A351677 Discriminants of imaginary quadratic fields with class number 39 (negated).

1439, 2207, 2791, 3767, 3919, 4111, 5099, 5119, 6199, 6779, 9059, 9967, 10091, 10163, 10399, 10567, 10667, 11743, 12539, 13163, 13523, 14843, 14867, 15607, 16087, 16139, 16787, 17383, 18127, 21851, 23027, 24499, 26539, 27827, 30211, 30347, 30803, 32027, 32491

Offset: 1

Author

Andy Huchala, Mar 27 2022

Keywords

• nonn
• fini
• full

Comments

Sequence contains 115 terms; largest is 253507.

The class group of Q[sqrt(-d)] is isomorphic to C_39 for all d in this sequence.

Links

• Andy Huchala, Table of n, a(n) for n = 1..115
• 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] == 39]