#10735: Simon 2-descent may not check for solubility at archimedean places.
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Reporter: weigandt | Owner: cremona
Type: defect | Status: new
Priority: major | Milestone: sage-6.2
Component: elliptic curves | Resolution:
Keywords: simon_two_descent | Merged in:
Authors: | Reviewers:
Report Upstream: Reported upstream. No | Work issues:
feedback yet. | Commit:
Branch: | Stopgaps:
Dependencies: #11005 |
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Comment (by wuthrich):
That is indeed bad. The fomula (after the first descent) is indeed
dim Sel_phi + dim Sel_phihat + dim E[2] - 2 .
this is a upper bound to dim Sel_2 and they have the same parity. But they
need not be equal as the second descent in mwrank finds. The difference is
a subquotient of Sha(E').
Conclusion: The output of Simon's algorithm is an upper bound on the
2-Selmer group, which is correct in parity, but not necessarily equal.
In propose that we change the documentation, for I don't image that
Simon's script could give back to full answer - though I have not looked
at it.
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Ticket URL: <http://trac.sagemath.org/ticket/10735#comment:8>
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