Re: ANTS
William Stein
> Hi William,
>
> I suppose that you noticed the recent email to NMBRTHRY, which reminded me
> that February 10th is getting close. I'm leaving today to go to Bristol, so
> I'll probably be busy this week, but I'll be back next week and will be able
> to work on the sqrt5 paper. I was just looking at what you've written so
> far, and I could fill in parts of Section 3, in particular.
See
http://wstein.org/papers/sqrt5/
My plan is just to incorporate the key ideas clearly from our paper
[1] from this summer into that, plus write a little tiny bit more
about Hilbert modular forms and add some more tables of statistics
about our data.
I asked Andrew about tables of curves, and he thinks there simply
isn't enough room due to the 15 page limit, and it appears he's right.
But we can give lots of stats about the data, like "number of curves
with property x". I give a sample table along these lines in the
paper linked to above.
[1] http://code.google.com/p/uw-nt-reu2011/
-- William
--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org
R. Andrew Ohana
1402 as you put). On the sage cluster:
sage: D = SQLDatabase('/home/ohanar/sqrt5/ellcurve_aplists_6000.db')
sage: len(list(D('select * from t_class where norm<=1831')))
1414
My guess is that the 12 isogeny classes you are missing come from the
failed levels from your table of newforms you created fall 2010. I
haven't yet checked to determine what twelve classes we do not have
equations for yet.
FYI, that sql database is saturated up to conductor norm 6000 (no
failures), has aplists up to norm 256, and class labels. It is
modelled after the sql cremona database in sage, although obviously a
lot of information is missing.
I've also attached a file for section 3.4, you should be able to
include it with the \include command.
--
Andrew
William Stein
> The number of isogeny classes of conductor norm <= 1831 is 1414 (not
> 1402 as you put). On the sage cluster:
>
> sage: D = SQLDatabase('/home/ohanar/sqrt5/ellcurve_aplists_6000.db')
> sage: len(list(D('select * from t_class where norm<=1831')))
> 1414
>
> My guess is that the 12 isogeny classes you are missing come from the
> failed levels from your table of newforms you created fall 2010. I
> haven't yet checked to determine what twelve classes we do not have
> equations for yet.
>
> FYI, that sql database is saturated up to conductor norm 6000 (no
> failures), has aplists up to norm 256, and class labels. It is
What are the counts up to norm conductor 6000?
How did you get up to 6000? Is this all using mod-jon, or much more?
> modelled after the sql cremona database in sage, although obviously a
> lot of information is missing.
>
> I've also attached a file for section 3.4, you should be able to
> include it with the \include command.
I'm just pasting it in. But what do you mean by "This technique is
the analog of wheel factorization for elliptic curves.". What is
"wheel factorization"?
-- william
William Stein
> 1402 as you put). On the sage cluster:
>
> sage: D = SQLDatabase('/home/ohanar/sqrt5/ellcurve_aplists_6000.db')
> sage: len(list(D('select * from t_class where norm<=1831')))
> 1414
Can you fill in the other entries in my table, which is the counts for
norm up to 6000 (instead), for each rank, and counts of isogeny
classes.
-- William