#8945: Cremona labels messed up
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Reporter: davidloeffler | Owner: craigcitro
Type: defect | Status: new
Priority: major | Milestone: sage-5.0
Component: modular forms | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by cremona):
I can explain how this arises. The labelling in the e.c. tables
corresponds with the order the newforms were found --once. (There's more
about this in my Berlin ANTS account). That order changed over time,
particularly for conductors up to 450, since I was developing the
algorithm as I went along, and it was just too expensive in those days
(late 1980s!) to rerun everything when I changed strategy.
So, if it is important to have the labels match (which it surely is), and
if the so-called Cremona labels are set in stone according to the 1992
book, then the only way out is to have hard-coded into the current
newforms code the order in the tables (for rational newforms only). Yes,
that is ugly. But the alternative is to cause confusion in all the
literature which has referred to curves by their Cremona label for 18
tears now...
I already have such hard-coding in my own code so that when I recompute
all the curves of conductor up to 500 they get reordered into the order in
which I first found them, so that the labels are right. Sage could use
this permutation data (which would save anyone having to do it again,
which is a real boon, believe me). See the file curvesort.cc in
eclib*/src/g0n. This contains the following functions:
1. booknumber(int level, int form_number) --> book's form number
(counting form 1)
1. booknumber0(level, form_number) same with numbers starting at 0
The good news is that the permutation is he identity for level <56 or >
450. But that is true for comparing two version of my own program; I
don't know the Sage order of newforms.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8945#comment:1>
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