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* The isogeny code in Sage by Dan Shumow: http://sagenb.org/src/schemes/elliptic_curves/ell_curve_isogeny.py | * The isogeny source code in Sage by Dan Shumow: http://nt.sagenb.org/src/schemes/elliptic_curves/ell_curve_isogeny.py * Documentation of Shumow's isogeny code: http://nt.sagenb.org/doc/static/reference/sage/schemes/elliptic_curves/ell_curve_isogeny.html |
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* Project idea: For each aplist in http://wstein.org/Tables/hmf/sqrt5/ellcurve_aplists.txt find all possible isogeny degrees. This would be extremely interesting!! |
Week 1
Monday, June 20
Introductions: http://tinyurl.com/3m6fs8f
Tutorial about how to compute things about elliptic curves: http://nt.sagenb.org/home/pub/45/
Cremona's online tables: http://www.warwick.ac.uk/~masgaj/ftp/data/
Cremona's book (see in particular Table 1): http://www.warwick.ac.uk/~masgaj/book/fulltext/
Assignment for today: Compute as much as you can about the curves listed here.
- Results of assignment:
William: See http://nt.sagenb.org/home/pub/46/ and in particular the pdf link at the bottom.
Tuesday, June 21
10am-12pm: Introduction to Sage in Communications B27. Video
- Presentation of assignments from June 20 (table up to norm conductor 124):
Rado Kirov: http://nt.sagenb.org/home/pub/47/
Ben Leveque: http://nt.sagenb.org/home/pub/50/
Andrew Ohana: http://nt.sagenb.org/home/pub/51/
Ashwath Rabindranath: http://nt.sagenb.org/home/pub/53/
Paul Sharaba: http://nt.sagenb.org/home/pub/56/
William Stein: http://nt.sagenb.org/home/pub/46/
- Demos of things you've done using Sage (e.g., interacts, etc.):
Ben Leveque's Farey Graph: http://nt.sagenb.org/home/pub/52/
Get started with the Wiki a little: http://wiki.sagemath.org/reu/2011
Andrew Ohana and Aly Deines: canonical stuff ohana1.pdf
- Mentioned: dumps, loads, save, load
nosqlite: http://code.google.com/p/nosqlite/ along with a worksheet that illustrates it.
Antwerp IV -- old tables of elliptic curves: http://modular.math.washington.edu/Tables/antwerp/
Read Ribet's awesome paper 'Galois representations and modular forms', in particular Sections 3 and 5.
Extensive data over Q(sqrt(5)) so far is here as plain text files. This can be used instead of http://db.modform.org, and is easier to parse.
Wednesday, June 22
- Rado's talk at 10am in Communications B27:
Best HTML5 canvas tutorial: https://developer.mozilla.org/en/canvas_tutorial
Graph editor source code: https://bitbucket.org/radokirov/js-graph-editor
- 11:30am -- meet in the Sage lab
Aly Deines -- Global minimal models at 3:10pm. http://nt.sagenb.org/home/pub/62/
Get started with Mercurial a little: http://code.google.com/p/uw-nt-reu2011/
William's idea for determining whether there is a p-isogeny: http://nt.sagenb.org/home/pub/61/
Elkies tables that have isogeny examples: http://www.math.harvard.edu/~elkies/nature.html
William: Added initial template version of our goal paper to the repository.
Here InitialCurveData.txt is an initial table that adds |T|, signs, ord(disc), ord_(j), Tamagawa numbers, and Kodaira symbols to the data at http://wstein.org/Tables/hmf/sqrt5/finding_weierstrass_equations/matched.txt
Here is the paper from the 2010 REU: On the Irreducibility of Galois Representations Associated to Elliptic Curves
Ashwath: Here is some very preliminary code that confirms William's idea to check if a certain curve has odd prime isogenies using the reducibility of the characteristic polynomial of Frobenius at primes of good reduction: http://nt.sagenb.org/home/pub/63
The isogeny source code in Sage by Dan Shumow: http://nt.sagenb.org/src/schemes/elliptic_curves/ell_curve_isogeny.py
Documentation of Shumow's isogeny code: http://nt.sagenb.org/doc/static/reference/sage/schemes/elliptic_curves/ell_curve_isogeny.html
Computing isogeny degrees and filling out the norm conductor 31 isogeny class: http://nt.sagenb.org/home/pub/65/
Project idea: For each aplist in http://wstein.org/Tables/hmf/sqrt5/ellcurve_aplists.txt find all possible isogeny degrees. This would be extremely interesting!!
Thursday, June 23
Official start meeting at 12pm at Pa$eo in Fremont. 4225 Fremont Ave N.
- Work afterwards in Sage lab starting 2pm.
Friday, June 24
Week 2
Monday, June 27
Tuesday, June 28
Wednesday, June 29
Thursday, June 30
Friday, July 1
Week 3
Monday, July 4
Tuesday, July 5
Wednesday, July 6
Thursday, July 7
Friday, July 8
Week 4 (William in Budapest this week)
Monday, July 11
Tuesday, July 12
Wednesday, July 13
Thursday, July 14
Friday, July 15
Week 5
Monday, July 18
Tuesday, July 19
Wednesday, July 20
Thursday, July 21
Friday, July 22
Week 6
Monday, July 25
Tuesday, July 26
Wednesday, July 27
Thursday, July 28
Friday, July 29
Week 7
Monday, August 1
Tuesday, August 2
Wednesday, August 3
Thursday, August 4
Friday, August 5
Week 8
Monday, August 8
Tuesday, August 9
Wednesday, August 10
Thursday, August 11