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

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

1,1

Comments

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}.

Links

Table of n, a(n) for n=1..57.

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.

Prog

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

Crossrefs

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.

Sequence in context: A102495 A133288 A322710 * A014603 A070222 A143321

Adjacent sequences: A316740 A316741 A316742 * A316744 A316745 A316746

Keyword

nonn,fini,full

Author

Jianing Song, Jul 20 2018

Status

approved