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Discriminants of imaginary quadratic fields with class number 7 (negated).
8

%I #24 Mar 01 2019 16:29:04

%S 71,151,223,251,463,467,487,587,811,827,859,1163,1171,1483,1523,1627,

%T 1787,1987,2011,2083,2179,2251,2467,2707,3019,3067,3187,3907,4603,

%U 5107,5923

%N Discriminants of imaginary quadratic fields with class number 7 (negated).

%H Steven Arno, M. L. Robinson, Ferrell S. Wheeler, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa83/aa8341.pdf">Imaginary quadratic fields with small odd class number</a>, Acta Arith. 83 (1998) 295-330.

%H Duncan A. Buell, <a href="https://dx.doi.org/10.1090/S0025-5718-1977-0439802-X">Small class numbers and extreme values of L-functions of quadratic fields</a>, Math. Comp., 31 (1977), 786-796.

%H Keith Matthews, <a href="http://www.numbertheory.org/classnos/">Tables of imaginary quadratic fields with small class numbers</a>.

%H C. Wagner, <a href="https://dx.doi.org/10.1090/S0025-5718-96-00722-3">Class Number 5, 6 and 7</a>, Math. Comput. 65, 785-800, 1996.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ClassNumber.html">Class Number.</a>

%H <a href="/index/Qua#quadfield">Index entries for sequences related to quadratic fields</a>

%t Union[(-NumberFieldDiscriminant[Sqrt[-#]] &) /@ Select[Range[6000], NumberFieldClassNumber[Sqrt[-#]] == 7 &]] (* _Jean-François Alcover_, Jun 27 2012 *)

%o (PARI) ok(n)={isfundamental(-n) && quadclassunit(-n).no == 7};

%o for(n=1, 6000, if(ok(n)==1, print1(n, ", "))) \\ _G. C. Greubel_, Mar 01 2019

%o (Sage) [n for n in (1..6000) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==7] # _G. C. Greubel_, Mar 01 2019

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

%Y Cf. A191410.

%K nonn,fini,full

%O 1,1

%A _Eric W. Weisstein_