The file

   phi_l.dec.gz

when uncompressed (by gunzip) contains the coefficients 
f(a,b) 0 <= b <= l , 0 <= a <= b 

of the modular polynomial

  phi_l(X,Y) =  

                                 l      l                 
                               -----  -----               
         (l + 1)    (l + 1)     \      \             a  b   
        X        + Y        +    )      )    f(a,b) X  Y
                                /      /                  
                               -----  -----               
                               a = 0  b = 0               


whose coefficients f(a,b) are determined from

                                   l - 1                     
                                  --------'                  
                                 '  |  |    /      tau + k \ 
                 (X - j(l tau))     |  |    |X - j(-------)| 
                                    |  |    \         l    / 
                                    |  |                     
                                   k = 0                     

   

                                         l      l                 
                                       -----  -----               
         (l + 1)           (l + 1)      \      \             a         b   
        X        + (j(tau))         +    )      )    f(a,b) X  (j(tau)) 
                                        /      /                  
                                       -----  -----               
                                       a = 0  b = 0               


Because f(a,b)=f(b,a) we only store the values for a<=b.

For example, the file phi_2.dec reads:

-157464000000000
8748000000
40773375
-162000
1488
-1


So,

   phi_2(X,Y) = 

 3    3
X  + Y  - 157464000000000 + 8748000000 X + 8748000000 Y + 40773375 X Y

               2           2           2         2      2  2
     - 162000 X  - 162000 Y  + 1488 X Y  + 1488 X  Y - X  Y