Isogeny Matrix Table

William Stein

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.)


    allisog.1-40000       (14MB)    

    allisog.1-40000.bz2   (2.8MB)

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.