A351665 Discriminants of imaginary quadratic fields with class number 27 (negated).

983, 1231, 1399, 1607, 1759, 1879, 1999, 3271, 3299, 3943, 4903, 6007, 6011, 7699, 8867, 10531, 10939, 11003, 11027, 11383, 11491, 11779, 11939, 13411, 14243, 14723, 15107, 15739, 16411, 16547, 17443, 17627, 17659, 17747, 18587, 18787, 18859, 19051, 19427

Offset

1,1

Comments

Sequence contains 93 terms; largest is 103387.

The class group of Q[sqrt(-d)] is isomorphic to C_9 X C_3 for d = 3299, 19427, 34603, 89923, and 98443. For all other d in this sequence, the class group of Q[sqrt(-d)] is isomorphic to C_27.

Links

Andy Huchala, Table of n, a(n) for n = 1..93

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] == 27]
(PARI) isok(n) = {isfundamental(-n) && quadclassunit(-n).no == 27}; \\ Michel Marcus, Mar 02 2022

Crossrefs

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

Sequence in context: A122472 A252402 A087907 * A182574 A096701 A345539

Adjacent sequences: A351662 A351663 A351664 * A351666 A351667 A351668

Keyword

nonn,fini,full

Author

Andy Huchala, Feb 16 2022

Status

approved