#8451: improve galois representation for elliptic curves
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Reporter: wuthrich | Owner: cremona
Type: defect | Status: new
Priority: major | Milestone: sage-4.3.4
Component: elliptic curves | Keywords: elliptic curves, galois
representation, is_surjective
Author: Chris Wuthrich | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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In #8118, I have moved Galois representation for elliptic curves into a
new file and I have modified the output of {{{is_surjective}}}. The
function does no longer give a reason.
I wish now to reintroduce this as a new function {{{image_type()}}} which
will give back a string describing the image as a subgroup in GL_2(F_p).
In the middle of doing this, I noted the severe bug in
{{{is_surjective}}}. The code does not check for exceptional images A_4,
S_4, and A_5 in PGL_2(F_p). Typically currently, sage claims that the
mod-5 representation of 324b1 is surjective.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8451>
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