#5153: bug in simon_two_descent for elliptic curves
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Reporter: was | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-4.4
Component: elliptic curves | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by cremona):
Replying to [comment:10 weigandt]:
> > the numbers 3,4 which are supposed to be lower and upper bounds on the
rank are wrong and
> > should be 3,3.
>
> The numbers 3,4, are correct. G has a point of order 2 over its base
feild, so the 2-rank of the 2-Selmer group is 4. However, an error like
the one you're describing does occur with 438e1 over Q.
Do you mean 438e1 over Q? #torsion=2 and rank=0 but the first descent
via 2-isogeny gives a rank upper bound of 2. If the rank were 2 then the
2-selmer rank would be 3. two_descent_simon() gives lower bound of 0 and
3 for the rank of the 2-Selmer group. That last one is clearly wrong. I
think it is similar to the problem my 2-descent used to have: Simon does
not do a second descent, so het gets the uppoer bound of 3 on the rank
(not wrong!) but incorrectly calls it the 2-Selmer rank.
We should correct the docstring of two_descent_simon, and I will tell
Simon that his documentation is incorrect.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5153#comment:11>
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