Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of )

Label	Polynomial	Discriminant	Galois group	Class group
8.0.22959825625.2	x^8 - 4x^7 + 16x^6 - 34x^5 + 109x^4 - 166x^3 + 343x^2 - 265x + 671	\( 5^{4}\cdot 11^{2}\cdot 19^{2}\cdot 29^{2} \)	$C_2^2 \wr C_2$ (as 8T18)	$[12]$
8.0.27328057344.2	x^8 - 2x^7 + 15x^6 - 20x^5 + 61x^4 + 6x^3 + 69x^2 + 126	\( 2^{12}\cdot 3^{4}\cdot 7^{2}\cdot 41^{2} \)	$C_2^2 \wr C_2$ (as 8T18)	$[12]$
8.0.27328057344.5	x^8 + 22x^6 + 179x^4 + 566x^2 + 289	\( 2^{12}\cdot 3^{4}\cdot 7^{2}\cdot 41^{2} \)	$C_2^2 \wr C_2$ (as 8T18)	$[2, 6]$
8.0.28288548864.31	x^8 + 10x^6 + 45x^4 + 28x^2 + 100	\( 2^{16}\cdot 3^{4}\cdot 73^{2} \)	$D_4\times C_2$ (as 8T9)	$[12]$
8.0.28288548864.32	x^8 - 12x^5 + 5x^4 + 60x^3 + 72x^2 + 120x + 100	\( 2^{16}\cdot 3^{4}\cdot 73^{2} \)	$D_4\times C_2$ (as 8T9)	$[12]$
8.0.32319410176.2	x^8 - 2x^7 + 12x^6 - 28x^5 + 66x^4 - 152x^3 + 288x^2 - 272x + 468	\( 2^{12}\cdot 53^{4} \)	$S_4$ (as 8T14)	$[12]$
8.0.33890333801.1	x^8 - x^7 + 7x^6 - 11x^5 + 44x^4 - 71x^3 + 153x^2 - 112x + 131	\( 19^{2}\cdot 103^{2}\cdot 8849 \)	$C_2 \wr S_4$ (as 8T44)	$[11]$
8.0.35296583633.1	x^8 - x^7 + 7x^6 - 18x^5 + 23x^4 - 72x^3 + 112x^2 - 64x + 256	\( 23\cdot 199\cdot 2777^{2} \)	$C_2 \wr S_4$ (as 8T44)	$[12]$
8.0.35806100625.3	x^8 - 4x^7 + 18x^6 - 40x^5 + 132x^4 - 202x^3 + 449x^2 - 354x + 979	\( 3^{4}\cdot 5^{4}\cdot 29^{4} \)	$D_4\times C_2$ (as 8T9)	$[12]$
8.0.35806100625.4	x^8 + 17x^6 + 253x^4 + 612x^2 + 1296	\( 3^{4}\cdot 5^{4}\cdot 29^{4} \)	$C_2^3$ (as 8T3)	$[12]$
8.0.36457875625.1	x^8 - 3x^7 + 19x^6 - 32x^5 + 119x^4 - 112x^3 + 342x^2 - 140x + 431	\( 5^{4}\cdot 29^{2}\cdot 139\cdot 499 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	$[12]$
8.0.37036232704.2	x^8 + 10x^6 - 4x^5 + 79x^4 - 136x^3 + 338x^2 - 392x + 136	\( 2^{12}\cdot 31^{2}\cdot 97^{2} \)	$C_2^2 \wr C_2$ (as 8T18)	$[15]$
8.0.37480572801.2	x^8 - 3x^7 - 14x^6 + 65x^5 - 58x^4 - 275x^3 + 1281x^2 - 2048x + 1492	\( 3^{4}\cdot 7^{4}\cdot 439^{2} \)	$D_4\times C_2$ (as 8T9)	$[15]$
8.0.37480960000.9	x^8 - 2x^6 + 53x^4 + 388x^2 + 676	\( 2^{12}\cdot 5^{4}\cdot 11^{4} \)	$C_2^3$ (as 8T3)	$[12]$
8.0.37480960000.10	x^8 - 2x^7 - 9x^6 - 4x^5 + 73x^4 + 36x^3 - 11x^2 - 678x + 729	\( 2^{12}\cdot 5^{4}\cdot 11^{4} \)	$D_4\times C_2$ (as 8T9)	$[12]$
8.0.37480960000.12	x^8 + 16x^6 + 152x^4 + 1144x^2 + 1936	\( 2^{12}\cdot 5^{4}\cdot 11^{4} \)	$D_4\times C_2$ (as 8T9)	$[12]$
8.0.39464206336.13	x^8 + 12x^6 + 66x^4 + 192x^2 + 256	\( 2^{22}\cdot 97^{2} \)	$C_2^2:C_4$ (as 8T10)	$[12]$
