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 48 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.6561000000000000.1	x^16 - 5x^15 + 15x^14 - 32x^13 + 56x^12 - 85x^11 + 114x^10 - 134x^9 + 131x^8 - 98x^7 + 42x^6 + 9x^5 - 28x^4 + 18x^3 - x^2 - 3x + 1	\( 2^{12}\cdot 3^{8}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	Trivial
16.0.33215062500000000.1	x^16 - 4x^15 + 3x^14 + 15x^13 - 40x^12 + 33x^11 + 20x^10 - 79x^9 + 111x^8 - 125x^7 + 125x^6 - 96x^5 + 53x^4 - 24x^3 + 12x^2 - 5x + 1	\( 2^{8}\cdot 3^{12}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	Trivial
16.0.45749199462890625.1	x^16 - x^15 - x^14 + x^13 + 2x^12 - 5x^11 + 5x^9 + 3x^8 - 8x^7 + 9x^6 - 4x^5 - x^4 - x^3 + 2x^2 - 2x + 1	\( 3^{8}\cdot 5^{12}\cdot 13^{4} \)	$C_4 \times D_4$ (as 16T19)	Trivial
16.0.311520957275390625.1	x^16 - x^15 - 2x^14 + 4x^13 + 2x^12 + 5x^11 - 13x^10 - 8x^9 + 40x^8 - 8x^7 - 13x^6 + 5x^5 + 2x^4 + 4x^3 - 2x^2 - x + 1	\( 3^{12}\cdot 5^{12}\cdot 7^{4} \)	$C_4 \times D_4$ (as 16T19)	Trivial
16.0.331776000000000000.1	x^16 - 6x^15 + 17x^14 - 24x^13 + 21x^12 - 17x^10 + 30x^9 - 28x^8 + 30x^7 - 17x^6 + 21x^4 - 24x^3 + 17x^2 - 6x + 1	\( 2^{24}\cdot 3^{4}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	Trivial
16.0.364791569817010176.1	x^16 - 8x^14 + 12x^12 + 24x^10 - 24x^8 + 24x^4 - 16x^2 + 4	\( 2^{52}\cdot 3^{4} \)	$C_4 \times D_4$ (as 16T19)	Trivial
16.0.531441000000000000.1	x^16 - x^15 + 3x^14 - 6x^13 + 17x^12 + 17x^10 - 13x^9 + 15x^8 + 97x^7 + 62x^6 - 13x^4 - 6x^3 + 3x^2 + 4x + 1	\( 2^{12}\cdot 3^{12}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	Trivial
16.0.703687441776640000.2	x^16 - 16x^12 + 66x^8 + 16x^4 + 1	\( 2^{50}\cdot 5^{4} \)	$C_4 \times D_4$ (as 16T19)	Trivial
16.0.1459166279268040704.3	x^16 - 8x^15 + 32x^14 - 72x^13 + 100x^12 - 64x^11 + 24x^10 - 80x^9 + 364x^8 - 736x^7 + 992x^6 - 992x^5 + 768x^4 - 480x^3 + 224x^2 - 64x + 8	\( 2^{54}\cdot 3^{4} \)	$C_4 \times D_4$ (as 16T19)	Trivial
16.8.8503056000000000000.1	x^16 - 8x^15 + 22x^14 - 14x^13 - 46x^12 + 94x^11 - 56x^10 + 38x^9 - 92x^8 + 30x^7 + 100x^6 - 60x^5 - 23x^4 + 4x^3 + 4x^2 + 6x + 1	\( 2^{16}\cdot 3^{12}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	Trivial (GRH)
16.0.8503056000000000000.2	x^16 - 6x^15 + 22x^14 - 64x^13 + 133x^12 - 234x^11 + 358x^10 - 414x^9 + 439x^8 - 290x^7 + 190x^6 - 28x^5 + 17x^4 - 10x^3 + 10x^2 - 4x + 1	\( 2^{16}\cdot 3^{12}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	$[2]$
16.0.8503056000000000000.3	x^16 - 7x^14 - 4x^12 + 29x^10 + 169x^8 + 232x^6 + 104x^4 + 16x^2 + 16	\( 2^{16}\cdot 3^{12}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	$[2]$
