Opened 12 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: Jamie Weigandt Owned by: Jamie Weigandt
Priority: major Milestone: sage-feature
Component: elliptic curves Keywords: descent, selmer, number field, simon_two_descent
Cc: William Stein, John Cremona, Robert Miller Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
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Description (last modified by Peter Bruin)

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 12 years ago by Jamie Weigandt

Milestone: sage-5.0sage-feature
Type: PLEASE CHANGEenhancement

comment:2 Changed 9 years ago by Peter Bruin

Description: modified (diff)
Keywords: simon_two_descent added

comment:3 Changed 9 years ago by John Cremona

I agree that there should be native 2-descent implemented which would work over number fields (and be an alternative to mwrank over Q). I don't understand the word "naive" in the description though.

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.

Version 0, edited 9 years ago by John Cremona (next)
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