Some Maple Class Number Calculation for Reese
# Imaginary quadratic Class Numbers
#
# with(numtheory):
# imagquadclassnum := proc(N)
# local i, h, a, b, b1, be, d;
# #we assume here that N is squarefree
# h:=0;
# if issqrfree(N) then
# if N < 4 then h := 1; else
# if N mod 4 = 3 then
# d := N; b := 1;
# else
# d := 4*N; b := 0;
# fi;
# h := 0;
# for b1 from b to isqrt( iquo(d,3) ) by 2 do
# be := iquo( b1^2 + d, 4);
# for a from max(1, b1) to isqrt(be) do
# if be mod a = 0 then h := h+1;
# if b1 <>0 and a<>b1 and a^2 <> be then h := h+1; fi;
# fi;
# od;
# od;
# fi;
# fi;
# h;
# end;
>
proc(N) ... end;
# imagquadclassnum((1025^2-2^10)*2); ifactor(%);
960
6
(2) (3) (5)
>
# imagquadclassnum((1025^2-2^11)*2); ifactor(%);
784
4 2
(2) (7)
# imagquadclassnum((1023^2-2)*2); ifactor(%);
2080
5
(2) (5) (13)
# imagquadclassnum((1023^2-2^11)*2); ifactor(%);
1104
4
(2) (3) (23)
# imagquadclassnum((513^2-2^9)*2); ifactor(%);
1040
4
(2) (5) (13)
# imagquadclassnum((513^2-2^11)*2);
0
# ifactor((513^2-2^11)*2);
2 2
(2) (7) (73)
# imagquadclassnum((511^2-2)*2); ifactor(%);
368
4
(2) (23)
# imagquadclassnum((511^2-2^11)*2); ifactor(%);
416
5
(2) (13)
# imagquadclassnum((257^2-2^8)*2); ifactor(%);
224
5
(2) (7)
# imagquadclassnum((257^2-2^9)*2); ifactor(%);
224
5
(2) (7)
# imagquadclassnum((257^2-2^11)*2); ifactor(%);
192
6
(2) (3)
# imagquadclassnum((255^2-2)*2); ifactor(%);
0
0
# ifactor((255^2-2)*2);
2
(2) (7) (1327)
# imagquadclassnum(2*(255^2-2)/7^2); ifactor(%);
48
4
(2) (3)
# imagquadclassnum((255^2-2^9)*2); ifactor(%);
516
2
(2) (3) (43)
# imagquadclassnum((255^2-2^11)*2); ifactor(%);
544
5
(2) (17)
# imagquadclassnum((129^2-2^7)*2); ifactor(%);
0
0
# ifactor(129^2-2^7);
2
(7) (337)
# imagquadclassnum(2*(129^2-2^7)/7^2); ifactor(%);
24
3
(2) (3)
# imagquadclassnum((129^2-2^9)*2); ifactor(%);
0
0
# ifactor((129^2-2^9)*2);
2
(2) (127)
# imagquadclassnum((65^2-2^6)*2); ifactor(%);
64
6
(2)
# imagquadclassnum((65^2-2^7)*2); ifactor(%);
48
4
(2) (3)
# imagquadclassnum((65^2-2^9)*2); ifactor(%);
64
6
(2)
# imagquadclassnum((63^2-2)*2); ifactor(%);
128
7
(2)
# imagquadclassnum((63^2-2^7)*2); ifactor(%);
72
3 2
(2) (3)
# imagquadclassnum((63^2-2^9)*2); ifactor(%);
108
2 3
(2) (3)
# imagquadclassnum((33^2-2^5)*2); ifactor(%);
56
3
(2) (7)
# imagquadclassnum((1025^2-2^10)*2); ifactor(%);
960
6
(2) (3) (5)
>
# imagquadclassnum((1025^2-2^11)*2); ifactor(%);
784
4 2
(2) (7)
# imagquadclassnum((1023^2-2)*2); ifactor(%);
2080
5
(2) (5) (13)
# imagquadclassnum((1023^2-2^11)*2); ifactor(%);
1104
4
(2) (3) (23)
# imagquadclassnum((513^2-2^9)*2); ifactor(%);
1040
4
(2) (5) (13)
# imagquadclassnum((513^2-2^11)*2);
0
# ifactor((513^2-2^11)*2);
2 2
(2) (7) (73)
# imagquadclassnum((511^2-2)*2); ifactor(%);
368
4
(2) (23)
# imagquadclassnum((511^2-2^11)*2); ifactor(%);
416
5
(2) (13)
# imagquadclassnum((257^2-2^8)*2); ifactor(%);
224
5
(2) (7)
# imagquadclassnum((257^2-2^9)*2); ifactor(%);
224
5
(2) (7)
# imagquadclassnum((257^2-2^11)*2); ifactor(%);
192
6
(2) (3)
# imagquadclassnum((255^2-2)*2); ifactor(%);
0
0
# ifactor((255^2-2)*2);
2
(2) (7) (1327)
# imagquadclassnum(2*(255^2-2)/7^2); ifactor(%);
48
