Friday January 8, 2016, 1:00 p.m.-5:50 p.m.
AMS Special Session on Number Theory and Cryptography, II
Room 606, Washington State Convention Center - See more at: http://jointmathematicsmeetings.org/meetings/national/jmm2016/2181_program_ss72.html#sthash.0qhNOcdn.dpuf

I will talk about how the SageMath (http://sagemath.org) software is incredibly useful for number theory and cryptography
research.

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# 15 minutes to talk about what SMC provides for writing a paper in practice.

## 8 min. A research project

- background: mazur-stein-watkins-bektemerov bulletins 2006: give a freshman a student project and see what happens

- crazy plots: the rank just keeps getting bigger in the data

- random matrix heuristics and other conjecture: rank is 1/2 in the limit

- manjul bharghava: the rank definitely doesn't just keep getting bigger!

- challenge: systematically compute the ranks of *all* elliptic curves BLAH of height BLAH far enough that we can finally see the rank going down!

- here's when it happens

- bonus: some other statistics

## 4 min. Features of SMC for writing this paper

- collaborative editing of latex documents

- collaborative persistent terminals (e.g., ssh to cluster somewhere)

- edit Python code; run from sage worksheets

- use sqlite easily

- run project on a 32-core big-memory VM at Google

- chat: post little comments on the side of any file being edited


## 4 min. Features of Sage for writing this paper


 1. - mwrank

- Simon Spicer's Elliptic curve enumeration

- Simon Spicer's L-function bounding code

- Magma interface