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* NOTE! ord(j) computed wrongly if E.j_invariant = 0. Should be a quick fix to update the database. Here's a modified list for the *original* curves in matched.txt: [[attachment:modifiedjinv2.txt]] | * NOTE! ord(j) computed incorrectly if E.j_invariant = 0. Should be a quick fix to update the database. Here's a modified list for the *original* curves in matched.txt: [[attachment:modifiedjinv3.txt]] * Related: Here is a modified version of the table provided last Thursday: [[attachment:modifiedellipticcurvedatafile2.txt]] |
Twitter Feed: http://twitter.com/?q=SageMathREU#!/SageMathREU <-- Use username: SageMathREU
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 modifiedellipticcurvedatafile.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://sagemath.org/doc/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!!
Hilbert modular forms: http://code.google.com/p/purplesage/source/browse/#hg%2Fpsage%2Fmodform%2Fhilbert%2Fsqrt5%253Fstate%253Dclosed
Thursday, June 23
Official start meeting at 12pm at Pa$eo in Fremont. 4225 Fremont Ave N.
- Work afterwards in Sage lab starting 2pm.
For each aplist in http://wstein.org/Tables/hmf/sqrt5/ellcurve_aplists.txt find all possible isogeny degrees. Isogeny Degrees The worksheet is published here: http://nt.sagenb.org/home/pub/70
Ashwath, Ben, Andrew: We have re-written the prime isogeny code from yesterday, making it significantly faster: http://nt.sagenb.org/home/pub/69/
Note: Initial curve data file above (modifiedellipticcurvedatafile.txt) is updated to have 0s where the ord(j) list is empty so it is easier to parse
- Paul has written the code for nosqlite to create a database for the elliptic curves. It is currently uploaded to the sage clusters, in the folder databases, labeled small_nosqlite.
Andrew: I made a short write-up on the ordering scheme that I was working on. It very briefly mentions the background used with specialized definitions. http://wstein.org/home/ohanar/sqrt5/element_ordering/element_ordering.pdf
Friday, June 24
- 10am in the Sage lab for status reports and planning.
Here's a table of isogenies. They were computed using just the ap values, and still include some really really big isogenies: IsogenyTable4.txt -- it corresponds to the curves in this table: matched.txt. This version does not have spaces in the isogenies column.
- Computed some isogeny graphs for specific curves using division polynomials. Task: Find an algorithm to do the same.
Explicit isogeny finding worksheet: http://nt.sagenb.org/home/pub/71/
Here's a table of isogenies that includes the a-invariants for easy reference. IsogenyTable7.txt
Worksheet which uses William and Ashwath's code to check which isogeny degrees appearing in the table above are actually valid. http://nt.sagenb.org/home/pub/72/
Week 2
Monday, June 27
Code for finding isogeny classes: http://nt.sagenb.org/home/pub/76/ Notice that it has a rating of 4.0!
- 2:30 pm - Talk by Ashwath on computing prime isogenies of Elliptic Curves.
Progress on graphing isogeny classes: http://nt.sagenb.org/home/pub/79/
Tuesday, June 28
Wednesday, June 29
2:10pm in Sieg Hall -- talk by Ralph Greenberg on Galois Representation
Created updated text file (Galois paired table) Paired_Table.txt
Elkies algorithm: see here
Here's our isogeny class/adjacency matrix data for N up to 3205! isogeny_partial_output.txt
Thursday, June 30
here is an updated list of all possible valuables calculated so far, now with labels! Table
Friday, July 1
NOTE! ord(j) computed incorrectly if E.j_invariant = 0. Should be a quick fix to update the database. Here's a modified list for the *original* curves in matched.txt: modifiedjinv3.txt
Related: Here is a modified version of the table provided last Thursday: modifiedellipticcurvedatafile2.txt
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