A046015 Discriminants of imaginary quadratic fields with class number 18 (negated).

335, 519, 527, 679, 1135, 1172, 1207, 1383, 1448, 1687, 1691, 1927, 2047, 2051, 2167, 2228, 2291, 2315, 2344, 2644, 2747, 2859, 3035, 3107, 3543, 3544, 3651, 3688, 4072, 4299, 4307, 4568, 4819, 4883, 5224, 5315, 5464, 5492, 5539, 5899

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• fini

Comments

The class group of Q[sqrt(-d)] is isomorphic to C_3 X C_6 for d = 9748, 12067, 16627, 17131, 19651, 22443, 23683, 34027, 34507. For all other known d in this sequence, the class group of Q[sqrt(-d)] is isomorphic to C_18. - Jianing Song, Dec 01 2019

Links

• Jianing Song, Table of n, a(n) for n = 1..150
• Steven Arno, M. L. Robinson and Ferrel S. Wheeler, Imaginary quadratic fields with small odd class number, Acta Arithm. 83.4 (1998), 295-330
• Duncan A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp., 31 (1977), 786-796.
• C. Wagner, Class Number 5, 6 and 7, Math. Comput. 65, 785-800, 1996.
• Eric Weisstein's World of Mathematics, Class Number.
• Index entries for sequences related to quadratic fields

Crossrefs

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

Programs

Mathematica

Reap[ For[n = 1, n < 6000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 18, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)