#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: | Author: John Cremona
Merged: | Dependencies:
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Comment(by was):
I've posted a patch that does the general case (up to degree 100) in a way
that is refactored in a more usable way. This is in
trac_12356-extended.patch, which does *not* depend on trac_12356.patch.
For refereeing there are basically two mathematical arguments that are
used in the code:
1. if a hilbert class polynomial F has a root in a field K of degree n,
then the degree of F is at most n.
2. {{{class_number(D) <= class_number(D*f^2)}}} for fundamental D and
integer f.
Of course, in 1, I think it would have to be a divisor of n, which could
be used to optimize the code further. I hope these two statements are
correct. I think I proved them to myself easily... but those are famous
last words.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12356#comment:4>
Sage <http://www.sagemath.org>
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