#9039: major error in E.sha().bound_kato() for E an elliptic curve
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Reporter: rlm | Owner: cremona
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.4.3
Component: elliptic curves | Keywords:
Author: Robert Miller | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by wuthrich):
Ooops, you are right. Elkies describes these curves (they are rare) and
shows that they do not contain SL_2(Z_p) in the p-adic Galois image. And
that is needed for Kato's theorem 12.5. I have the vague feeling that one
could lower it to the case of mod-p-surjectivity with some work, but I am
sure it is not yet known if that is true.
That makes the check at 3 quite painful. Maybe we should just include 3 by
default. I will look at the galois representations in sage soon again.
Maybe I find an easy way to check it for p=3.
Chris.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9039#comment:6>
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