#8238: heegner_index_bound may be incorrect for curves with rational torsion
-------------------------------+--------------------------------------------
Reporter: rlm | Owner: cremona
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.4.4
Component: elliptic curves | Keywords:
Author: Robert Miller | Upstream: N/A
Reviewer: John Cremona | Merged:
Work_issues: |
-------------------------------+--------------------------------------------
Changes (by cremona):
* status: needs_review => needs_work
* reviewer: => John Cremona
Comment:
I applied the patch to 4.4.3 and it worked fine (patch applies cleanly,
all long tests in heegner.py pass,
Some minor quibbles:
1. on line 6365: instead of "an interval that contains the index, or
the index over 2" say "... or half the index".
2. line 6454++: this code is reached whe then rank is 0 (or it appears
to be) but then F.gens()[0] would fail. If it is the case that the rank
would never be 0 here. I would prefer a comment to that effect and change
the test to if F.rank() == 1. (I assume that in this context calling
F.rank() and F.gens() is not expensive?)
3. After setting a=2 in line 6460 the loop should break. (OK, so there
will not be that many torsion points o nEK, but still.) Even better would
be to first compute EK.torsion_points() and only run the loop at all if it
has even length? (But still test if z itself can be divided by 2). I'm
sure I once wrote a function which returned a list of points generating
torsion modulo 2*torsion....if you did
{{{
sage: for T in EK.torsion_subgroup().gens():
....: if T.order()%2==0:
}}}
you would have at most 2 points to check.
I'll give this a positive review once these have been fixed.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8238#comment:7>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
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-trac?hl=en.