8.0.39649172641.2	x^8 - 2x^6 + 85x^4 - 84x^2 + 64	\( 13^{2}\cdot 17^{4}\cdot 53^{2} \)	$C_2^2 \wr C_2$ (as 8T18)	$[11]$
8.0.40804000000.1	x^8 + 9x^6 + 36x^4 + 69x^2 + 121	\( 2^{8}\cdot 5^{6}\cdot 101^{2} \)	$C_2^2:C_4$ (as 8T10)	$[12]$
8.0.40804000000.9	x^8 - x^6 + 181x^4 - 2121x^2 + 10201	\( 2^{8}\cdot 5^{6}\cdot 101^{2} \)	$C_2^2:C_4$ (as 8T10)	$[2, 6]$
8.0.41463140625.9	x^8 - 3x^7 + 17x^6 - 30x^5 + 91x^4 - 90x^3 + 228x^2 - 54x + 261	\( 3^{4}\cdot 5^{6}\cdot 181^{2} \)	$C_2^3: C_4$ (as 8T20)	$[2, 6]$
8.0.43057910016.1	x^8 - 46x^6 + 721x^4 - 4224x^2 + 9216	\( 2^{8}\cdot 3^{4}\cdot 11^{2}\cdot 131^{2} \)	$D_4\times C_2$ (as 8T9)	$[11]$
8.0.43177515264.1	x^8 - 2x^7 + 9x^6 - 32x^5 + 28x^4 - 120x^3 + 228x^2 - 96x + 384	\( 2^{8}\cdot 3^{6}\cdot 13^{2}\cdot 37^{2} \)	$C_2^2 \wr C_2$ (as 8T18)	$[12]$
8.0.43177515264.22	x^8 + 11x^6 - 24x^5 + 48x^4 - 30x^3 + 23x^2 + 6x + 1	\( 2^{8}\cdot 3^{6}\cdot 13^{2}\cdot 37^{2} \)	$C_2^2 \wr C_2$ (as 8T18)	$[12]$
8.0.46128300625.1	x^8 - 4x^7 + 36x^6 - 94x^5 + 402x^4 - 652x^3 + 1821x^2 - 1510x + 2729	\( 5^{4}\cdot 11^{4}\cdot 71^{2} \)	$C_2^2 \wr C_2$ (as 8T18)	$[12]$
8.0.46128300625.2	x^8 + 14x^6 + 47x^4 + 206x^2 + 1	\( 5^{4}\cdot 11^{4}\cdot 71^{2} \)	$D_4\times C_2$ (as 8T9)	$[2, 6]$
8.0.46352367616.7	x^8 - 4x^7 + 10x^6 - 16x^5 + 54x^4 - 28x^3 + 86x^2 - 16x + 45	\( 2^{16}\cdot 29^{4} \)	$S_4$ (as 8T14)	$[12]$
8.0.47436840000.4	x^8 + x^6 - 53x^4 + 159x^2 + 36	\( 2^{6}\cdot 3^{4}\cdot 5^{4}\cdot 11^{4} \)	$D_4\times C_2$ (as 8T9)	$[2, 6]$
8.0.47436840000.5	x^8 - 3x^7 + 8x^6 - 12x^5 + 43x^4 + 27x^3 + 180x^2 + 108x + 144	\( 2^{6}\cdot 3^{4}\cdot 5^{4}\cdot 11^{4} \)	$D_4\times C_2$ (as 8T9)	$[12]$
8.0.48180689001.3	x^8 - x^7 + 8x^6 + 6x^5 + 8x^4 + 6x^3 + 8x^2 - x + 1	\( 3^{4}\cdot 29^{6} \)	$S_4$ (as 8T14)	$[12]$
8.0.48297515625.1	x^8 - x^7 + 13x^6 - 10x^5 + 81x^4 - 50x^3 + 232x^2 - 62x + 241	\( 3^{4}\cdot 5^{6}\cdot 31\cdot 1231 \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[12]$
8.0.48576160000.4	x^8 + 27x^6 + 258x^4 + 957x^2 + 961	\( 2^{8}\cdot 5^{4}\cdot 19^{2}\cdot 29^{2} \)	$C_2^2 \wr C_2$ (as 8T18)	$[4, 4]$
8.0.48576160000.5	x^8 - 2x^7 + 13x^6 - 14x^5 + 112x^4 - 36x^3 + 500x^2 - 134x + 1199	\( 2^{8}\cdot 5^{4}\cdot 19^{2}\cdot 29^{2} \)	$C_2^2 \wr C_2$ (as 8T18)	$[2, 8]$
8.0.48576160000.9	x^8 - 4x^7 + 2x^6 + 8x^5 + 8x^4 - 34x^3 + 209x^2 - 190x + 1805	\( 2^{8}\cdot 5^{4}\cdot 19^{2}\cdot 29^{2} \)	$C_2^2 \wr C_2$ (as 8T18)	$[2, 8]$
