A046007 - OEIS

A046007

Discriminants of imaginary quadratic fields with class number 10 (negated).

119, 143, 159, 296, 303, 319, 344, 415, 488, 611, 635, 664, 699, 724, 779, 788, 803, 851, 872, 916, 923, 1115, 1268, 1384, 1492, 1576, 1643, 1684, 1688, 1707, 1779, 1819, 1835, 1891, 1923, 2152, 2164, 2363, 2452, 2643, 2776, 2836, 2899, 3028

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OFFSET

1,1

COMMENTS

87 discriminants in this sequence (almost certainly but not proved).

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..87

Steven Arno, M. L. Robinson and Ferrel S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arithm. 83.4 (1998), 295-330

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

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[14000], NumberFieldClassNumber[Sqrt[-#]] == 10 &]] (* Jean-François Alcover, Jun 27 2012 *)

PROG

(PARI) ok(n)={isfundamental(-n) && qfbclassno(-n) == 10} \\ Andrew Howroyd, Jul 24 2018

(SageMath) [n for n in (1..3500) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==10] # G. C. Greubel, Mar 01 2019

CROSSREFS

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

Cf. A191410.

Sequence in context: A103154 A039557 A095629 * A333789 A135716 A026049

Adjacent sequences: A046004 A046005 A046006 * A046008 A046009 A046010

KEYWORD

nonn,fini

AUTHOR

Eric W. Weisstein

STATUS

approved