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 all 20 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.486416793600000000.2	x^16 - 4x^15 + 13x^14 - 36x^13 + 85x^12 - 162x^11 + 285x^10 - 450x^9 + 607x^8 - 718x^7 + 762x^6 - 700x^5 + 518x^4 - 292x^3 + 120x^2 - 32x + 4	\( 2^{20}\cdot 3^{8}\cdot 5^{8}\cdot 181 \)	16T1378	Trivial
16.0.526614392658198528.2	x^16 - 8x^15 + 36x^14 - 108x^13 + 246x^12 - 456x^11 + 708x^10 - 944x^9 + 1102x^8 - 1128x^7 + 1000x^6 - 752x^5 + 476x^4 - 256x^3 + 112x^2 - 32x + 4	\( 2^{40}\cdot 3^{8}\cdot 73 \)	16T1378	Trivial
16.8.243057301232025600000000.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 58x^12 + 16x^11 - 152x^10 + 232x^9 - 156x^8 - 20x^7 + 126x^6 - 92x^5 + 11x^4 + 24x^3 - 12x^2 + 1	\( 2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 71\cdot 311 \)	16T1378	Trivial (GRH)
16.6.366671879051673600000000.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 254x^12 - 432x^11 + 532x^10 - 416x^9 + 50x^8 + 404x^7 - 678x^6 + 640x^5 - 389x^4 + 144x^3 - 22x^2 - 4x + 1	\( -\,2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 33311 \)	16T1378	Trivial (GRH)
16.12.382005370316390400000000.1	x^16 - 4x^15 - 10x^14 + 52x^13 + 4x^12 - 180x^11 + 104x^10 + 124x^9 + 85x^8 - 28x^7 - 256x^6 + 48x^5 + 130x^4 - 28x^3 - 22x^2 + 4x + 1	\( 2^{36}\cdot 3^{10}\cdot 5^{8}\cdot 241 \)	16T1378	Trivial (GRH)
16.4.382005370316390400000000.1	x^16 - 8x^15 + 24x^14 - 24x^13 - 70x^12 + 368x^11 - 866x^10 + 1224x^9 - 881x^8 - 412x^7 + 2338x^6 - 4100x^5 + 5028x^4 - 5268x^3 + 4710x^2 - 2976x + 961	\( 2^{36}\cdot 3^{10}\cdot 5^{8}\cdot 241 \)	16T1378	$[2]$ (GRH)
16.12.382005370316390400000000.2	x^16 - 4x^15 - 12x^14 + 52x^13 + 102x^12 - 516x^11 + 56x^10 + 1848x^9 - 2086x^8 - 1232x^7 + 3188x^6 - 808x^5 - 1304x^4 + 760x^3 + 16x^2 - 64x + 4	\( 2^{36}\cdot 3^{10}\cdot 5^{8}\cdot 241 \)	16T1378	Trivial (GRH)
16.4.382005370316390400000000.2	x^16 - 4x^15 - 4x^14 + 36x^13 - 38x^12 - 92x^11 + 352x^10 - 656x^9 + 1046x^8 - 1400x^7 + 796x^6 + 2448x^5 - 8112x^4 + 12328x^3 - 11672x^2 + 6624x - 1724	\( 2^{36}\cdot 3^{10}\cdot 5^{8}\cdot 241 \)	16T1378	$[2]$ (GRH)
16.14.1019726702995046400000000.1	x^16 - 8x^15 + 20x^14 - 82x^12 + 128x^11 + 4x^10 - 240x^9 + 258x^8 + 100x^7 - 334x^6 + 56x^5 + 163x^4 - 40x^3 - 30x^2 + 4x + 1	\( -\,2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 92639 \)	16T1378	Trivial (GRH)
