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A351674 Discriminants of imaginary quadratic fields with class number 36 (negated).

%I A351674 #15 Feb 16 2025 08:34:03
%S A351674 959,1055,1295,1599,1727,1967,2199,2504,2516,2895,3055,3495,3656,3711,
%T A351674 3716,3896,3956,4164,4255,4280,4388,4472,4615,4619,4623,4664,4772,
%U A351674 5007,5048,5055,5063,5156,5240,5291,5316,5343,5455,5636,5732,5767,5960,6015,6055
%N A351674 Discriminants of imaginary quadratic fields with class number 36 (negated).
%C A351674 Sequence contains 668 terms; largest is 217627.
%C A351674 The class groups associated to 255 of the above discriminants are isomorphic to C_36, 374 have a class group isomorphic to C_18 X C_2, 16 have a class group isomorphic to C_12 X C_3, and the remaining 23 have a class group isomorphic to C_6 X C_6.
%H A351674 Andy Huchala, <a href="/A351674/b351674.txt">Table of n, a(n) for n = 1..668</a>
%H A351674 Mark Watkins, <a href="https://doi.org/10.1090/S0025-5718-03-01517-5">Class numbers of imaginary quadratic fields</a>, Mathematics of Computation, 73, pp. 907-938.
%H A351674 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClassNumber.html">Class Number</a>
%o A351674 (Sage)
%o A351674 ls = [(QuadraticField(-n, 'a').discriminant(), QuadraticField(-n, 'a').class_number()) for n in (0..10000) if is_fundamental_discriminant(-n) and not is_square(n)];
%o A351674 [-a[0] for a in ls if a[1] == 36]
%Y A351674 Cf. A006203, A013658, A014602, A014603, A046002-A046020, A046125, A056987, A351664-A351680.
%K A351674 nonn,fini,full
%O A351674 1,1
%A A351674 _Andy Huchala_, Mar 27 2022