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 143)

Label	Polynomial	Discriminant	Galois group	Class group
16.6.11281314379479862243.1	x^16 - 3x^15 - 4x^14 + 22x^13 - 19x^12 - 17x^11 + 30x^10 + 15x^9 - 49x^8 + 15x^7 + 30x^6 - 17x^5 - 19x^4 + 22x^3 - 4x^2 - 3x + 1	\( -\,17^{14}\cdot 67 \)	16T1351	Trivial
16.8.17006160482499493829.1	x^16 - x^15 - 6x^14 + 3x^13 + 7x^12 - x^11 + 5x^10 + 6x^9 + 6x^8 + 39x^7 + 20x^6 - 60x^5 - 58x^4 + 6x^3 + 24x^2 + 9x + 1	\( 17^{14}\cdot 101 \)	16T1351	Trivial
16.6.17342916135618295687.1	x^16 - 5x^15 + x^14 + 31x^13 - 37x^12 - 80x^11 + 199x^10 - 77x^9 - 170x^8 + 210x^7 - 57x^6 - 38x^5 + 29x^4 - 8x^3 + 2x^2 + x - 1	\( -\,17^{14}\cdot 103 \)	16T1351	Trivial
16.8.23067762238637927273.1	x^16 - 2x^15 - 5x^14 + 12x^13 + 15x^12 - 34x^11 - 20x^10 + 50x^9 - 15x^8 - 22x^7 + 44x^6 - 17x^5 - 26x^4 + 15x^3 + 7x^2 - 3x - 1	\( 17^{14}\cdot 137 \)	16T1351	Trivial
16.6.43104723599206637824.1	x^16 + 6x^14 + 3x^12 - 38x^10 - 76x^8 - 32x^6 + 22x^4 + 12x^2 - 1	\( -\,2^{8}\cdot 17^{14} \)	16T1351	Trivial
16.10.43104723599206637824.1	x^16 - 3x^14 - 12x^12 + 26x^10 + 42x^8 - 33x^6 - 14x^4 + 10x^2 - 1	\( -\,2^{8}\cdot 17^{14} \)	16T1351	Trivial (GRH)
16.10.191782344451157658131.1	x^16 - 3x^15 - 8x^14 + 24x^13 + 13x^12 - 39x^11 - 19x^10 - 11x^9 + 67x^8 + 20x^7 - 43x^6 - 7x^5 - 13x^4 + 22x^3 + 2x^2 - 6x + 1	\( -\,17^{15}\cdot 67 \)	16T1351	Trivial (GRH)
16.6.732780301186512843008.1	x^16 - 34x^12 - 68x^10 + 51x^8 + 204x^6 + 119x^4 - 17x^2 - 17	\( -\,2^{8}\cdot 17^{15} \)	16T1351	Trivial
16.10.732780301186512843008.1	x^16 - 34x^12 + 102x^10 - 51x^8 - 136x^6 + 153x^4 - 17x^2 - 17	\( -\,2^{8}\cdot 17^{15} \)	16T1351	Trivial (GRH)
16.12.2888016481146844734208.1	x^16 - 11x^14 + 37x^12 - 4x^10 - 229x^8 + 478x^6 - 318x^4 - 22x^2 + 67	\( 2^{8}\cdot 17^{14}\cdot 67 \)	16T1351	Trivial (GRH)
16.8.2888016481146844734208.1	x^16 - 5x^15 + 2x^14 + 33x^13 - 85x^12 + 67x^11 + 63x^10 - 172x^9 + 85x^8 + 164x^7 - 232x^6 + 24x^5 + 102x^4 - 73x^3 + 13x^2 + 13x - 1	\( 2^{8}\cdot 17^{14}\cdot 67 \)	16T1351	Trivial (GRH)
16.4.2888016481146844734208.1	x^16 - 3x^15 + 2x^14 + 2x^13 - 11x^12 + 9x^11 - 139x^10 + 155x^9 - 140x^8 + 63x^7 - 295x^6 + 57x^5 + 7x^4 + 14x^3 - x^2 + 9x - 1	\( 2^{8}\cdot 17^{14}\cdot 67 \)	16T1351	Trivial
16.8.2888016481146844734208.2	x^16 + 3x^14 - 29x^12 - 60x^10 + 195x^8 + 118x^6 - 388x^4 + 92x^2 + 67	\( 2^{8}\cdot 17^{14}\cdot 67 \)	16T1351	Trivial (GRH)
