The On-Line Encyclopedia of Integer Sequences (OEIS)

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A046015

Discriminants of imaginary quadratic fields with class number 18 (negated).
(history; published version)

#25 by Charles R Greathouse IV at Sun Feb 16 08:32:38 EST 2025

LINKS

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

Discussion

Sun Feb 16

08:32

OEIS Server: https://oeis.org/edit/global/3014

#24 by Peter Luschny at Tue Dec 03 03:28:36 EST 2019

STATUS

reviewed

approved

#23 by Joerg Arndt at Sun Dec 01 06:26:16 EST 2019

STATUS

proposed

reviewed

#22 by Jianing Song at Sun Dec 01 06:04:20 EST 2019

STATUS

editing

proposed

#21 by Jianing Song at Sun Dec 01 06:03:49 EST 2019

COMMENTS

The class group of Q[sqrt(-d)] is isomorphic to C_3 X C_6 for d = 9748, 12067, 16627, 17131, 19651, 22443, 23683, 34027, 34507. For all other known d in this sequence, the clas class group of Q[sqrt(-d)] is isomorphic to C_18. - Jianing Song, Dec 01 2019

#20 by Jianing Song at Sun Dec 01 06:03:14 EST 2019

COMMENTS

The class group of Q[sqrt(-d)] is isomorphic to C_3 X C_6 for d = 9748, 12067, 16627, 17131, 19651, 22443, 23683, 34027, 34507. For all other known d in this sequence, the clas group of Q[sqrt(-d)] is isomorphic to C_18. - Jianing Song, Dec 01 2019

LINKS

Jianing Song, <a href="/A046015/b046015.txt">Table of n, a(n) for n = 1..150</a>

STATUS

approved

editing

#19 by Georg Fischer at Mon Dec 31 08:20:46 EST 2018

STATUS

editing

approved

#18 by Georg Fischer at Mon Dec 31 08:20:18 EST 2018

LINKS

S. Steven Arno, M. L. Robinson and F. Ferrel S. Wheller, Wheeler, <a href="http://www.mathmatwbn.uiucicm.edu.pl/ksiazki/Algebraic-Number-Theoryaa/0009aa83/aa8341.pdf">Imaginary Quadratic Fields quadratic fields with Small Odd Class Numbersmall odd class number</a>, Acta Arithm. 83.4 (1998), 295-330

STATUS

approved

editing

Discussion

Mon Dec 31

08:20

Georg Fischer: Link repaired - to orig. publ.

#17 by Bruno Berselli at Wed Jul 08 04:48:25 EDT 2015

STATUS

proposed

approved

#16 by Michel Marcus at Wed Jul 08 04:42:11 EDT 2015

STATUS

editing

proposed