find_some_curves() = { v = vector(6,j,S^(j-1)*T^(5-j+1)); vec = vector(63,j,0); n = 1; for(b1 =0,1, for(b2 =0,1, for(b3 =0,1, for(b4 =0,1, for(b5 =0,1, for(b6 = 0,1, if(b1==0 && b2==0 && b3==0 && b4==0 && b5==0 && b6==0,, vec[n] = Mod(1,2)*(b1*v[1] + b2*v[2] + b3*v[3] + b4*v[4] + b5*v[5] + b6*v[6]); n = n+1;); )))))); for(a1 = 1,63, for(a2 = a1,63, for(a3 = a2,63, for(a4 = a3,63, for(a5 = a4,63, for(a6 = a5,63, if(gcd(gcd(gcd(gcd(gcd(vec[a1],vec[a2]),vec[a3]),vec[a4]),vec[a5]),vec[a6])==1 && (Mod(1,2)*(vec[a1]^5 + vec[a2]^5 + vec[a3]^5 + vec[a4]^5 + vec[a5]^5 + vec[a6]^5) == 0), print([vec[a1],vec[a2],vec[a3], vec[a4], vec[a5], vec[a6]]); print();); )))))); }