Isogenies, Modular polynomials
Luca De Feo
To continue my work on isogenies between elliptic curves (by the way,
ticket 11095 needs review), I need modular equations. Pari has precomputed
modular equations for levels up to 500 in the seadata optional db, and I
am thinking of writing a function to make these data accessible from Sage.
What would be a sensible place to put such function? I see that the source
tree contains an empty package sage.modular.curves, would it make sense to
add a 'modular_polynomials' module in there?
Luca
John Cremona
Having the modular equations in Sage is a great idea.
Good idea. I don't know who made that but the notes files suggests it
was William. He's a few yards from me right now and I'll ask him
about this.
John
>
> Luca
>
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William Stein
> I am reviewing #11095 right now!
>
> Having the modular equations in Sage is a great idea.
>
> On Tue, May 3, 2011 at 6:17 PM, Luca De Feo <de...@lix.polytechnique.fr> wrote:
>> Hello,
>>
>> To continue my work on isogenies between elliptic curves (by the way, ticket
>> 11095 needs review), I need modular equations. Pari has precomputed modular
>> equations for levels up to 500 in the seadata optional db, and I am thinking
>> of writing a function to make these data accessible from Sage. What would be
>> a sensible place to put such function? I see that the source tree contains
>> an empty package sage.modular.curves, would it make sense to add a
>> 'modular_polynomials' module in there?
>
> Good idea. I don't know who made that but the notes files suggests it
> was William. He's a few yards from me right now and I'll ask him
> about this.
Still true about our relative location, but you didn't ask me.
I guess I made that directory in 2005, but it never got it used. It
would be a great place to pur your functionality.
>
> John
>
>>
>> Luca
>>
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>>
>>
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>
--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org
Hamish Ivey-Law
"database_kohel-20060803". Unless some work has been done on the
Seadata DB in the last two years, its contents should be a subset of
what's found in David K's database. If I recall correctly, at the
time I just augmented the existing Seadata DB with David's Atkin
modular polynomials up to level 500. David's database contains more:
- Classical modular polynomials of prime level < 114
- Atkin modular polynomials of prime level < 500
- Dedekind eta (aka Canonical) modular polynomials of prime level <
100
Cheers,
Hamish.
Luca De Feo
Thanks for your mail, I'm glad to see that David Kohel's database is
easily available in Sage.
I installed the package via
sage -i database_kohel
but the levels available do not correspond to what you say. I have:
- classical m.p. of prime level < 114
- Atkin's m.p. of prime level < 234
- Dedekind eta m.p. of prime level < 300, with some gaps
- Dedekind eta modular correspondences for primes < 50
- no Atkin modular correspondences
There is also a bug when trying to retrieve a modular correspondence that
is not in the database.
Maybe the version of database_kohel on sagemath.org is out of date ?
Cheers,
Luca
Hamish Ivey-Law
On May 6, 5:47 pm, Luca De Feo <de...@lix.polytechnique.fr> wrote:
> Thanks for your mail, I'm glad to see that David Kohel's database is
> easily available in Sage.
>
> I installed the package via
> sage -i database_kohel
>
> but the levels available do not correspond to what you say. I have:
> - classical m.p. of prime level < 114
> - Atkin's m.p. of prime level < 234
> - Dedekind eta m.p. of prime level < 300, with some gaps
> - Dedekind eta modular correspondences for primes < 50
> - no Atkin modular correspondences
>
> There is also a bug when trying to retrieve a modular correspondence that
> is not in the database.
>
> Maybe the version of database_kohel on sagemath.org is out of date ?
original databases; I mistakenly assumed that the Sage package was
just a wrapper around the original databases (which do definitely
include the modular polynomials up to the levels I mentioned in my
previous post). What is perhaps a bit strange is that (at least
according to the timestamps) the original databases were constructed
in 2002, whereas the Sage package seems to be from 2006. So perhaps
what happened instead is that when the Sage package of David's DBs was
created, the creator decided to reduce the size a bit by not including
some of the larger polynomials (bandwidth not being as plentiful back
then in the olden days). That's just a guess though.
In any case, it seems like the Sage package should be updated. The
original databases can be found at
http://echidna.maths.usyd.edu.au/echidna/dbs/index.html
There's no "readme" file explaining the format of the files, but it
should be pretty self-explanatory if I remember correctly. I've got
notes about the file format lying around somewhere that I could dig up
if necessary, as well as the script I used to convert them to a form
suitable for Pari's Seadata package; let me know if you want me to
email them to you.
Cheers,
Hamish.