A046006 Discriminants of imaginary quadratic fields with class number 9 (negated).

199, 367, 419, 491, 563, 823, 1087, 1187, 1291, 1423, 1579, 2003, 2803, 3163, 3259, 3307, 3547, 3643, 4027, 4243, 4363, 4483, 4723, 4987, 5443, 6043, 6427, 6763, 6883, 7723, 8563, 8803, 9067, 10627

Offset

1,1

Comments

The class group of Q[sqrt(-4027)] is isomorphic to C_3 X C_3. For all other d in this sequence, the class group of Q[sqrt(-d)] is isomorphic to C_9. - Jianing Song, Dec 01 2019

Links

Table of n, a(n) for n=1..34.

Steven Arno, M. L. Robinson, Ferrell S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arith. 83 (1998) 295-330.

Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796.

Keith Matthews, Tables of imaginary quadratic fields with small class numbers

C. Wagner, Class Number 5, 6 and 7, Math. Comput. 65, 785-800, 1996.

Eric Weisstein's World of Mathematics, Class Number.

Index entries for sequences related to quadratic fields

Mathematica

Union[(-NumberFieldDiscriminant[Sqrt[-#]] &) /@ Select[Range[10700], NumberFieldClassNumber[Sqrt[-#]] == 9 &]] (* Jean-François Alcover, Jun 27 2012 *)

Prog

(PARI)
ok(n)={isfundamental(-n) && quadclassunit(-n).no == 9};
for(n=1, 11000, if(ok(n)==1, print1(n, ", "))) \\ G. C. Greubel, Mar 01 2019
(Sage)
[n for n in (1..4000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==9] # G. C. Greubel, Mar 01 2019

Crossrefs

Cf. A006203, A013658, A014602, A014603, A046002-A046020.

Cf. A191410.

Sequence in context: A122091 A142749 A142123 * A147262 A106759 A004926

Adjacent sequences: A046003 A046004 A046005 * A046007 A046008 A046009

Keyword

nonn,fini,full

Author

Eric W. Weisstein

Status

approved