#16959: p-primary bound for Sha can be improved
-------------------------------------+-------------------------------------
Reporter: wuthrich | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: elliptic curves | Resolution:
Keywords: tate-shafarevich, | Merged in:
shark | Reviewers:
Authors: Chris Wuthrich | Work issues:
Report Upstream: N/A | Commit:
Branch: | e20fe2691428bf33958cdc3a716a9f2248dde789
u/wuthrich/ticket/16959 | Stopgaps:
Dependencies: |
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Comment (by was):
Please run doctests, e.g., -- your changes here impact the file BSD.py,
causing 5 doctest failures:
{{{
/scratch/wstein/sage-6.4.beta0$ ./sage -t --warn-long 108.4
src/sage/schemes/elliptic_curves/BSD.py
Running doctests with ID 2014-09-10-16-21-02-4fc7534a.
Doctesting 1 file.
sage -t --warn-long 108.4 src/sage/schemes/elliptic_curves/BSD.py
**********************************************************************
File "src/sage/schemes/elliptic_curves/BSD.py", line 304, in
sage.schemes.elliptic_curves.BSD.?
Failed example:
EllipticCurve('11a').prove_BSD(verbosity=2)
Expected:
p = 2: True by 2-descent...
True for p not in {2, 5} by Kolyvagin.
True for p=5 by Mazur
[]
Got:
p = 2: True by 2-descent
True for p not in {2, 5} by Kolyvagin.
Kato further implies that #Sha[5] is trivial.
[]
**********************************************************************
File "src/sage/schemes/elliptic_curves/BSD.py", line 310, in
sage.schemes.elliptic_curves.BSD.?
Failed example:
EllipticCurve('14a').prove_BSD(verbosity=2)
Expected:
p = 2: True by 2-descent
True for p not in {2, 3} by Kolyvagin.
Remaining primes:
p = 3: reducible, not surjective, good ordinary, divides a Tamagawa
number
(no bounds found)
ord_p(#Sha_an) = 0
[3]
Got:
p = 2: True by 2-descent
True for p not in {2, 3} by Kolyvagin.
Kato further implies that #Sha[3] is trivial.
[]
**********************************************************************
File "src/sage/schemes/elliptic_curves/BSD.py", line 318, in
sage.schemes.elliptic_curves.BSD.?
Failed example:
EllipticCurve('14a').prove_BSD(two_desc='simon')
Expected:
[3]
Got:
[]
**********************************************************************
...
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/16959#comment:4>
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