Global number field search results

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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 64)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.123566310400000000.1	x^16 - 4x^15 + 7x^14 - 10x^13 + 18x^12 - 38x^11 + 71x^10 - 104x^9 + 119x^8 - 104x^7 + 71x^6 - 38x^5 + 18x^4 - 10x^3 + 7x^2 - 4x + 1	\( 2^{16}\cdot 5^{8}\cdot 13^{6} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.129356443496218624.1	x^16 - 8x^15 + 32x^14 - 84x^13 + 158x^12 - 220x^11 + 228x^10 - 172x^9 + 105x^8 - 92x^7 + 136x^6 - 172x^5 + 148x^4 - 84x^3 + 32x^2 - 8x + 1	\( 2^{40}\cdot 7^{6} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.429496729600000000.1	x^16 + 8x^14 - 4x^13 + 26x^12 - 24x^11 + 44x^10 - 36x^9 + 38x^8 - 16x^7 - 8x^6 - 4x^5 + 26x^4 - 8x^3 + 4x^2 - 4x + 1	\( 2^{40}\cdot 5^{8} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.4.429496729600000000.1	x^16 - 8x^14 - 4x^13 + 20x^12 + 8x^11 - 20x^10 - 24x^9 + 31x^8 + 32x^7 - 60x^6 + 8x^5 + 36x^4 - 24x^3 + 4x - 1	\( 2^{40}\cdot 5^{8} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.617921766400000000.1	x^16 - 4x^15 + 5x^14 + 6x^13 - 35x^12 + 64x^11 - 56x^10 - 18x^9 + 155x^8 - 294x^7 + 358x^6 - 320x^5 + 216x^4 - 106x^3 + 36x^2 - 8x + 1	\( 2^{16}\cdot 5^{8}\cdot 17^{6} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.835308258304000000.1	x^16 - x^14 - 6x^13 + x^12 + 2x^11 + 4x^10 - 14x^9 + 39x^8 - 8x^7 + 6x^6 - 30x^5 + 58x^4 - 44x^3 + 20x^2 - 4x + 1	\( 2^{16}\cdot 5^{6}\cdot 13^{8} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.1253826625536000000.1	x^16 - 2x^15 + 3x^14 - 10x^13 + 14x^12 - 12x^11 + 31x^10 - 32x^9 + 15x^8 - 32x^7 + 31x^6 - 12x^5 + 14x^4 - 10x^3 + 3x^2 - 2x + 1	\( 2^{24}\cdot 3^{14}\cdot 5^{6} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.5155870532308107264.1	x^16 - 2x^15 - 7x^14 + 16x^13 + 19x^12 - 52x^11 - 22x^10 + 74x^9 + 55x^8 - 96x^7 - 126x^6 + 216x^5 + 42x^4 - 270x^3 + 216x^2 - 72x + 9	\( 2^{16}\cdot 3^{12}\cdot 23^{6} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.5258930030792146944.1	x^16 - 4x^15 + 8x^14 - 12x^13 + 8x^12 + 4x^11 - 44x^10 + 108x^9 - 5x^8 - 156x^7 + 88x^6 + 68x^5 - 70x^4 + 20x^2 - 8x + 1	\( 2^{40}\cdot 3^{14} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.5258930030792146944.2	x^16 - 8x^15 + 28x^14 - 56x^13 + 76x^12 - 68x^11 + 4x^10 + 112x^9 - 173x^8 + 84x^7 + 60x^6 - 96x^5 + 36x^4 + 12x^3 - 12x^2 + 3	\( 2^{40}\cdot 3^{14} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.4.6338465731314712576.1	x^16 - 4x^14 + 6x^12 - 24x^11 - 8x^10 + 36x^9 - 7x^8 + 60x^6 + 36x^5 + 20x^4 + 48x^3 + 40x^2 + 12x + 1	\( 2^{40}\cdot 