4
(2) (3)
# imagquadclassnum((255^2-2^9)*2); ifactor(%);
516
2
(2) (3) (43)
# imagquadclassnum((255^2-2^11)*2); ifactor(%);
544
5
(2) (17)
# imagquadclassnum((129^2-2^7)*2); ifactor(%);
0
0
# ifactor(129^2-2^7);
2
(7) (337)
# imagquadclassnum(2*(129^2-2^7)/7^2); ifactor(%);
24
3
(2) (3)
# imagquadclassnum((129^2-2^9)*2); ifactor(%);
0
0
# ifactor((129^2-2^9)*2);
2
(2) (127)
# imagquadclassnum((65^2-2^6)*2); ifactor(%);
64
6
(2)
# imagquadclassnum((65^2-2^7)*2); ifactor(%);
48
4
(2) (3)
# imagquadclassnum((65^2-2^9)*2); ifactor(%);
64
6
(2)
# imagquadclassnum((63^2-2)*2); ifactor(%);
128
7
(2)
# imagquadclassnum((63^2-2^7)*2); ifactor(%);
72
3 2
(2) (3)
# imagquadclassnum((63^2-2^9)*2); ifactor(%);
108
2 3
(2) (3)
# imagquadclassnum((33^2-2^5)*2); ifactor(%);
56
3
(2) (7)
# imagquadclassnum((33^2-2^7)*2); ifactor(%);
0
0
# ifactor(33^2-2^7);
2
(31)
# ; ifactor(%);
0
0
# ifactor(33^2-2^7);
2
(31)
>
# imagquadclassnum((1025^2-2^10)*2); ifactor(%);
960
6
(2) (3) (5)
>
# imagquadclassnum((1025^2-2^11)*2); ifactor(%);
784
4 2
(2) (7)
# imagquadclassnum((1023^2-2)*2); ifactor(%);
2080
5
(2) (5) (13)
# imagquadclassnum((1023^2-2^11)*2); ifactor(%);
1104
4
(2) (3) (23)
# imagquadclassnum((513^2-2^9)*2); ifactor(%);
1040
4
(2) (5) (13)
# imagquadclassnum((513^2-2^11)*2);
0
# ifactor((513^2-2^11)*2);
2 2
(2) (7) (73)
# imagquadclassnum((511^2-2)*2); ifactor(%);
368
4
(2) (23)
# imagquadclassnum((511^2-2^11)*2); ifactor(%);
416
5
(2) (13)
# imagquadclassnum((257^2-2^8)*2); ifactor(%);
224
5
(2) (7)
# imagquadclassnum((257^2-2^9)*2); ifactor(%);
224
5
(2) (7)
# imagquadclassnum((257^2-2^11)*2); ifactor(%);
192
6
(2) (3)
# imagquadclassnum((255^2-2)*2); ifactor(%);
0
0
# ifactor((255^2-2)*2);
2
(2) (7) (1327)
# imagquadclassnum(2*(255^2-2)/7^2); ifactor(%);
48
4
(2) (3)
# imagquadclassnum((255^2-2^9)*2); ifactor(%);
516
2
(2) (3) (43)
# imagquadclassnum((255^2-2^11)*2); ifactor(%);
544
5
(2) (17)
# imagquadclassnum((129^2-2^7)*2); ifactor(%);
0
0
# ifactor(129^2-2^7);
2
(7) (337)
# imagquadclassnum(2*(129^2-2^7)/7^2); ifactor(%);
24
3
(2) (3)
# imagquadclassnum((129^2-2^9)*2); ifactor(%);
0
0
# ifactor((129^2-2^9)*2);
2
(2) (127)
# imagquadclassnum((65^2-2^6)*2); ifactor(%);
64
6
(2)
# imagquadclassnum((65^2-2^7)*2); ifactor(%);
48
4
(2) (3)
# imagquadclassnum((65^2-2^9)*2); ifactor(%);
64
6
(2)
# imagquadclassnum((63^2-2)*2); ifactor(%);
128
7
(2)
# imagquadclassnum((63^2-2^7)*2); ifactor(%);
72
3 2
(2) (3)
# imagquadclassnum((63^2-2^9)*2); ifactor(%);
108
2 3
(2) (3)
# imagquadclassnum((33^2-2^5)*2); ifactor(%);
56
3
(2) (7)
# imagquadclassnum((33^2-2^7)*2); ifactor(%);
0
0
# ifactor(33^2-2^7);
2
(31)
>
# for r from 5 to 11 do print(r, imagquadclassnum(33^3-2^r), imagquadclassnum((33^3-2^r)*2)) end do;
5, 72, 216
6, 144, 188
7, 80, 168
8, 240, 80
9, 0, 0
10, 132, 148
11, 108, 252
# imagquadclassnum((33^3-2^9)*2); ifactor(33^3-2^9);
0
2
(5) (13) (109)
# imagquadclassnum(2*(33^3-2^9)/5^2);
84
>
# for r from 4 to 9 do print(r, imagquadclassnum(15^3-2^r), imagquadclassnum((15^3-2^r)*2)) end do;
4, 69, 40
5, 19, 72
6, 72, 32
7, 32, 96
8, 69, 24
9, 22, 96
>
>
>