Pete
L. Clark |
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Note: To load magma with any one of these programs, type e.g.

(in general replacing "tors" with the name of the program).

Creates the function TC(i,N,B). Here i is one of the 13 integral j-invariants, accorded according to increasing discriminant of the quadratic order (in particular i = 4 corresponds to j = 1728, unlike in arxivpreprint.pdf), N > 3 is an odd prime, and B is a bound. The program begins with the generic Kubert curve E(b,c), computes one polynomial corresponding to j(E(b,c)) = j

This final output number -- let us call it d(i,N,B) -- is a

Remark: One can input any odd value of N into the program. But since the equations for an N-torsion point in Kubert normal form are really N*(0,0) = O, M*(0,0) =\= O for 1 <= M < N, when N is not prime (except, I suppose, N = 9), the degree sequences for N will include degree sequences for all M > 3 which divide N. However, by running the program also for such divisors M and removing the degree sequences from those of TC(i,N,B), one should get the appropriate degree sequences for N. This should be implemented!

This program is identical to Version 1.0 of TC except that it does not ouput any of the degree sequences, only the final lower bound d(i,N,B).