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 all 36 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.12370583534765625.1	x^16 - 7x^15 + 24x^14 - 50x^13 + 65x^12 - 40x^11 - 28x^10 + 94x^9 - 94x^8 + 16x^7 + 82x^6 - 128x^5 + 108x^4 - 59x^3 + 22x^2 - 6x + 1	\( 3^{8}\cdot 5^{8}\cdot 13^{6} \)	$D_8:C_2$ (as 16T44)	Trivial
16.0.36877862166921216.1	x^16 - 4x^15 + 8x^14 - 18x^13 + 44x^12 - 80x^11 + 109x^10 - 144x^9 + 211x^8 - 282x^7 + 301x^6 - 250x^5 + 164x^4 - 84x^3 + 32x^2 - 8x + 1	\( 2^{16}\cdot 3^{14}\cdot 7^{6} \)	$D_8:C_2$ (as 16T44)	Trivial
16.4.232292068597265625.1	x^16 - x^15 + 5x^14 - x^13 + x^11 - 19x^10 - 13x^9 - 20x^8 - 11x^7 + 17x^6 + 35x^5 + 46x^4 + 36x^3 + 22x^2 + 4x - 1	\( 3^{6}\cdot 5^{8}\cdot 13^{8} \)	$D_8:C_2$ (as 16T44)	Trivial
16.0.440301256704000000.1	x^16 - 8x^15 + 32x^14 - 84x^13 + 168x^12 - 276x^11 + 370x^10 - 384x^9 + 295x^8 - 164x^7 + 78x^6 - 60x^5 + 62x^4 - 40x^3 + 14x^2 - 4x + 1	\( 2^{32}\cdot 3^{8}\cdot 5^{6} \)	$D_8:C_2$ (as 16T44)	Trivial
16.0.531312517142544384.1	x^16 - 4x^15 + 4x^14 - 2x^13 + 16x^12 - 38x^11 + 67x^10 - 168x^9 + 338x^8 - 474x^7 + 495x^6 - 388x^5 + 231x^4 - 106x^3 + 36x^2 - 8x + 1	\( 2^{24}\cdot 3^{8}\cdot 13^{6} \)	$D_8:C_2$ (as 16T44)	Trivial
16.0.555307587640295424.1	x^16 - 4x^15 - x^14 + 24x^13 - 22x^12 - 50x^11 + 85x^10 + 24x^9 - 119x^8 + 66x^7 + 61x^6 - 100x^5 + 20x^4 + 42x^3 - 37x^2 - 2x + 13	\( 2^{16}\cdot 3^{14}\cdot 11^{6} \)	$D_8:C_2$ (as 16T44)	Trivial
16.0.590315622400000000.1	x^16 - 2x^15 + 3x^14 - 7x^13 + 12x^12 - 11x^11 + 14x^10 - 9x^9 + 5x^8 - 3x^7 + x^6 - 8x^5 + 27x^4 - 14x^3 + 2x^2 - x + 1	\( 2^{18}\cdot 5^{8}\cdot 7^{8} \)	$D_8:C_2$ (as 16T44)	Trivial
16.4.771024486400000000.1	x^16 - 2x^15 - x^14 - 6x^11 + 24x^10 + 20x^9 - 24x^8 - 38x^7 + 5x^6 + 20x^5 - 18x^4 + 6x^3 - 4x^2 + 1	\( 2^{24}\cdot 5^{8}\cdot 7^{6} \)	$D_8:C_2$ (as 16T44)	Trivial
16.0.1099511627776000000.1	x^16 - 12x^12 + 46x^8 + 68x^4 + 25	\( 2^{46}\cdot 5^{6} \)	$D_8:C_2$ (as 16T44)	Trivial
16.0.1524467112922265625.1	x^16 - x^15 + 3x^14 + 2x^13 - 6x^12 + 24x^11 - 32x^10 + 40x^9 - 55x^7 + 163x^6 - 233x^5 + 292x^4 - 262x^3 + 194x^2 - 100x + 31	\( 3^{8}\cdot 5^{8}\cdot 29^{6} \)	$D_8:C_2$ (as 16T44)	Trivial
16.4.1807015246179139584.1	x^16 - 6x^15 + 16x^14 - 18x^13 + 4x^12 + 6x^11 - 5x^10 + 24x^9 - 47x^8 + 24x^7 - 5x^6 + 6x^5 + 4x^4 - 18x^3 + 16x^2 - 6x + 1	\( 2^{16}\cdot 3^{14}\cdot 7^{8} \)	$D_8:C_2$ (as 16T44)	Trivial (GRH)
