A351672 - OEIS

A351672

Discriminants of imaginary quadratic fields with class number 34 (negated).

%I #11 Sep 22 2025 16:01:34

%S 1079,1343,1415,2103,2119,2391,2456,2463,2804,3031,3183,3287,4303,

%T 4331,4499,4927,5108,5287,5339,5411,5459,5672,6184,6376,6731,6932,

%U 7251,7327,7508,7711,7859,7863,8047,8051,8104,8116,8936,9223,9332,9535,9556,9703,10931

%N Discriminants of imaginary quadratic fields with class number 34 (negated).

%C Sequence contains 219 terms; largest is 189883.

%C The class group of Q[sqrt(-d)] is isomorphic to C_34 for all d in this sequence.

%H Andy Huchala, <a href="/A351672/b351672.txt">Table of n, a(n) for n = 1..219</a>

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

%o (SageMath)

%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] == 34]

%K nonn,fini,full

%O 1,1

%A _Andy Huchala_, Mar 25 2022