A351670 Discriminants of imaginary quadratic fields with class number 32 (negated).

791, 1119, 1239, 1463, 1551, 1767, 1784, 1943, 2084, 2180, 2276, 2343, 2840, 2847, 2996, 3080, 3156, 3199, 3207, 3236, 3247, 3295, 3428, 3476, 3679, 3812, 3895, 4088, 4296, 4340, 4495, 4584, 4647, 4767, 4868, 4884, 4964, 4980, 4996, 5012, 5064, 5192, 5215

Offset: 1

Author

Andy Huchala, Mar 24 2022

Keywords

• nonn
• fini
• full

Comments

Sequence contains 708 terms; largest is 164803.

The class groups associated to 187 of the above discriminants are isomorphic to C_32, 273 have a class group isomorphic to C_16 X C_2, 160 isomorphic to C_8 X C_2 X C_2, 60 have a class group isomorphic to C_8 X C_4, 15 have a class group isomorphic to C_4 X C_2 X C_2 X C_2, and the remaining 13 have a class group isomorphic to C_4 X C_4 X C_2.

Links

• Andy Huchala, Table of n, a(n) for n = 1..708
• Eric Weisstein's World of Mathematics, Class Number

Crossrefs

Cf. A006203, A013658, A014602, A014603, A046002-A046020, A046125, A056987, A351664.

Programs

Sage

ls = [(QuadraticField(-n, 'a').discriminant(), QuadraticField(-n, 'a').class_number()) for n in (0..10000) if is_fundamental_discriminant(-n) and not is_square(n)];
[-a[0] for a in ls if a[1] == 32]