16.0.8503056000000000000.4	x^16 - 3x^14 + 6x^12 - 9x^10 + 9x^8 - 27x^6 + 54x^4 - 81x^2 + 81	\( 2^{16}\cdot 3^{12}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	Trivial
16.0.16131393652587890625.1	x^16 - x^15 + 2x^14 - 4x^13 + 6x^12 + 5x^11 + 3x^10 - 8x^8 + 3x^6 + 5x^5 + 6x^4 - 4x^3 + 2x^2 - x + 1	\( 3^{4}\cdot 5^{12}\cdot 13^{8} \)	$C_4 \times D_4$ (as 16T19)	Trivial
16.8.26873856000000000000.4	x^16 - 2x^15 - 7x^14 + 16x^13 - 2x^12 - 6x^11 - 12x^10 + 68x^9 - 25x^8 - 116x^7 + 82x^6 - 24x^5 + 36x^4 + 64x^3 - 88x^2 + 16	\( 2^{24}\cdot 3^{8}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	Trivial (GRH)
16.0.26873856000000000000.11	x^16 - 4x^15 + 14x^14 - 30x^13 + 41x^12 - 62x^11 + 45x^10 - 128x^9 + 267x^8 - 454x^7 + 1110x^6 - 1124x^5 + 1666x^4 - 1540x^3 + 1071x^2 - 798x + 361	\( 2^{24}\cdot 3^{8}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	$[2]$
16.8.29548117155177824256.1	x^16 - 8x^14 + 36x^12 - 104x^10 + 192x^8 - 224x^6 + 152x^4 - 48x^2 + 4	\( 2^{52}\cdot 3^{8} \)	$C_4 \times D_4$ (as 16T19)	Trivial (GRH)
16.0.29548117155177824256.5	x^16 + 8x^14 + 36x^12 + 104x^10 + 192x^8 + 224x^6 + 152x^4 + 48x^2 + 4	\( 2^{52}\cdot 3^{8} \)	$C_4 \times D_4$ (as 16T19)	$[2]$
16.0.29548117155177824256.6	x^16 - 8x^15 + 20x^14 - 8x^13 - 12x^12 - 104x^11 + 316x^10 - 224x^9 - 126x^8 + 40x^7 + 512x^6 - 680x^5 + 232x^4 + 144x^3 - 120x^2 + 18	\( 2^{52}\cdot 3^{8} \)	$C_4 \times D_4$ (as 16T19)	$[2]$
16.8.109951162777600000000.3	x^16 - 4x^14 + 6x^12 - 36x^10 + 103x^8 - 108x^6 + 44x^4 - 8x^2 + 1	\( 2^{48}\cdot 5^{8} \)	$C_4 \times D_4$ (as 16T19)	Trivial (GRH)
16.0.109951162777600000000.8	x^16 + 4x^14 + 6x^12 + 36x^10 + 103x^8 + 108x^6 + 44x^4 + 8x^2 + 1	\( 2^{48}\cdot 5^{8} \)	$C_4 \times D_4$ (as 16T19)	Trivial (GRH)
16.0.116985856000000000000.1	x^16 - 6x^15 + 25x^14 - 70x^13 + 158x^12 - 284x^11 + 451x^10 - 500x^9 + 389x^8 - 168x^7 + 57x^6 - 8x^5 + 52x^4 - 22x^3 + 7x^2 - 2x + 1	\( 2^{24}\cdot 5^{12}\cdot 13^{4} \)	$C_4 \times D_4$ (as 16T19)	$[3]$
16.8.118192468620711297024.1	x^16 - 8x^15 + 28x^14 - 40x^13 - 32x^12 + 160x^11 - 108x^10 - 248x^9 + 532x^8 - 304x^7 - 268x^6 + 544x^5 - 304x^4 + 8x^3 + 52x^2 - 16x + 1	\( 2^{54}\cdot 3^{8} \)	$C_4 \times D_4$ (as 16T19)	Trivial (GRH)
16.0.118192468620711297024.12	x^16 - 8x^15 + 24x^14 - 16x^13 - 72x^12 + 224x^11 - 208x^10 - 288x^9 + 1364x^8 - 2064x^7 + 1328x^6 + 416x^5 - 816x^4 + 128x^3 + 288x^2 + 64x + 4	\( 2^{54}\cdot 3^{8} \)	$C_4 \times D_4$ (as 16T19)	$[2]$
