A046002 Discriminants of imaginary quadratic fields with class number 5 (negated).

47, 79, 103, 127, 131, 179, 227, 347, 443, 523, 571, 619, 683, 691, 739, 787, 947, 1051, 1123, 1723, 1747, 1867, 2203, 2347, 2683

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• fini
• full

Links

• 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

Crossrefs

Cf. A006203, A013658, A014602, A014603, A046003-A046020.

Cf. A191410.

Programs

Mathematica

Union[(-NumberFieldDiscriminant[Sqrt[-#]] &) /@ Select[Range[2700], NumberFieldClassNumber[Sqrt[-#]] == 5 &]] (* Jean-François Alcover, Jun 27 2012 *)

PARI

select(n->qfbclassno(-n)==5,vector(670,n,4*n+3)) \\ Charles R Greathouse IV, Apr 25 2013

Sage

[n for n in (1..3000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==5] # G. C. Greubel, Mar 01 2019