#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: positive_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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Comment(by cremona):
Comment: (1) running discriminants_with_bounded_class_number(hmax)
creates a dict giving all the pairs (D,f) with class number h for h up to
hmax. (2) running cm_orders(h) runs that with hmax=h and then throws away
everything but the list for h itself; nothing is cached. This is rather
inefficient! (3) I ran discriminants_with_bounded_class_number(100) --
100 being teh largest value implemented -- and it took 19.5 hours; the
output saves as a sobj file of size 630168 bytes.
Two possible speedups would be (1) cache all calls to pari's qfbclassno()
which is where most of the time is spent, and (2) cache the dict produced
and only do any computations if called with a larger value. And, now that
this computation has been done once we could easily create a once-and-for-
all Watkins-style table for non-maximal orders.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12356#comment:16>
Sage <http://www.sagemath.org>
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