#
Isogeny Matrix Table

### April 2005

This is a table that gives the output of Cremona's program
**allisog** with precision 70 for all curves of conductor <= 40000.
My understanding is it is possible that some isogenies are missed,
though I suppose it is unlikely given the precision parameter. I
intend to, but have not done, double checks on the data, to prove that
no isogenies are missed. (Mark Watkins's program ec could be used
here.)

For each optimal curve of conductor <= 40000, there is one row in the table:
N iso num ainvs [isogenous curves] [isogeny matrix]

Thus the table begins as follows:
11 A 1 [0,-1,1,-10,-20] [[0,-1,1,-10,-20],[0,-1,1,-7820,-263580],[0,-1,1,0,0]] [[0,5,5],[5,0,0],[5,0,0]]
14 A 1 [1,0,1,4,-6] [[1,0,1,4,-6],[1,0,1,-36,-70],[1,0,1,-171,-874],[1,0,1,-1,0],[1,0,1,-2731,-55146],[1,0,1,-11,12]] [[0,2,3,3,0,0],[2,0,0,0,3,3],[3,0,0,0,2,0],[3,0,0,0,0,2],[0,3,2,0,0,0],[0,3,0,2,0,0]]
15 A 1 [1,1,1,-10,-10] [[1,1,1,-10,-10],[1,1,1,35,-28],[1,1,1,-135,-660],[1,1,1,-5,2],[1,1,1,-110,-880],[1,1,1,-2160,-39540],[1,1,1,0,0],[1,1,1,-80,242]] [[0,2,2,2,0,0,0,0],[2,0,0,0,0,0,0,0],[2,0,0,0,2,2,0,0],[2,0,0,0,0,0,2,2],[0,0,2,0,0,0,0,0],[0,0,2,0,0,0,0,0],[0,0,0,2,0,0,0,0],[0,0,0,2,0,0,0,0]]
17 A 1 [1,-1,1,-1,-14] [[1,-1,1,-1,-14],[1,-1,1,-6,-4],[1,-1,1,-1,0],[1,-1,1,-91,-310]] [[0,2,0,0],[2,0,2,2],[0,2,0,0],[0,2,0,0]]

I created this table using the following program, which requires
that SAGE and the SAGE elliptic curves database
be installed:

isog.tar.bz2

With the above program installed (and SAGE),
I typed `go 1 40000` and waited many hours. The underlying
calculation makes uses of Cremona's tables,
PARI, and SAGE.