16.0.118192468620711297024.14	x^16 - 8x^15 + 28x^14 - 40x^13 - 44x^12 + 320x^11 - 680x^10 + 624x^9 + 686x^8 - 3912x^7 + 8352x^6 - 11312x^5 + 10284x^4 - 6176x^3 + 2328x^2 - 496x + 46	\( 2^{54}\cdot 3^{8} \)	$C_4 \times D_4$ (as 16T19)	$[2]$
16.0.149587343098087735296.2	x^16 - 4x^14 + 26x^12 - 76x^10 + 118x^8 - 140x^6 + 122x^4 - 20x^2 + 1	\( 2^{48}\cdot 3^{12} \)	$C_4 \times D_4$ (as 16T19)	Trivial
16.0.149587343098087735296.6	x^16 + 4x^14 + 26x^12 + 76x^10 + 118x^8 + 140x^6 + 122x^4 + 20x^2 + 1	\( 2^{48}\cdot 3^{12} \)	$C_4 \times D_4$ (as 16T19)	Trivial
16.0.342102016000000000000.1	x^16 - 2x^15 + x^14 + x^12 - 16x^11 + 25x^10 - 6x^9 - 3x^8 - 12x^7 + 100x^6 - 128x^5 + 16x^4 + 64x^2 - 256x + 256	\( 2^{24}\cdot 5^{12}\cdot 17^{4} \)	$C_4 \times D_4$ (as 16T19)	Trivial
16.0.439804651110400000000.7	x^16 - 24x^14 + 240x^12 - 1272x^10 + 3684x^8 - 4960x^6 + 1000x^4 + 2000x^2 + 2500	\( 2^{50}\cdot 5^{8} \)	$C_4 \times D_4$ (as 16T19)	$[2]$
16.8.598349372392350941184.1	x^16 - 8x^14 + 44x^12 - 128x^10 + 166x^8 - 136x^6 + 68x^4 - 16x^2 + 1	\( 2^{50}\cdot 3^{12} \)	$C_4 \times D_4$ (as 16T19)	Trivial (GRH)
16.0.598349372392350941184.4	x^16 + 8x^14 + 44x^12 + 128x^10 + 166x^8 + 136x^6 + 68x^4 + 16x^2 + 1	\( 2^{50}\cdot 3^{12} \)	$C_4 \times D_4$ (as 16T19)	$[2]$
16.0.747961818418212890625.1	x^16 - x^15 + 4x^14 - 8x^13 + 20x^12 + 29x^11 + 35x^10 + 40x^9 + 16x^8 + 40x^7 + 35x^6 + 29x^5 + 20x^4 - 8x^3 + 4x^2 - x + 1	\( 3^{12}\cdot 5^{12}\cdot 7^{8} \)	$C_4 \times D_4$ (as 16T19)	$[2]$
16.8.747961818418212890625.1	x^16 - 3x^15 + x^14 - 3x^13 - 16x^12 + 63x^11 - 98x^10 + 141x^9 - 77x^8 - 42x^7 + 53x^6 - 84x^5 + 89x^4 - 39x^3 + 14x^2 - 6x + 1	\( 3^{12}\cdot 5^{12}\cdot 7^{8} \)	$C_4 \times D_4$ (as 16T19)	Trivial (GRH)
16.0.747961818418212890625.2	x^16 - 3x^15 + 13x^14 - 27x^13 + 38x^12 - 33x^11 - 56x^10 + 189x^9 - 122x^8 - 33x^7 + 401x^6 - 1140x^5 + 1283x^4 - 666x^3 + 212x^2 - 72x + 16	\( 3^{12}\cdot 5^{12}\cdot 7^{8} \)	$C_4 \times D_4$ (as 16T19)	$[2]$
16.8.1306642885859619140625.1	x^16 - 4x^15 + 4x^14 + 6x^13 - 37x^12 + 62x^11 - 46x^10 + 13x^9 + 136x^8 - 332x^7 + 209x^6 + 110x^5 - 160x^4 + 59x^3 - 82x^2 + 91x - 29	\( 3^{8}\cdot 5^{12}\cdot 13^{8} \)	$C_4 \times D_4$ (as 16T19)	Trivial (GRH)
16.0.1306642885859619140625.6	x^16 - x^15 - x^14 + x^13 + 32x^12 - 15x^11 - 200x^10 - 95x^9 + 768x^8 + 717x^7 - 2341x^6 - 534x^5 + 3049x^4 - 916x^3 - 528x^2 - 192x + 256	\( 3^{8}\cdot 5^{12}\cdot 13^{8} \)	$C_4 \times D_4$ (as 16T19)	$[2, 2]$ (GRH)
16.0.2176782336000000000000.1	x^16 - 2x^15 + 4x^14 - 10x^13 + 23x^12 + 10x^11 - 4x^10 - 28x^9 + 13x^8 - 28x^7 - 4x^6 + 10x^5 + 23x^4 - 10x^3 + 4x^2 - 2x + 1	\( 2^{24}\cdot 3^{12}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	$[2, 2]$
