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

%I A046009 #26 Feb 16 2025 08:32:38
%S A046009 231,255,327,356,440,516,543,655,680,687,696,728,731,744,755,804,888,
%T A046009 932,948,964,984,996,1011,1067,1096,1144,1208,1235,1236,1255,1272,
%U A046009 1336,1355,1371,1419,1464,1480,1491,1515,1547,1572,1668,1720,1732
%N A046009 Discriminants of imaginary quadratic fields with class number 12 (negated).
%C A046009 206 discriminants in this sequence (almost certainly but not proved).
%H A046009 Andrew Howroyd, <a href="/A046009/b046009.txt">Table of n, a(n) for n = 1..206</a>
%H A046009 Steven Arno, M. L. Robinson and Ferrel S. Wheeler, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa83/aa8341.pdf">Imaginary quadratic fields with small odd class number</a>, Acta Arithm. 83.4 (1998), 295-330
%H A046009 Duncan A. Buell, <a href="http://dx.doi.org/10.1090/S0025-5718-1977-0439802-X">Small class numbers and extreme values of L-functions of quadratic fields</a>, Math. Comp., 31 (1977), 786-796.
%H A046009 C. Wagner, <a href="http://dx.doi.org/10.1090/S0025-5718-96-00722-3">Class Number 5, 6 and 7</a>, Math. Comput. 65, 785-800, 1996.
%H A046009 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClassNumber.html">Class Number.</a>
%H A046009 <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>
%t A046009 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 *)
%o A046009 (PARI) ok(n)={isfundamental(-n) && qfbclassno(-n) == 12} \\ _Andrew Howroyd_, Jul 24 2018
%o A046009 (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
%Y A046009 Cf. A006203, A013658, A014602, A014603, A046002-A046020.
%Y A046009 Cf. A191410.
%K A046009 nonn,fini
%O A046009 1,1
%A A046009 _Eric W. Weisstein_