#14577: Bug in the case S_4 in Galois representations of elliptic curves
-----------------------------------------------------------+----------------
Reporter: wuthrich | Owner:
cremona
Type: defect | Status:
needs_review
Priority: major | Milestone:
sage-5.10
Component: elliptic curves | Resolution:
Keywords: galois representations, elliptic curves | Work issues:
Report Upstream: N/A | Reviewers:
Frédéric Chapoton
Authors: Chris Wuthrich | Merged in:
Dependencies: | Stopgaps:
-----------------------------------------------------------+----------------
Comment (by wuthrich):
Yes, I am sure this improves this function.
The function {{{_ex_set(p)}}} at the start of the file lists the elements
in PGL_2(F_p) that may appear in an exceptional subgroup A_n or S_n. Or
rather it lists what `trace^2/det` evaluates on them. (This is taken from
Serre's paper). In particular the elements of order 5 are the roots of
{{{(X**2 - 3*X+1)}}}, which we add at the end to the list.
Now later this is used in the function {{{image_type}}}. Unfortunately, I
took the last two elements, when in fact for some `p` there is are no such
elements of order 5. As a consequence, the example that John found all
possibilities for what the subgroup could be were eliminated. Hence the
answer "bug". Now it gives the correct answer.(X**2 - 3*X+1)(X**2 - 3*X+1)
So the maths did not change, just a silly bug was eliminated.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14577#comment:11>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac?hl=en.
For more options, visit https://groups.google.com/groups/opt_out.
