#6384: elliptic curve -- isogeny function seems completely totally broken in
first
example I try
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Reporter: was | Owner: shumow
Type: defect | Status: new
Priority: major | Milestone: sage-4.1
Component: algebra | Keywords:
Reviewer: | Author:
Merged: |
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Changes (by shumow):
* owner: tbd => shumow
Comment:
The problem is where you do:
> sage: phi = E.isogeny([P]); phi
That is not the correct way to specify a kernel. You are trying to
specify the generator, and expecting the isogeny function to determine
this. (We could, at some point modify this to be the case in some sense.)
However, the correct way to specify an isogeny with a kernel list is to
specify the whole kernel. So, what you would need to do is this:
> sage: phi = E.isogeny([E(0), P, 2*P, 3*P, 4*P]); phi
You have a good point about the typo in the docstring.
Replying to [ticket:6384 was]:
> First the docstring for E.isogeny? has a typo
> {{{
> (defaul:None)
> }}}
> Note the missing t.
>
> Next, I tried taking the elliptic curve 11a and one 5-torsion point P on
it and trying to make the isogeny {{{E --> E/<P>}}}. It seems that the
result is a '''total disaster in every imaginable way'''.
>
> {{{
> sage: E = EllipticCurve('11a'); P = E.torsion_subgroup().gens()[0]; P
> (5 : 5 : 1)
> sage: phi = E.isogeny([P]); phi
> Isogeny of degree 1 from Elliptic Curve defined by y^2 + y = x^3 - x^2 -
10*x - 20 over Rational Field to Elliptic Curve defined by y^2 + y = x^3 -
x^2 - 560*x - 4277 over Rational Field
> sage: phi.codomain().conductor()
> 530575705
> sage: phi.codomain().conductor().factor()
> 5 * 11 * 1531 * 6301
> }}}
>
> Note that:
>
> * the two curves are not isogenous, since their conductors are
different
>
> * the degree of the isogeny is reported to be 1, but it should be 5.
>
>
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6384#comment:1>
Sage <http://sagemath.org/>
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