/*******************************************************************

   Stage 1 in deciding if all prime-conductor curves of 
   conductor p with W_q = sign are contained in the table. 
   Outputs 

             <p, sign, 1, additional data> 

   if we succeed in showing that they are all in the table, and

             <p, sign, 0, additional data>
  
   if this stage is inconclusive.

   Stage 1 test:
 
 *******************************************************************/

Attach("/home/was/magma_database/magma/prime_curves/graph_method.m");
load "/home/was/magma_database/magma/prime_curves/curves.m";
   
t := Cputime();
p := arg[1];
sign := arg[2];

time X := SupersingularModule(p);
time E := EllipticFactors(X, sign, GF(37), 7);

curve_bound := &+[Integers() | Dimension(A) : A in E];  

ans := <p, sign, curve_bound, Cputime(t)>;
ans;