16.4.2888016481146844734208.2	x^16 - 4x^15 + 5x^14 + 17x^13 - 83x^12 + 176x^11 - 198x^10 + 117x^9 - 23x^8 + 43x^7 - 74x^6 + 61x^5 + 36x^4 - 85x^3 - 22x^2 - 35x + 1	\( 2^{8}\cdot 17^{14}\cdot 67 \)	16T1351	Trivial
16.12.2888016481146844734208.2	x^16 - 4x^15 - 8x^14 + 54x^13 - 28x^12 - 207x^11 + 314x^10 + 212x^9 - 695x^8 + 155x^7 + 536x^6 - 352x^5 - 79x^4 + 141x^3 - 43x^2 + x + 1	\( 2^{8}\cdot 17^{14}\cdot 67 \)	16T1351	Trivial (GRH)
16.4.2888016481146844734208.3	x^16 - 3x^15 - 2x^14 + 4x^13 + 17x^12 + 13x^11 - 63x^10 - 77x^9 + 68x^8 + 231x^7 + 113x^6 - 317x^5 - 527x^4 - 20x^3 + 565x^2 + 509x + 101	\( 2^{8}\cdot 17^{14}\cdot 67 \)	16T1351	Trivial
16.10.4608669490757362827659.1	x^16 - 8x^15 + 27x^14 - 49x^13 + 42x^12 + 21x^11 - 106x^10 + 123x^9 - 36x^8 - 77x^7 + 103x^6 - 36x^5 - 25x^4 + 30x^3 - 6x^2 - 4x + 1	\( -\,17^{14}\cdot 101\cdot 271 \)	16T1351	Trivial (GRH)
16.6.10516710669073622624411.1	x^16 - 8x^15 + 35x^14 - 105x^13 + 231x^12 - 385x^11 + 482x^10 - 430x^9 + 225x^8 + 19x^7 - 150x^6 + 128x^5 - 40x^4 - 15x^3 + 15x^2 - 3x - 1	\( -\,17^{14}\cdot 62459 \)	16T1351	Trivial (GRH)
16.2.11034809241396899282944.1	x^16 + 11x^14 + 37x^12 + 38x^10 - 25x^8 - 70x^6 - 46x^4 - 12x^2 - 1	\( -\,2^{16}\cdot 17^{14} \)	16T1351	$[2]$
16.14.11034809241396899282944.1	x^16 - 11x^14 + 37x^12 - 38x^10 - 25x^8 + 70x^6 - 46x^4 + 12x^2 - 1	\( -\,2^{16}\cdot 17^{14} \)	16T1351	Trivial (GRH)
16.10.11034809241396899282944.1	x^16 - 10x^14 + 31x^12 - 18x^10 - 59x^8 + 76x^6 - 5x^4 - 14x^2 - 1	\( -\,2^{16}\cdot 17^{14} \)	16T1351	Trivial (GRH)
16.6.11034809241396899282944.1	x^16 + 5x^14 - 5x^12 - 36x^10 - 9x^8 + 38x^6 + 14x^4 - 6x^2 - 1	\( -\,2^{16}\cdot 17^{14} \)	16T1351	Trivial (GRH)
16.10.11034809241396899282944.2	x^16 - 5x^14 - 5x^12 + 36x^10 - 9x^8 - 38x^6 + 14x^4 + 6x^2 - 1	\( -\,2^{16}\cdot 17^{14} \)	16T1351	Trivial (GRH)
16.6.11034809241396899282944.2	x^16 + 10x^14 + 31x^12 + 18x^10 - 59x^8 - 76x^6 - 5x^4 + 14x^2 - 1	\( -\,2^{16}\cdot 17^{14} \)	16T1351	Trivial (GRH)
16.10.11034809241396899282944.3	x^16 - 11x^14 + 37x^12 - 21x^10 - 76x^8 + 53x^6 + 39x^4 - 5x^2 - 1	\( -\,2^{16}\cdot 17^{14} \)	16T1351	Trivial (GRH)
16.10.11034809241396899282944.4	x^16 - 7x^14 + 14x^12 + x^10 - 25x^8 + 9x^6 + 12x^4 - 3x^2 - 1	\( -\,2^{16}\cdot 17^{14} \)	16T1351	Trivial (GRH)
