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A046009
Discriminants of imaginary quadratic fields with class number 12 (negated).
3
231, 255, 327, 356, 440, 516, 543, 655, 680, 687, 696, 728, 731, 744, 755, 804, 888, 932, 948, 964, 984, 996, 1011, 1067, 1096, 1144, 1208, 1235, 1236, 1255, 1272, 1336, 1355, 1371, 1419, 1464, 1480, 1491, 1515, 1547, 1572, 1668, 1720, 1732
OFFSET
1,1
COMMENTS
206 discriminants in this sequence (almost certainly but not proved).
LINKS
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.
MATHEMATICA
Reap[ For[n = 1, n < 2000, n++, s = Sqrt[-n]; If[ NumberFieldClassNumber[s] == 12, d = -NumberFieldDiscriminant[s]; Print[d]; Sow[d]]]][[2, 1]] // Union (* Jean-François Alcover, Oct 05 2012 *)
PROG
(PARI) ok(n)={isfundamental(-n) && qfbclassno(-n) == 12} \\ Andrew Howroyd, Jul 24 2018
(Sage) [n for n in (1..3000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==12] # G. C. Greubel, Mar 01 2019
CROSSREFS
KEYWORD
nonn,fini
STATUS
approved