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

Author

Andy Huchala, Feb 16 2022

Keywords

• nonn
• fini
• full

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

Crossrefs

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

Programs

PARI

isok(n) = {isfundamental(-n) && quadclassunit(-n).no == 27}; \\ 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] == 27]