16.0.4199513631529734144.1	x^16 - 3x^15 + 4x^14 + 6x^13 - 29x^12 + 60x^11 - 50x^10 - 24x^9 + 196x^8 - 366x^7 + 496x^6 - 468x^5 + 349x^4 - 189x^3 + 64x^2 - 12x + 1	\( 2^{12}\cdot 3^{14}\cdot 11^{8} \)	$D_8:C_2$ (as 16T44)	Trivial
16.4.6871947673600000000.6	x^16 - 6x^12 - 33x^8 + 6x^4 + 1	\( 2^{44}\cdot 5^{8} \)	$D_8:C_2$ (as 16T44)	Trivial (GRH)
16.0.7044820107264000000.1	x^16 - 8x^14 + 22x^12 - 12x^10 - 41x^8 + 68x^6 + 18x^4 - 60x^2 + 25	\( 2^{36}\cdot 3^{8}\cdot 5^{6} \)	$D_8:C_2$ (as 16T44)	Trivial
16.0.9440732714731831296.2	x^16 - 2x^15 - 5x^14 + 28x^13 - 47x^12 - 2x^11 + 187x^10 - 464x^9 + 658x^8 - 606x^7 + 366x^6 - 126x^5 + 21x^4 - 18x^3 + 33x^2 - 18x + 3	\( 2^{24}\cdot 3^{14}\cdot 7^{6} \)	$D_8:C_2$ (as 16T44)	Trivial
16.4.9976868377454444544.2	x^16 - 4x^15 + 10x^13 - 22x^12 + 42x^11 - 67x^10 + 82x^9 - 93x^8 + 82x^7 - 67x^6 + 42x^5 - 22x^4 + 10x^3 - 4x + 1	\( 2^{24}\cdot 3^{6}\cdot 13^{8} \)	$D_8:C_2$ (as 16T44)	Trivial (GRH)
16.4.11007531417600000000.2	x^16 - 14x^12 - 73x^8 - 46x^4 + 1	\( 2^{32}\cdot 3^{8}\cdot 5^{8} \)	$D_8:C_2$ (as 16T44)	Trivial (GRH)
16.4.11610102169600000000.1	x^16 - 4x^15 - 2x^14 + 22x^13 + x^12 - 66x^11 + 5x^10 + 144x^9 - 137x^8 + 88x^7 - 168x^6 + 180x^5 - 69x^4 + 10x^3 - 7x^2 + 2x + 1	\( 2^{24}\cdot 5^{8}\cdot 11^{6} \)	$D_8:C_2$ (as 16T44)	Trivial (GRH)
16.0.23806000582036291584.1	x^16 - 5x^15 + 4x^14 + 18x^13 - 20x^12 - 39x^11 + 17x^10 + 85x^9 + 62x^8 - 189x^7 - 152x^6 + 233x^5 + 174x^4 - 77x^3 - 197x^2 - 26x + 127	\( 2^{18}\cdot 3^{8}\cdot 7^{12} \)	$D_8:C_2$ (as 16T44)	Trivial
16.0.51283073678705015625.1	x^16 - 8x^15 + 26x^14 - 42x^13 + 36x^12 - 34x^11 + 76x^10 - 116x^9 + 114x^8 - 134x^7 + 136x^6 - 34x^5 - 24x^4 - 18x^3 + 16x^2 + 5x + 1	\( 3^{8}\cdot 5^{6}\cdot 29^{8} \)	$D_8:C_2$ (as 16T44)	$[3]$
16.0.56192894500864000000.1	x^16 - 2x^15 - 3x^14 + 6x^13 + 6x^12 + 8x^11 - 33x^10 - 92x^9 + 347x^8 - 470x^7 + 373x^6 - 204x^5 + 97x^4 - 54x^3 + 28x^2 - 8x + 1	\( 2^{24}\cdot 5^{6}\cdot 11^{8} \)	$D_8:C_2$ (as 16T44)	Trivial
16.0.84142880492674351104.3	x^16 - 30x^12 + 303x^8 - 90x^4 + 9	\( 2^{44}\cdot 3^{14} \)	$D_8:C_2$ (as 16T44)	Trivial
16.0.118192468620711297024.6	x^16 - 12x^14 + 66x^12 - 176x^10 + 250x^8 - 192x^6 + 76x^4 - 16x^2 + 4	\( 2^{54}\cdot 3^{8} \)	$D_8:C_2$ (as 16T44)	Trivial
