#7935: local_data for elliptic curves over number fields
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Reporter: wuthrich | Owner: cremona
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.3.1
Component: elliptic curves | Keywords: elliptic curve, number fields,
local data, tamagawa
Work_issues: | Author:
Upstream: N/A | Reviewer:
Merged: |
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Comment(by cremona):
Thanks for all the excellent documentation!
About the bug: I am puzzled by this, as I still don't see how either my
original code failed or how the change (of uniformiser) works best. Here
was my thinking: if val(a_i)<0 for some i, then find the minimal e such
that e*i+valuation(a_i) is >=0 for i in [1,2,3,4,6] and then replace a_i
by {{{a_i/pi^(e*i)}}}. The point about using the "negative" flag on the
uniformiser was so ensure that dividing by a power of pi maintained
integrality at all other primes. Your new code will not do that.
Would this be better:
{{{
D = self.discriminant()
for P in D.prime_factors():
if not all([a.valuation(P)>=0 for a in ai]):
pi=K.uniformizer(P,'negative')
e = min([(ai[i].valuation(P)/[1,2,3,4,6][i]) for i in
range(5)]).floor()
ai = [ai[i]/pi**(e*[1,2,3,4,6][i]) for i in range(5)]
}}}
?
I have not looked at your last point yet. I am not so keen on
tamagawa_product() not giving the product of the Tamagawa numbers. Are
you sure that over Q when an equation is non-minimal at p that the number
returned by tamagawa_number() is not the index for the minimal model? I
thought that was what Tate's algorithm would give. I'll need to look at
it more closely.
I am leaving this as "needs review" as I have not actually tested it yet!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7935#comment:5>
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