A046009 Discriminants of imaginary quadratic fields with class number 12 (negated).

231, 255, 327, 356, 440, 516, 543, 655, 680, 687, 696, 728, 731, 744, 755, 804, 888, 932, 948, 964, 984, 996, 1011, 1067, 1096, 1144, 1208, 1235, 1236, 1255, 1272, 1336, 1355, 1371, 1419, 1464, 1480, 1491, 1515, 1547, 1572, 1668, 1720, 1732

Offset

1,1

Comments

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

Links

Andrew Howroyd, Table of n, a(n) for n = 1..206

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

Reap[ For[n = 1, n < 2000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 12, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)

Prog

(PARI) ok(n)={isfundamental(-n) && qfbclassno(-n) == 12} \\ Andrew Howroyd, Jul 24 2018
(Sage) [n for n in (1..3000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==12] # G. C. Greubel, Mar 01 2019

Crossrefs

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

Cf. A191410.

Sequence in context: A316095 A345795 A088289 * A350367 A337231 A117223

Adjacent sequences: A046006 A046007 A046008 * A046010 A046011 A046012

Keyword

nonn,fini

Author

Eric W. Weisstein

Status

approved