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

1,1

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

Prog

(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]

Crossrefs

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

Sequence in context: A237735 A252517 A263010 * A282547 A104398 A186057

Adjacent sequences: A351667 A351668 A351669 * A351671 A351672 A351673

Keyword

nonn,fini,full

Author

Andy Huchala, Mar 24 2022

Status

approved