A351675 Discriminants of imaginary quadratic fields with class number 37 (negated).

1487, 2447, 3391, 5839, 6367, 8147, 9803, 10739, 12343, 12583, 12967, 14767, 15259, 16927, 18947, 19403, 20011, 20147, 21139, 21587, 22807, 23371, 23627, 26731, 28283, 28307, 31699, 31723, 36691, 37171, 37243, 38371, 39139, 39451, 40531, 41659, 42283, 42443

Offset: 1

Author

Andy Huchala, Mar 27 2022

Keywords

• nonn
• fini
• full

Comments

Sequence contains 85 terms; largest is 158923.

The class group of Q[sqrt(-d)] is isomorphic to C_37 for all d in this sequence.

Links

• Andy Huchala, Table of n, a(n) for n = 1..85
• Mark Watkins, Class numbers of imaginary quadratic fields, Mathematics of Computation, 73, pp. 907-938.
• Eric Weisstein's World of Mathematics, Class Number

Crossrefs

Cf. A006203, A013658, A014602, A014603, A046002-A046020, A046125, A056987, A351664-A351680.

Programs

Sage

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)];
[-a[0] for a in ls if a[1] == 37]