16.10.1091487735713843814334464.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 50x^12 + 64x^11 - 272x^10 + 392x^9 - 260x^8 - 36x^7 + 214x^6 - 156x^5 + 19x^4 + 40x^3 - 20x^2 + 1	\( -\,2^{32}\cdot 3^{8}\cdot 7^{8}\cdot 6719 \)	16T1378	Trivial (GRH)
16.10.1368569050405273600000000.1	x^16 - 12x^14 - 8x^13 + 60x^12 + 72x^11 - 210x^10 - 284x^9 + 494x^8 + 880x^7 + 132x^6 - 1328x^5 - 2129x^4 + 212x^3 + 1720x^2 + 232x - 316	\( -\,2^{32}\cdot 5^{8}\cdot 13^{8} \)	16T1378	$[2]$ (GRH)
16.6.1368569050405273600000000.1	x^16 + 12x^14 + 12x^12 - 220x^10 - 233x^8 + 1256x^6 - 154x^4 - 792x^2 - 81	\( -\,2^{32}\cdot 5^{8}\cdot 13^{8} \)	16T1378	$[2]$ (GRH)
16.8.11666627390481638400000000.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 55x^12 + 34x^11 - 197x^10 + 292x^9 - 192x^8 - 38x^7 + 177x^6 - 128x^5 + 17x^4 + 30x^3 - 15x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 7^{8}\cdot 12049 \)	16T1378	$[2]$ (GRH)
16.2.55363821251434905600000000.1	x^16 - 8x^15 + 44x^14 - 168x^13 + 506x^12 - 1216x^11 + 2392x^10 - 3864x^9 + 5076x^8 - 5348x^7 + 4214x^6 - 2164x^5 + 43x^4 + 1040x^3 - 1140x^2 + 592x - 191	\( -\,2^{32}\cdot 3^{8}\cdot 5^{8}\cdot 911\cdot 5521 \)	16T1378	$[2, 4]$ (GRH)
16.14.57155522167855796069597184.1	x^16 - 8x^15 + 20x^14 - 90x^12 + 176x^11 - 68x^10 - 320x^9 + 514x^8 + 84x^7 - 630x^6 + 136x^5 + 315x^4 - 72x^3 - 62x^2 + 4x + 1	\( -\,2^{32}\cdot 3^{8}\cdot 7^{8}\cdot 193\cdot 1823 \)	16T1378	Trivial (GRH)
16.0.97793374800995942400000000.1	x^16 - 8x^15 + 48x^14 - 172x^13 + 572x^12 - 1332x^11 + 3264x^10 - 5016x^9 + 9315x^8 - 3980x^7 + 3760x^6 + 27384x^5 - 15300x^4 + 38868x^3 + 27072x^2 - 8996x + 36241	\( 2^{44}\cdot 3^{10}\cdot 5^{8}\cdot 241 \)	16T1378	$[2, 76]$ (GRH)
16.16.97793374800995942400000000.1	x^16 - 40x^14 + 554x^12 - 3752x^10 + 14023x^8 - 29784x^6 + 34374x^4 - 18144x^2 + 2169	\( 2^{44}\cdot 3^{10}\cdot 5^{8}\cdot 241 \)	16T1378	Trivial (GRH)
16.0.97793374800995942400000000.2	x^16 + 40x^14 + 554x^12 + 3752x^10 + 14023x^8 + 29784x^6 + 34374x^4 + 18144x^2 + 2169	\( 2^{44}\cdot 3^{10}\cdot 5^{8}\cdot 241 \)	16T1378	$[2, 68]$ (GRH)
16.16.97793374800995942400000000.2	x^16 - 8x^15 - 8x^14 + 172x^13 - 76x^12 - 1364x^11 + 684x^10 + 5560x^9 - 889x^8 - 12268x^7 - 3444x^6 + 12440x^5 + 8660x^4 - 2884x^3 - 4772x^2 - 1684x - 191	\( 2^{44}\cdot 3^{10}\cdot 5^{8}\cdot 241 \)	16T1378	Trivial (GRH)
16.2.137785409585912217600000000.1	x^16 + 16x^14 + 100x^12 + 304x^10 + 423x^8 + 56x^6 - 548x^4 - 592x^2 - 191	\( -\,2^{48}\cdot 3^{8}\cdot 5^{8}\cdot 191 \)	16T1378	$[10]$ (GRH)