Opened 11 years ago
Last modified 9 years ago
#11041 new enhancement
Implement the number field method for computing 2-Selmer groups of elliptic curves natively in Sage.
| Reported by: | weigandt | Owned by: | weigandt |
|---|---|---|---|
| Priority: | major | Milestone: | sage-feature |
| Component: | elliptic curves | Keywords: | descent, selmer, number field, simon_two_descent |
| Cc: | was, cremona, rlm | Merged in: | |
| Authors: | Reviewers: | ||
| Report Upstream: | N/A | Work issues: | |
| Branch: | Commit: | ||
| Dependencies: | Stopgaps: |
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Description (last modified by )
There are many concerns about simon_two_descent(). See tickets: #5153, #9322, #10735, #10745, #10832, #11005, #15483.
As a step toward implementing a general framework for Selmer group computations as discussed in #11039. A native implementation of the "number field method" for computed 2-Selmer groups should be produced.
Change History (3)
comment:1 Changed 11 years ago by
- Milestone changed from sage-5.0 to sage-feature
- Type changed from PLEASE CHANGE to enhancement
comment:2 Changed 9 years ago by
- Description modified (diff)
- Keywords simon_two_descent added
comment:3 Changed 9 years ago by
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I agree that there should be native 2-descent implemented which would work over number fields (and be an alternative to mwrank over Q).
There is a good description of the method in Simon's LMS JCM paper, and rather a lot of it has been implemented by various people. I also have my own Magma version which might be a useful starting point.