7^{8} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.9766449236141015625.1	x^16 - 6x^15 + 14x^14 - 12x^13 - 7x^12 + 15x^11 + 8x^10 - 15x^9 - 14x^8 + 15x^7 + 7x^6 + 8x^4 + 6x^3 + x^2 - 3x + 1	\( 3^{12}\cdot 5^{8}\cdot 19^{6} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.10497600000000000000.2	x^16 - 8x^15 + 26x^14 - 42x^13 + 31x^12 - 4x^11 - 21x^10 + 94x^9 - 133x^8 - 76x^7 + 259x^6 - 54x^5 - 154x^4 + 88x^3 + 21x^2 - 28x + 16	\( 2^{18}\cdot 3^{8}\cdot 5^{14} \)	$C_8:C_2^2$ (as 16T38)	$[2]$
16.0.10770650185222265625.1	x^16 - 5x^15 + 13x^14 - 17x^13 + 10x^12 - 2x^11 + 22x^10 - 59x^9 + 79x^8 - 84x^7 + 117x^6 - 144x^5 + 120x^4 - 72x^3 + 54x^2 - 27x + 9	\( 3^{14}\cdot 5^{8}\cdot 7^{8} \)	$C_8:C_2^2$ (as 16T38)	$[2]$
16.4.10770650185222265625.1	x^16 - 7x^15 + 17x^14 - 15x^13 + 2x^12 + x^11 - 26x^10 + 72x^9 - 44x^8 - 9x^7 - 2x^6 - 7x^5 + 44x^4 - 15x^3 - 31x^2 + 25x - 5	\( 3^{14}\cdot 5^{8}\cdot 7^{8} \)	$C_8:C_2^2$ (as 16T38)	Trivial (GRH)
16.0.15184705577789362176.1	x^16 - x^15 - x^14 + 8x^12 - 8x^11 + 7x^10 - 3x^9 + 25x^8 - 24x^7 + 16x^6 + 20x^5 + 20x^4 - 48x^3 + 32x^2 + 16x + 16	\( 2^{12}\cdot 3^{12}\cdot 17^{8} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.17592186044416000000.1	x^16 + 4x^12 - 72x^10 + 206x^8 - 240x^6 + 124x^4 - 40x^2 + 25	\( 2^{50}\cdot 5^{6} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.18049771555189161984.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 268x^12 - 516x^11 + 818x^10 - 1076x^9 + 1171x^8 - 1044x^7 + 766x^6 - 472x^5 + 252x^4 - 116x^3 + 44x^2 - 12x + 2	\( 2^{32}\cdot 3^{6}\cdot 7^{8} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.29863208046433665024.1	x^16 - 3x^15 + 6x^14 - 9x^13 + 16x^12 - 15x^11 + 12x^10 - 27x^9 + 72x^8 - 93x^7 + 102x^6 - 39x^5 - 23x^4 - 72x^3 + 216x^2 - 192x + 64	\( 2^{18}\cdot 3^{12}\cdot 11^{8} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.4.31345665638400000000.2	x^16 - 4x^15 + 6x^14 + 4x^13 - 37x^12 + 84x^11 - 92x^10 + 8x^9 + 132x^8 - 220x^7 + 118x^6 + 108x^5 - 214x^4 + 160x^3 + 30x^2 - 100x + 25	\( 2^{24}\cdot 3^{14}\cdot 5^{8} \)	$C_8:C_2^2$ (as 16T38)	Trivial (GRH)
16.0.33115249535031967744.3	x^16 - 8x^14 + 36x^12 - 88x^10 + 111x^8 - 88x^6 + 100x^4 - 112x^2 + 49	\( 2^{48}\cdot 7^{6} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.35664401793024000000.1	x^16 - 4x^15 + 2x^14 + 44x^12 - 104x^11 + 124x^10 - 276x^9 + 475x^8 - 444x^7 + 604x^6 - 796x^5 + 284x^4 + 120x^3 + 2x^2 + 4x + 1	\( 2^{32}\cdot 3^{12}\cdot 5^{6} \)	$C_8:C_2^2$ (as 16T38)	$[2]$
