A351666 Discriminants of imaginary quadratic fields with class number 28 (negated).

831, 935, 1095, 1311, 1335, 1364, 1455, 1479, 1496, 1623, 1703, 1711, 1855, 1976, 2024, 2055, 2120, 2127, 2324, 2359, 2431, 2455, 2564, 2607, 2616, 2703, 3224, 3272, 3396, 3419, 3487, 3535, 3572, 3576, 3608, 3624, 3731, 3848, 3995, 4040, 4183, 4279, 4344

Offset: 1

Author

Andy Huchala, Feb 16 2022

Keywords

• nonn
• fini
• full

Comments

Sequence contains 457 terms; largest is 126043.

The class groups associated to 174 of the above discriminants are isomorphic to C_28, and the remaining 283 have a class group isomorphic to C_14 X C_2.

Links

• Andy Huchala, Table of n, a(n) for n = 1..457
• Eric Weisstein's World of Mathematics, Class Number

Crossrefs

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

Programs

PARI

isok(n) = {isfundamental(-n) && quadclassunit(-n).no == 28}; \\ Michel Marcus, Mar 02 2022

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] == 28]