16.4.176120502681600000000.2	x^16 + 14x^12 - 73x^8 + 46x^4 + 1	\( 2^{36}\cdot 3^{8}\cdot 5^{8} \)	$D_8:C_2$ (as 16T44)	Trivial (GRH)
16.0.210119944214597861376.1	x^16 - 8x^14 + 32x^12 - 72x^10 + 94x^8 - 56x^6 + 32x^4 - 24x^2 + 9	\( 2^{58}\cdot 3^{6} \)	$D_8:C_2$ (as 16T44)	Trivial
16.4.336571521970697404416.3	x^16 - 36x^12 - 66x^8 + 108x^4 + 9	\( 2^{46}\cdot 3^{14} \)	$D_8:C_2$ (as 16T44)	Trivial
16.4.462595903021859733504.3	x^16 - 6x^15 + 11x^14 - 38x^12 + 120x^11 - 172x^10 - 96x^9 + 604x^8 - 450x^7 - 598x^6 + 1080x^5 - 203x^4 - 690x^3 + 623x^2 - 210x + 25	\( 2^{24}\cdot 3^{14}\cdot 7^{8} \)	$D_8:C_2$ (as 16T44)	Trivial
16.4.1523584037250322661376.1	x^16 - 6x^15 + 13x^14 - 20x^13 + 82x^12 - 298x^11 + 502x^10 - 202x^9 - 629x^8 + 1246x^7 - 1104x^6 + 494x^5 - 12x^4 - 120x^3 + 67x^2 - 14x + 1	\( 2^{24}\cdot 3^{8}\cdot 7^{12} \)	$D_8:C_2$ (as 16T44)	Trivial (GRH)
16.4.1891079497931380752384.1	x^16 - 8x^14 + 8x^12 + 40x^10 - 42x^8 - 120x^6 - 72x^4 - 8x^2 + 1	\( 2^{58}\cdot 3^{8} \)	$D_8:C_2$ (as 16T44)	Trivial (GRH)
16.0.1891079497931380752384.5	x^16 - 8x^14 + 40x^12 - 120x^10 + 238x^8 - 280x^6 + 216x^4 - 72x^2 + 25	\( 2^{58}\cdot 3^{8} \)	$D_8:C_2$ (as 16T44)	$[2]$
16.4.1891079497931380752384.5	x^16 - 8x^12 - 10x^8 + 8x^4 + 1	\( 2^{58}\cdot 3^{8} \)	$D_8:C_2$ (as 16T44)	Trivial (GRH)
16.4.1891079497931380752384.6	x^16 - 12x^12 + 2x^8 + 12x^4 + 1	\( 2^{58}\cdot 3^{8} \)	$D_8:C_2$ (as 16T44)	Trivial (GRH)
16.0.3898234116505600000000.7	x^16 - 4x^15 + 10x^14 - 32x^13 + 63x^12 - 74x^11 + 162x^10 - 380x^9 + 947x^8 - 2244x^7 + 3921x^6 - 4596x^5 + 3793x^4 - 2200x^3 + 877x^2 - 226x + 31	\( 2^{24}\cdot 5^{8}\cdot 29^{6} \)	$D_8:C_2$ (as 16T44)	Trivial
16.0.131136595679248384000000.1	x^16 - 8x^15 + 54x^14 - 238x^13 + 843x^12 - 2328x^11 + 5179x^10 - 9274x^9 + 13292x^8 - 15124x^7 + 13533x^6 - 9398x^5 + 4964x^4 - 1930x^3 + 522x^2 - 88x + 7	\( 2^{24}\cdot 5^{6}\cdot 29^{8} \)	$D_8:C_2$ (as 16T44)	Trivial (GRH)
16.16.174125907386032334045184.1	x^16 - 28x^14 - 8x^13 + 250x^12 + 8x^11 - 1036x^10 + 380x^9 + 2009x^8 - 1632x^7 - 1216x^6 + 1932x^5 - 612x^4 - 144x^3 + 116x^2 - 20x + 1	\( 2^{40}\cdot 3^{8}\cdot 17^{6} \)	$D_8:C_2$ (as 16T44)	Trivial (GRH)
16.16.997947933825433600000000.1	x^16 - 32x^14 - 16x^13 + 359x^12 + 312x^11 - 1762x^10 - 2152x^9 + 3697x^8 + 6200x^7 - 2208x^6 - 7340x^5 - 1651x^4 + 2856x^3 + 1652x^2 + 164x - 31	\( 2^{32}\cdot 5^{8}\cdot 29^{6} \)	$D_8:C_2$ (as 16T44)	Trivial (GRH)