#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 | Work issues:
Report Upstream: N/A | Commit:
Branch: u/cremona/8829 | 2f20f7373a13e2267bc5ae3d2a7cae93278a76c4
Dependencies: #8828 | Stopgaps:
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Comment (by cremona):
Progress report: I am currently running the p-saturation (for single
primes) on lots of LMFDB curves and all is well so far. This is almost
always for very small p (mainly 2 and 3) though, since I am starting with
some saturated points on one curve (provided by Magma) and using
p-isogenies to map to other curves in the isogeny class. Higher degree
isogenies are not so common.
I did start to veryify that the points from Magma were fully saturated,
but ran into problems computing the saturation index, using (line 3717)
the lower bound on the height of all non-torsion points -- previously
implemented and merged i n6.3 (see #8828). For example, I had a curve
where the value of 5 in that line was insufficient *and led to an infinite
loop in the call to min()*, while 10 worked fine, but now I have a curve
where I have not yet found a value which gives anything. For the record I
will give that example here:
{{{
K.<phi> = NumberField(x^2-x-1) # Q(sqrt(5))
E = EllipticCurve([phi + 1, -phi + 1, 1, 20*phi - 39, 196*phi + 237])
H = E.height_function()
H.min(.1,10,verbose=True) # does not appear to terminate
}}}
Strictly this is about the code merged in #8828, but it will need fixing
here before we can let this (useful!) function out into the world.
--
Ticket URL: <http://trac.sagemath.org/ticket/8829#comment:32>
Sage <http://www.sagemath.org>
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