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Discriminants of imaginary quadratic fields with class number 31 (negated).
1

%I #9 Mar 27 2022 22:54:53

%S 719,911,2927,3251,3727,3779,4159,4951,5651,6131,6491,7639,8647,9203,

%T 10427,11863,12347,12923,13043,13219,13687,14627,14731,15923,17987,

%U 18803,19219,20611,24691,24979,28051,32083,32363,35491,38851,39667,39883,41227,41539

%N Discriminants of imaginary quadratic fields with class number 31 (negated).

%C Sequence contains 73 terms; largest is 133387.

%C The class group of Q[sqrt(-d)] is isomorphic to C_31 for all d in this sequence.

%H Andy Huchala, <a href="/A351669/b351669.txt">Table of n, a(n) for n = 1..73</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ClassNumber.html">Class Number</a>

%o (Sage)

%o 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 [-a[0] for a in ls if a[1] == 31]

%Y Cf. A006203, A013658, A014602, A014603, A046002-A046020, A046125, A056987, A351664.

%K nonn,fini,full

%O 1,1

%A _Andy Huchala_, Mar 24 2022