cp's OEIS Frontend

A351678 Discriminants of imaginary quadratic fields with class number 40 (negated).

%I A351678 #11 Feb 16 2025 08:34:03
%S A351678 1271,1839,2255,2415,2559,2751,2756,2919,2936,2959,3044,3135,3255,
%T A351678 3399,3423,3524,3704,3927,4004,4047,4071,4407,4607,4760,4807,4820,
%U A351678 4836,4856,5060,5143,5191,5304,5367,5727,6020,6036,6212,6324,6807,6980,6996,7063,7080
%N A351678 Discriminants of imaginary quadratic fields with class number 40 (negated).
%C A351678 Sequence contains 912 terms; largest is 260947.
%C A351678 The class groups associated to 251 of the above discriminants are isomorphic to C_40, 438 have a class group isomorphic to C_20 X C_2, and the remaining 223 have a class group isomorphic to C_10 X C_2 X C_2.
%H A351678 Andy Huchala, <a href="/A351678/b351678.txt">Table of n, a(n) for n = 1..912</a>
%H A351678 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 A351678 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ClassNumber.html">Class Number</a>
%o A351678 (Sage)
%o A351678 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 A351678 [-a[0] for a in ls if a[1] == 40]
%Y A351678 Cf. A006203, A013658, A014602, A014603, A046002-A046020, A046125, A056987, A351664-A351680.
%K A351678 nonn,fini,full
%O A351678 1,1
%A A351678 _Andy Huchala_, Mar 27 2022