8.0.49798971392.1	x^8 - 4x^7 + 14x^6 - 28x^5 + 63x^4 - 56x^3 + 140x^2 - 32x + 158	\( 2^{22}\cdot 31\cdot 383 \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[16]$
8.0.49946886144.4	x^8 + 6x^6 + 53x^4 + 132x^2 + 100	\( 2^{16}\cdot 3^{4}\cdot 97^{2} \)	$D_4\times C_2$ (as 8T9)	$[2, 8]$
8.0.49946886144.36	x^8 - 4x^7 + 14x^6 - 28x^5 + 79x^4 - 116x^3 + 98x^2 - 44x + 334	\( 2^{16}\cdot 3^{4}\cdot 97^{2} \)	$D_4\times C_2$ (as 8T9)	$[2, 6]$
8.0.50269227264.1	x^8 + 11x^6 + 33x^4 + 17x^2 + 1	\( 2^{8}\cdot 3^{8}\cdot 173^{2} \)	$C_2^3:S_4$ (as 8T39)	$[12]$
8.0.50651578125.1	x^8 - 3x^7 + 17x^6 - 30x^5 + 106x^4 - 105x^3 + 273x^2 - 99x + 261	\( 3^{4}\cdot 5^{6}\cdot 31\cdot 1291 \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[12]$
8.0.50712825625.1	x^8 - 3x^7 + 20x^6 - 41x^5 + 149x^4 - 205x^3 + 500x^2 - 375x + 625	\( 5^{4}\cdot 7^{2}\cdot 11\cdot 29^{2}\cdot 179 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	$[2, 6]$
8.0.53075650625.1	x^8 + 7x^6 - 10x^5 + 23x^4 - 40x^3 + 112x^2 + 256	\( 5^{4}\cdot 71\cdot 89^{2}\cdot 151 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	$[12]$
8.0.53557067776.15	x^8 - 4x^7 + 30x^6 - 76x^5 + 205x^4 - 288x^3 + 356x^2 - 224x + 98	\( 2^{22}\cdot 113^{2} \)	$C_2^3: C_4$ (as 8T20)	$[14]$
8.0.53824000000.4	x^8 - 2x^7 + 5x^6 - 2x^5 + 54x^4 - 18x^3 + 185x^2 - 138x + 711	\( 2^{12}\cdot 5^{6}\cdot 29^{2} \)	$D_4\times C_2$ (as 8T9)	$[12]$
8.0.53824000000.6	x^8 - 2x^7 + 15x^6 - 12x^5 + 129x^4 + 12x^3 + 525x^2 - 118x + 1321	\( 2^{12}\cdot 5^{6}\cdot 29^{2} \)	$C_2^2:C_4$ (as 8T10)	$[12]$
8.0.53824000000.12	x^8 + 6x^6 + 136x^4 + 1856x^2 + 13456	\( 2^{12}\cdot 5^{6}\cdot 29^{2} \)	$C_2^2:C_4$ (as 8T10)	$[12]$
8.0.54414344192.14	x^8 + 14x^6 - 8x^5 + 47x^4 - 68x^3 + 34x^2 - 68x + 102	\( 2^{16}\cdot 13^{2}\cdot 17^{3} \)	$(C_4^2 : C_2):C_2$ (as 8T26)	$[12]$
8.0.55283765625.12	x^8 - x^7 + 13x^6 + 10x^5 + 21x^4 + 185x^3 - 23x^2 - 122x + 316	\( 3^{4}\cdot 5^{6}\cdot 11^{2}\cdot 19^{2} \)	$C_2^2 \wr C_2$ (as 8T18)	$[2, 8]$
8.0.55283765625.14	x^8 - x^7 + 23x^6 - 5x^5 + 136x^4 + 15x^3 + 177x^2 + 18x + 531	\( 3^{4}\cdot 5^{6}\cdot 11^{2}\cdot 19^{2} \)	$C_2^2:C_4$ (as 8T10)	$[2, 8]$
8.0.55296463104.2	x^8 + 42x^6 + 635x^4 + 4086x^2 + 9409	\( 2^{8}\cdot 3^{4}\cdot 23^{2}\cdot 71^{2} \)	$D_4\times C_2$ (as 8T9)	$[12]$
8.0.55749348769.1	x^8 - 2x^6 + 53x^4 - 52x^2 + 64	\( 17^{4}\cdot 19^{2}\cdot 43^{2} \)	$C_2^2 \wr C_2$ (as 8T18)	$[13]$

In order to download results, .