over Q has an order but not the structure of an abelian > group. I'm sure that there are good reasons for this, but this end user is > kind of amazed. Before the sage session above, I used to think that elliptic > curves and abelian varieties of dimension 1 were the same thing! Live and > learn.... > Best, > Ken > > > > -- > 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 > athttp://groups.google.com/group/sage-support > URL:http://www.sagemath.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
