A351676 Discriminants of imaginary quadratic fields with class number 38 (negated).

1199, 1535, 1671, 2031, 3047, 3415, 4916, 5127, 5528, 6423, 6548, 6559, 6927, 7016, 7091, 7135, 7444, 8276, 8315, 8651, 8939, 8983, 9179, 9487, 9524, 9659, 9727, 9908, 10216, 10715, 10779, 10984, 11432, 11463, 11507, 11915, 12779, 12904, 13667, 14099, 14164

Offset: 1

Author

Andy Huchala, Mar 27 2022

Keywords

• nonn
• fini
• full

Comments

Sequence contains 237 terms; largest is 289963.

The class group of Q[sqrt(-d)] is isomorphic to C_38 for all d in this sequence.

Links

• Andy Huchala, Table of n, a(n) for n = 1..237
• 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] == 38]