16.12.24748341325527307945349.1	x^16 - 8x^15 + 19x^14 + 7x^13 - 91x^12 + 91x^11 + 104x^10 - 234x^9 + 53x^8 + 191x^7 - 168x^6 - 28x^5 + 96x^4 - 27x^3 - 15x^2 + 9x + 1	\( 17^{14}\cdot 103\cdot 1427 \)	16T1351	Trivial (GRH)
16.6.50641820249485101608827.1	x^16 - 7x^15 + 14x^14 + x^13 - 42x^12 + 77x^11 - 107x^10 + 167x^9 - 188x^8 + 102x^7 - 34x^6 + 34x^5 + 34x^4 - 102x^3 + 17x^2 - 17x - 17	\( -\,17^{14}\cdot 67^{3} \)	16T1351	Trivial (GRH)
16.14.50641820249485101608827.1	x^16 - 2x^15 - 14x^14 + 15x^13 + 104x^12 - 35x^11 - 420x^10 - 45x^9 + 899x^8 + 376x^7 - 925x^6 - 658x^5 + 280x^4 + 377x^3 + 109x^2 + 6x - 1	\( -\,17^{14}\cdot 67^{3} \)	16T1351	Trivial (GRH)
16.10.50641820249485101608827.1	x^16 - 3x^15 - 9x^14 + 33x^13 + 3x^12 - 89x^11 + 122x^10 - 64x^9 - 147x^8 + 350x^7 - 232x^6 - 139x^5 + 250x^4 - 282x^3 + 149x^2 + 178x - 137	\( -\,17^{14}\cdot 67^{3} \)	16T1351	Trivial (GRH)
16.6.50641820249485101608827.2	x^16 - 2x^15 + 3x^14 - 2x^13 + 19x^12 - 69x^11 - 97x^10 - 113x^9 + 100x^8 + 240x^7 + 299x^6 + 243x^5 + 93x^4 - 31x^3 - 78x^2 - 28x - 1	\( -\,17^{14}\cdot 67^{3} \)	16T1351	Trivial (GRH)
16.10.50641820249485101608827.2	x^16 - 6x^15 + 3x^14 + 21x^13 + 9x^12 - 2x^11 - 165x^10 - 46x^9 - 86x^8 + 1275x^7 - 918x^6 - 442x^5 + 289x^4 - 17x^3 + 68x^2 + 17x - 17	\( -\,17^{14}\cdot 67^{3} \)	16T1351	Trivial (GRH)
16.10.50641820249485101608827.3	x^16 - 4x^15 + 9x^13 - 12x^12 - 28x^11 + 11x^10 + 213x^9 - 181x^8 - 214x^7 + 541x^6 - 26x^5 - 547x^4 - 96x^3 + 68x^2 + 10x - 1	\( -\,17^{14}\cdot 67^{3} \)	16T1351	Trivial (GRH)
16.6.50641820249485101608827.3	x^16 - 6x^15 + 18x^14 - 45x^13 + 104x^12 - 153x^11 + 152x^10 - 205x^9 + 87x^8 + 183x^7 - 16x^6 - 17x^5 - 185x^4 + 194x^3 - 137x^2 - 95x + 103	\( -\,17^{14}\cdot 67^{3} \)	16T1351	Trivial (GRH)
16.4.173479843081977336549629.1	x^16 - 3x^15 + 2x^14 + 2x^13 - 28x^12 + 77x^11 - 139x^10 + 308x^9 - 344x^8 + 437x^7 - 550x^6 - 45x^5 - 826x^4 - 904x^3 - 579x^2 - 637x - 103	\( 17^{14}\cdot 101^{3} \)	16T1351	Trivial (GRH)
16.12.173479843081977336549629.1	x^16 - 2x^15 - 23x^14 + 69x^13 + 113x^12 - 596x^11 + 152x^10 + 2057x^9 - 2359x^8 - 2873x^7 + 6156x^6 + 609x^5 - 6484x^4 + 1677x^3 + 2870x^2 - 857x - 613	\( 17^{14}\cdot 101^{3} \)	16T1351	Trivial (GRH)
