#8829: Saturation for MW-groups of elliptic curves over number fields.
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Reporter: robertwb | Owner: cremona
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.4
Component: elliptic curves | Resolution:
Keywords: saturation | Merged in:
Authors: Robert Bradshaw, | Reviewers: John Cremona
John Cremona | Work issues:
Report Upstream: N/A | Commit:
Branch: u/cremona/8829 | a85f40629df89da829e3a38d9e0443576bced01d
Dependencies: #8828 | Stopgaps:
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Comment (by cremona):
The latest commit involves more than adding more doctests to the new
functions, since bugs were revealed which led to a rewrite of the sieving
code for the two cases where the p-rank of the reduction is 1 or 2; the
former uses discrete log in the reduction, the latter uses Weil pairing
and discrte log in the multiplicative group. In the sieve I restrict to
primes of degree 1. It is a Theorem (see
http://eprints.nottingham.ac.uk/10052/) that this will suffice to prove
p-saturation, provided that one does use reductions with p-rank 2 and not
just those of p-rank 1 as originally suggested by Siksek in
https://ore.exeter.ac.uk/repository/handle/10871/8323 .
I will mark this as ready for review so the bots get to work on it, and of
course humans are welcome to look at the new code, but I will now test it
thoroughly on the LMFDB curves and report back.
--
Ticket URL: <http://trac.sagemath.org/ticket/8829#comment:24>
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