16.4.74649600000000000000.2	x^16 - 4x^15 + 6x^14 - 16x^13 + 28x^12 - 24x^11 + 24x^10 + 42x^9 - 117x^8 + 36x^7 + 6x^6 + 42x^5 - 17x^4 + 2x^3 - 21x^2 + 2x + 1	\( 2^{24}\cdot 3^{6}\cdot 5^{14} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.118192468620711297024.7	x^16 - 12x^14 + 54x^12 - 72x^10 + 38x^8 - 12x^4 + 4	\( 2^{54}\cdot 3^{8} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.119574225000000000000.2	x^16 - 3x^15 - x^14 + 12x^13 - 2x^12 + 12x^11 - 109x^10 + 111x^9 + 193x^8 - 408x^7 + 554x^6 - 384x^5 + 148x^4 - 336x^3 + 416x^2 - 384x + 256	\( 2^{12}\cdot 3^{14}\cdot 5^{14} \)	$C_8:C_2^2$ (as 16T38)	$[4]$
16.0.119842600295694598144.2	x^16 - 6x^14 + 9x^12 + 10x^10 - 28x^8 + 130x^6 + 25x^4 + 10x^2 + 1	\( 2^{34}\cdot 17^{8} \)	$C_8:C_2^2$ (as 16T38)	$[2]$
16.4.119842600295694598144.2	x^16 + 6x^14 + 9x^12 - 10x^10 - 28x^8 - 130x^6 + 25x^4 - 10x^2 + 1	\( 2^{34}\cdot 17^{8} \)	$C_8:C_2^2$ (as 16T38)	Trivial (GRH)
16.0.136016004388491362304.4	x^16 - 4x^15 + 6x^14 - 8x^13 + 46x^12 - 168x^11 + 338x^10 - 520x^9 + 786x^8 - 1108x^7 + 1370x^6 - 1512x^5 + 1406x^4 - 960x^3 + 430x^2 - 112x + 13	\( 2^{32}\cdot 3^{8}\cdot 13^{6} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.4.162447943996702457856.1	x^16 - 6x^12 - 17x^8 - 6x^4 + 1	\( 2^{32}\cdot 3^{8}\cdot 7^{8} \)	$C_8:C_2^2$ (as 16T38)	Trivial (GRH)
16.0.178579390489600000000.2	x^16 + 6x^14 - 14x^13 + 11x^12 - 44x^11 + x^10 - 8x^9 - 52x^8 + 72x^7 + 233x^6 + 166x^5 + 387x^4 - 334x^3 - 149x^2 + 60x + 25	\( 2^{16}\cdot 5^{8}\cdot 17^{8} \)	$C_8:C_2^2$ (as 16T38)	$[2]$
16.0.182059119829942534144.5	x^16 + 4x^14 + 14x^12 + 56x^10 + 105x^8 + 196x^6 + 392x^4 + 144x^2 + 16	\( 2^{28}\cdot 7^{14} \)	$C_8:C_2^2$ (as 16T38)	$[2]$
16.0.210119944214597861376.3	x^16 - 12x^12 + 72x^8 - 192x^6 + 328x^4 - 192x^2 + 36	\( 2^{58}\cdot 3^{6} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.215212989780710129664.1	x^16 - 6x^15 + 17x^14 - 30x^13 + 38x^12 - 48x^11 + 89x^10 - 168x^9 + 217x^8 - 156x^7 + 7x^6 + 72x^5 - 10x^4 - 30x^3 + 7x^2 + 6x + 1	\( 2^{24}\cdot 3^{12}\cdot 17^{6} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.4.242955289244629794816.1	x^16 - 11x^14 + 32x^12 - 38x^10 + 58x^8 - 112x^6 + 41x^4 - 7x^2 + 4	\( 2^{16}\cdot 3^{12}\cdot 17^{8} \)	$C_8:C_2^2$ (as 16T38)	Trivial (GRH)
16.4.268435456000000000000.1	x^16 - 4x^15 + 20x^13 - 36x^12 + 36x^11 - 48x^10 + 100x^9 - 69x^8 - 84x^7 + 212x^6 - 148x^5 + 114x^4 - 168x^3 + 56x^2 + 128x - 79	\( 2^{40}\cdot 5^{12} \)	$C_8:C_2^2$ (as 16T38)	Trivial (GRH)
16.0.268435456000000000000.5	x^16 - 4x^15 + 8x^14 - 8x^13 - 8x^12 + 48x^11 - 48x^10 - 104x^9 + 445x^8 - 968x^7 + 1256x^6 - 1048x^5 + 828x^4 - 412x^3 + 180x^2 - 56x + 11	\( 2^{40}\cdot 5^{12} \)	$C_8:C_2^2$ (as 16T38)	$[2]$ (GRH)