16.8.2176782336000000000000.1	x^16 - 2x^15 - 15x^14 + 18x^13 + 122x^12 - 180x^11 - 253x^10 + 460x^9 + 123x^8 - 316x^7 - 55x^6 + 24x^5 + 116x^4 - 66x^3 + 33x^2 - 10x + 1	\( 2^{24}\cdot 3^{12}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	Trivial (GRH)
16.0.2176782336000000000000.2	x^16 - 2x^15 + 7x^14 - 16x^13 + 47x^12 + 4x^11 + 83x^10 + 2x^9 + 355x^8 - 364x^7 + 194x^6 - 56x^5 - 52x^4 - 16x^3 + 40x^2 - 32x + 16	\( 2^{24}\cdot 3^{12}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	$[2]$
16.8.2176782336000000000000.2	x^16 - 4x^15 + 20x^13 - 33x^12 - 18x^11 + 90x^10 - 80x^9 - 36x^8 + 306x^7 - 162x^6 - 324x^5 + 278x^4 + 46x^3 - 138x^2 - 6x + 1	\( 2^{24}\cdot 3^{12}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	Trivial (GRH)
16.0.2176782336000000000000.8	x^16 - 6x^15 + 15x^14 + 2x^13 - 94x^12 + 234x^11 - 123x^10 - 282x^9 + 498x^8 - 178x^7 + 1437x^6 - 2994x^5 - 579x^4 - 2072x^3 + 5130x^2 + 2296x + 916	\( 2^{24}\cdot 3^{12}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	$[2]$ (GRH)
16.0.2176782336000000000000.10	x^16 - 2x^15 + 18x^14 - 32x^13 + 138x^12 - 198x^11 + 552x^10 - 562x^9 + 1119x^8 - 510x^7 + 840x^6 + 726x^5 - 178x^4 + 1220x^3 + 570x^2 - 282x + 1021	\( 2^{24}\cdot 3^{12}\cdot 5^{12} \)	$C_4 \times D_4$ (as 16T19)	$[2, 2]$
16.0.7676563456000000000000.1	x^16 - 6x^15 + 9x^14 + 12x^13 - 31x^12 - 84x^11 + 321x^10 - 126x^9 - 740x^8 + 774x^7 + 807x^6 - 1668x^5 + 65x^4 + 2436x^3 - 1617x^2 - 2058x + 2401	\( 2^{24}\cdot 5^{12}\cdot 37^{4} \)	$C_4 \times D_4$ (as 16T19)	Trivial (GRH)
16.0.11574317056000000000000.1	x^16 - 2x^15 + 7x^14 - 18x^13 + 52x^12 + 20x^11 + 73x^10 + 36x^9 + 135x^8 - 36x^7 + 73x^6 - 20x^5 + 52x^4 + 18x^3 + 7x^2 + 2x + 1	\( 2^{24}\cdot 5^{12}\cdot 41^{4} \)	$C_4 \times D_4$ (as 16T19)	$[2, 2]$
16.0.29948379136000000000000.1	x^16 + 10x^14 + 53x^12 + 90x^10 + 124x^8 + 70x^6 + 317x^4 - 90x^2 + 81	\( 2^{32}\cdot 5^{12}\cdot 13^{4} \)	$C_4 \times D_4$ (as 16T19)	$[6]$
16.16.29948379136000000000000.1	x^16 - 8x^15 + 8x^14 + 84x^13 - 222x^12 - 124x^11 + 908x^10 - 448x^9 - 1280x^8 + 1296x^7 + 442x^6 - 956x^5 + 231x^4 + 116x^3 - 48x^2 + 1	\( 2^{32}\cdot 5^{12}\cdot 13^{4} \)	$C_4 \times D_4$ (as 16T19)	Trivial (GRH)
16.0.73870292887944560640000.1	x^16 + 8x^14 + 52x^12 + 184x^10 + 480x^8 + 992x^6 + 2728x^4 + 2416x^2 + 2116	\( 2^{54}\cdot 3^{8}\cdot 5^{4} \)	$C_4 \times D_4$ (as 16T19)	$[6]$
16.16.73870292887944560640000.1	x^16 - 24x^14 + 212x^12 - 872x^10 + 1728x^8 - 1568x^6 + 552x^4 - 80x^2 + 4	\( 2^{54}\cdot 3^{8}\cdot 5^{4} \)	$C_4 \times D_4$ (as 16T19)	Trivial (GRH)