login
Discriminants of imaginary quadratic fields with class number 10 (negated).
3

%I #25 Mar 15 2019 22:51:30

%S 119,143,159,296,303,319,344,415,488,611,635,664,699,724,779,788,803,

%T 851,872,916,923,1115,1268,1384,1492,1576,1643,1684,1688,1707,1779,

%U 1819,1835,1891,1923,2152,2164,2363,2452,2643,2776,2836,2899,3028

%N Discriminants of imaginary quadratic fields with class number 10 (negated).

%C 87 discriminants in this sequence (almost certainly but not proved).

%H Andrew Howroyd, <a href="/A046007/b046007.txt">Table of n, a(n) for n = 1..87</a>

%H Steven Arno, M. L. Robinson and Ferrel S. Wheeler, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa83/aa8341.pdf">Imaginary quadratic fields with small odd class number</a>, Acta Arithm. 83.4 (1998), 295-330

%H Duncan A. Buell, <a href="http://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 C. Wagner, <a href="http://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[14000], NumberFieldClassNumber[Sqrt[-#]] == 10 &]] (* _Jean-François Alcover_, Jun 27 2012 *)

%o (PARI) ok(n)={isfundamental(-n) && qfbclassno(-n) == 10} \\ _Andrew Howroyd_, Jul 24 2018

%o (Sage) [n for n in (1..3500) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==10] # _G. C. Greubel_, Mar 01 2019

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

%Y Cf. A191410.

%K nonn,fini

%O 1,1

%A _Eric W. Weisstein_