16.0.288796344883026591744.1	x^16 + 24x^12 + 120x^8 + 160x^4 + 144	\( 2^{36}\cdot 3^{6}\cdot 7^{8} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.291623507129944571904.1	x^16 - 2x^15 + 4x^14 + 14x^10 - 16x^9 + 11x^8 + 6x^7 + 49x^4 - 14x^3 + 25x^2 + 6x + 9	\( 2^{16}\cdot 3^{8}\cdot 7^{14} \)	$C_8:C_2^2$ (as 16T38)	$[2]$
16.4.291623507129944571904.1	x^16 - 6x^15 + 10x^14 - 21x^12 + 42x^11 - 49x^10 + 36x^9 - 48x^8 + 66x^7 - 77x^6 + 42x^5 + 7x^4 - 42x^3 + 45x^2 - 18x + 9	\( 2^{16}\cdot 3^{8}\cdot 7^{14} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.4.336571521970697404416.1	x^16 - 4x^14 + 4x^12 - 24x^11 - 40x^10 - 96x^9 - 176x^8 + 48x^7 + 272x^6 + 240x^5 + 184x^4 - 96x^3 - 112x^2 - 8	\( 2^{46}\cdot 3^{14} \)	$C_8:C_2^2$ (as 16T38)	Trivial
16.0.336571521970697404416.2	x^16 + 4x^14 + 4x^12 - 24x^11 - 20x^10 + 72x^9 + 214x^8 + 288x^7 + 316x^6 + 432x^5 + 556x^4 + 504x^3 + 340x^2 + 168x + 49	\( 2^{46}\cdot 3^{14} \)	$C_8:C_2^2$ (as 16T38)	$[2]$
16.0.439804651110400000000.3	x^16 - 8x^14 + 40x^12 - 136x^10 + 340x^8 - 544x^6 + 472x^4 - 80x^2 + 4	\( 2^{50}\cdot 5^{8} \)	$C_8:C_2^2$ (as 16T38)	$[2]$
16.0.462595903021859733504.1	x^16 - 4x^15 + 8x^14 - 12x^13 + 53x^12 - 164x^11 + 304x^10 - 426x^9 + 586x^8 - 786x^7 + 904x^6 - 844x^5 + 608x^4 - 312x^3 + 98x^2 - 14x + 1	\( 2^{24}\cdot 3^{14}\cdot 7^{8} \)	$C_8:C_2^2$ (as 16T38)	$[4]$
16.4.462595903021859733504.1	x^16 + 4x^14 - 44x^12 - 260x^10 - 170x^8 - 260x^6 - 44x^4 + 4x^2 + 1	\( 2^{24}\cdot 3^{14}\cdot 7^{8} \)	$C_8:C_2^2$ (as 16T38)	Trivial (GRH)
16.0.472769874482845188096.2	x^16 - 6x^12 + 13x^8 - 6x^4 + 1	\( 2^{56}\cdot 3^{8} \)	$C_8:C_2^2$ (as 16T38)	Trivial (GRH)
16.0.671846400000000000000.1	x^16 - 2x^15 + x^14 + 2x^13 + 6x^12 - 36x^11 + 29x^10 + 36x^9 + 7x^8 + 36x^7 + 29x^6 - 36x^5 + 6x^4 + 2x^3 + x^2 - 2x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{14} \)	$C_8:C_2^2$ (as 16T38)	$[4]$
16.0.671846400000000000000.4	x^16 - 4x^14 - 3x^12 - 2x^10 + 80x^8 - 8x^6 - 48x^4 - 256x^2 + 256	\( 2^{24}\cdot 3^{8}\cdot 5^{14} \)	$C_8:C_2^2$ (as 16T38)	$[4]$
16.0.728236479319770136576.3	x^16 - 2x^15 - x^14 + 14x^12 - 28x^11 + 14x^10 + 12x^9 - 45x^8 + 86x^7 + 49x^6 - 84x^5 - 126x^4 - 112x^3 + 258x^2 + 128x + 92	\( 2^{30}\cdot 7^{14} \)	$C_8:C_2^2$ (as 16T38)	$[2]$
16.0.891610044825600000000.9	x^16 - 8x^15 + 32x^14 - 84x^13 + 186x^12 - 388x^11 + 760x^10 - 1292x^9 + 1957x^8 - 2628x^7 + 2424x^6 - 1016x^5 - 216x^4 + 408x^3 - 56x^2 - 80x + 40	\( 2^{32}\cdot 3^{12}\cdot 5^{8} \)	$C_8:C_2^2$ (as 16T38)	$[4]$
16.0.896905412873600106496.1	x^16 - 4x^15 + 8x^14 - 8x^13 + 8x^12 - 24x^11 + 40x^10 + 32x^9 - 131x^8 - 176x^7 + 648x^6 - 288x^5 - 604x^4 + 732x^3 + 36x^2 - 432x + 243	\( 2^{40}\cdot 13^{8} \)	$C_8:C_2^2$ (as 16T38)	$[3]$ (GRH)