#12356: many missing class number 2 orders in CM j-invariant function over
quadratic fields
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Reporter: cremona | Owner: cremona
Type: defect | Status: needs_review
Priority: critical | Milestone: sage-5.0
Component: elliptic curves | Keywords:
Work_issues: | Upstream: N/A
Reviewer: John Cremona, William Stein | Author: John Cremona,
William Stein
Merged: | Dependencies:
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Changes (by newvalueoldvalue):
* reviewer: => John Cremona, William Stein
* author: John Cremona => John Cremona, William Stein
Comment:
John Cremona found a mistake in my algorithm, which I've addressed via a
new patch.
I've written a new version based on some of Cremona's comments and with a
big comment explaining what I'm doing. Basically I just compute a
pessimistic bound on the quotient (as you suggest) by applying a "big
theorem" (probably from Hardy & Wright) bounding phi from below, and
noting that phi_D(f) >= phi(f). The new code seems to work fine (and
even found a class number 8 counterexample to the code I posted) and is
pretty fast, but of course has plenty of room for optimization and
improvement by your student, who could also run it to make tables, etc.
Of course, I very much hope John will extremely critically review this!
I didn't mention it, but the *reason* I wrote this code was not to scoop
your student or something -- it was so I could better referee your patch!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12356#comment:5>
Sage <http://www.sagemath.org>
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