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== Description == 1. Tabulating modular elliptic curves over Q (based on the first chapter of my book) 2. Finding all elliptic curves with good reduction outside a finite set S of prime, over number fields. I could lecture on the theory, based on my paper on the subject which reduces it to finding all S-integral points on e.c.s over number fields, and then the project could be to implement it in Sage. Over Q, I already did that, using the S-integral points functions implemented two summers ago. But over number fields there will be other challenges, and this is likely to spill over into more general computation of Mordell-Weil groups. |
John Cremona (Warwick University): Tables of elliptic curves
Description
- Tabulating modular elliptic curves over Q (based on the first chapter of my book)
- Finding all elliptic curves with good reduction outside a finite set S of prime, over number fields. I could lecture on the theory, based on my paper on the subject which reduces it to finding all S-integral points on e.c.s over number fields, and then the project could be to implement it in Sage. Over Q, I already did that, using the S-integral points functions implemented two summers ago. But over number fields there will be other challenges, and this is likely to spill over into more general computation of Mordell-Weil groups.