#19229: Bug in elliptic curve Galois Representation
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Reporter: cremona | Owner:
Type: defect | Status: needs_work
Priority: major | Milestone: sage-6.10
Component: elliptic curves | Resolution:
Keywords: Galois | Merged in:
representations | Reviewers:
Authors: John Cremona | Work issues:
Report Upstream: N/A | Commit:
Branch: u/cremona/19229 | 62accc077ff28e2306364abaa60199846e292fdd
Dependencies: | Stopgaps:
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Comment (by cremona):
Replying to [comment:18 jdemeyer]:
> Just a question (not something to do for this ticket): did you ever
consider computing the CM discriminant using the period lattice? If you
have a sufficiently good (I guess this is the hard part) approximation to
τ, you can compute its minimal polynomial A τ^2^ + B τ + C and from that
the discriminant.
Interesting idea. Note that the existing code involves computing Hilbert
Class Polynomials which does something similar. We can get tau to high
precision easily since there is such a fast convergence for the periods.
But some care would be needed to make this rigorous.
Improving the detection of CM would certainly be useful.
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Ticket URL: <http://trac.sagemath.org/ticket/19229#comment:21>
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