A046018 Discriminants of imaginary quadratic fields with class number 21 (negated).

431, 503, 743, 863, 1931, 2503, 2579, 2767, 2819, 3011, 3371, 4283, 4523, 4691, 5011, 5647, 5851, 5867, 6323, 6691, 7907, 8059, 8123, 8171, 8243, 8387, 8627, 8747, 9091, 9187, 9811, 9859, 10067, 10771, 11731, 12107, 12547, 13171, 13291

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• fini
• full

Comments

85 discriminants in this sequence (proved).

Links

• Giovanni Resta, Table of n, a(n) for n = 1..85 (full sequence, from Weisstein's World of Mathematics)
• Steven Arno, M. L. Robinson, Ferrell S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arith. 83 (1998) 295-330.
• Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796.
• Keith Matthews, Tables of imaginary quadratic fields with small class numbers
• C. Wagner, Class Number 5, 6 and 7, Math. Comput. 65, 785-800, 1996.
• Eric Weisstein's World of Mathematics, Class Number.

Crossrefs

Cf. A006203, A013658, A014602, A014603, A046002 - A046020.

Programs

Mathematica

Reap[ For[n = 1, n < 14000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 21, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)