

A351670


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


1



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
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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, A046002A046020, 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



