#9320: Implement root numbers for elliptic curves over number fields
-------------------------------------+-------------------------------------
Reporter: arminstraub | Owner: cremona
Type: enhancement | Status: needs_work
Priority: minor | Milestone:
Component: elliptic curves | Resolution:
Keywords: root number | Merged in:
Authors: Tim Dokchitser | Reviewers:
and group (Sage Days 22) | Work issues: fix ReST formatting,
Report Upstream: N/A | coverage
Branch: u/chapoton/9320 | Commit:
Dependencies: | 87938e0bdccc397f9527b1db39b9c85006f40232
| Stopgaps:
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Comment (by cremona):
An example which is additive at 3:
{{{
sage: K.<r> = NumberField(x^2-x+1)
sage: E = EllipticCurve([r-1,r,1,r-1,-1])
sage: P3 = K.ideal(2*r-1)
sage: assert P3.is_prime() and P3.norm()==3
sage: assert E.has_additive_reduction(P3)
sage: assert P.root_number(P3)==1 ## not implemented
}}}
Here the value is taken from page 115 of my thesis, and agrees with
Magma's value.
For additional testing we could put in an 'algorithm' parameter which
could be 'magma' and then (of course) only work when Magma is installed,
so you could have optional doctests conditional on Magma of the form
{{{
assert E.root_number(P) == E.root_number(P, algorithm='magma')
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/9320#comment:16>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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