A305416 -id:A305416 - cp's OEIS frontend

A046005 Discriminants of imaginary quadratic fields with class number 8 (negated).

95, 111, 164, 183, 248, 260, 264, 276, 295, 299, 308, 371, 376, 395, 420, 452, 456, 548, 552, 564, 579, 580, 583, 616, 632, 651, 660, 712, 820, 840, 852, 868, 904, 915, 939, 952, 979, 987, 995, 1032, 1043, 1060, 1092, 1128, 1131, 1155, 1195, 1204

Offset: 1

Eric W. Weisstein

131 discriminants in this sequence (almost certainly but not proved).

Andrew Howroyd, Table of n, a(n) for n = 1..131
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

Cf. A006203, A013658, A014602, A014603, A046002-A046020, A305416.

Cf. A191410.

Union[(-NumberFieldDiscriminant[Sqrt[-#]] &) /@ Select[Range[6400], NumberFieldClassNumber[Sqrt[-#]] == 8 &]] (* Jean-François Alcover, Jun 27 2012 *)

ok(n)={isfundamental(-n) && quadclassunit(-n).no == 8} \\ Andrew Howroyd, Jul 20 2018

[n for n in (1..6500) if is_fundamental_discriminant(-n) and QuadraticField(-n, 'a').class_number()==8] # G. C. Greubel, Mar 01 2019

A316743 Discriminants of imaginary fields whose class group has exponent 2, negated.

Original entry on oeis.org

15, 20, 24, 35, 40, 51, 52, 84, 88, 91, 115, 120, 123, 132, 148, 168, 187, 195, 228, 232, 235, 267, 280, 312, 340, 372, 403, 408, 420, 427, 435, 483, 520, 532, 555, 595, 627, 660, 708, 715, 760, 795, 840, 1012, 1092, 1155, 1320, 1380, 1428, 1435, 1540, 1848, 1995, 2280, 3003, 3315, 5460

Offset: 1

Jianing Song, Jul 20 2018

This sequence lists the negated discriminants of imaginary fields whose class group is isomorphic to (C_2)^r, r > 0.
These are the negated fundamental discriminants in A133288.
Also numbers in A003644 but not in A014602. Equals A014603 union A192322 union A305416 union {5460}.

Shin-ichi Katayama, Rational Points on the Parabola and the Arithmetic of Related Algebraic Tori, J. Math. Tokushima Univ. (2024) Vol. 58, 11-31. See p. 30.
Rick L. Shepherd, Binary quadratic forms and genus theory, Master of Arts Thesis, University of North Carolina at Greensboro, 2013.
P. J. Weinberger, Exponents of the class groups of complex quadratic fields, Acta Arith. 22 (1973), 117-124.

Cf. Negated discriminants of imaginary fields whose class group is isomorphic to (C_2)^r: A014602 (r=0), A014603 (r=1), A192322 (r=2), A305416 (r=3).

Subsequence of A003644 and A133288.

ok(n)={isfundamental(-n) && quadclassunit(-n).no > 1 && !#select(k->k<>2, quadclassunit(-n).cyc)} \\ Andrew Howroyd, Jul 20 2018

cp's OEIS Frontend

A046005 Discriminants of imaginary quadratic fields with class number 8 (negated).

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