16.12.173479843081977336549629.2	x^16 - 5x^15 + 2x^14 + 50x^13 - 136x^12 - 18x^11 + 590x^10 - 665x^9 - 935x^8 + 1779x^7 + 414x^6 - 1693x^5 + 306x^4 + 522x^3 - 242x^2 + 30x - 1	\( 17^{14}\cdot 101^{3} \)	16T1351	Trivial (GRH)
16.4.173479843081977336549629.2	x^16 - 2x^15 - 6x^14 + 35x^13 - 74x^12 + 50x^11 + 220x^10 - 867x^9 + 1891x^8 - 3213x^7 + 4099x^6 - 4338x^5 + 3818x^4 - 2794x^3 + 1425x^2 - 483x + 101	\( 17^{14}\cdot 101^{3} \)	16T1351	Trivial (GRH)
16.2.187591757103747287810048.1	x^16 + 17x^14 + 102x^12 + 272x^10 + 323x^8 + 102x^6 - 102x^4 - 85x^2 - 17	\( -\,2^{16}\cdot 17^{15} \)	16T1351	$[4]$ (GRH)
16.10.187591757103747287810048.1	x^16 - 34x^12 + 51x^10 + 102x^8 - 136x^6 - 68x^4 + 85x^2 - 17	\( -\,2^{16}\cdot 17^{15} \)	16T1351	Trivial (GRH)
16.8.325257603193665241481216.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 62x^12 - 8x^11 - 92x^10 + 152x^9 - 99x^8 - 32x^7 + 112x^6 - 80x^5 + 4x^4 + 32x^3 - 16x^2 + 2	\( 2^{62}\cdot 70529 \)	16T1351	Trivial (GRH)
16.4.739332219173592251957248.1	x^16 + 10x^14 + 14x^12 - 118x^10 - 399x^8 - 314x^6 + 131x^4 + 235x^2 + 67	\( 2^{16}\cdot 17^{14}\cdot 67 \)	16T1351	Trivial (GRH)
16.16.739332219173592251957248.1	x^16 - 20x^14 + 158x^12 - 654x^10 + 1555x^8 - 2158x^6 + 1669x^4 - 619x^2 + 67	\( 2^{16}\cdot 17^{14}\cdot 67 \)	16T1351	Trivial (GRH)
16.12.739332219173592251957248.1	x^16 - 3x^14 - 46x^12 + 162x^10 + 195x^8 - 1036x^6 + 1142x^4 - 483x^2 + 67	\( 2^{16}\cdot 17^{14}\cdot 67 \)	16T1351	Trivial (GRH)
16.0.739332219173592251957248.1	x^16 + 20x^14 + 158x^12 + 654x^10 + 1555x^8 + 2158x^6 + 1669x^4 + 619x^2 + 67	\( 2^{16}\cdot 17^{14}\cdot 67 \)	16T1351	$[2, 18]$ (GRH)
16.8.739332219173592251957248.1	x^16 + 5x^14 - 39x^12 - 70x^10 + 399x^8 + 72x^6 - 836x^4 + 232x^2 + 67	\( 2^{16}\cdot 17^{14}\cdot 67 \)	16T1351	Trivial (GRH)
16.8.739332219173592251957248.2	x^16 + 7x^14 - 20x^12 - 154x^10 + 9x^8 + 450x^6 + 46x^4 - 303x^2 + 67	\( 2^{16}\cdot 17^{14}\cdot 67 \)	16T1351	Trivial (GRH)
16.8.739332219173592251957248.3	x^16 - 6x^14 - 14x^12 + 106x^10 + 43x^8 - 478x^6 - 97x^4 + 515x^2 + 67	\( 2^{16}\cdot 17^{14}\cdot 67 \)	16T1351	Trivial (GRH)
16.8.739332219173592251957248.4	x^16 - 7x^14 - 20x^12 + 103x^10 + 281x^8 + 43x^6 - 260x^4 - 71x^2 + 67	\( 2^{16}\cdot 17^{14}\cdot 67 \)	16T1351	Trivial (GRH)
16.8.739332219173592251957248.5	x^16 - 7x^14 - 20x^12 + 154x^10 + 9x^8 - 450x^6 + 46x^4 + 303x^2 + 67	\( 2^{16}\cdot 17^{14}\cdot 67 \)	16T1351	Trivial (GRH)