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 59)

Label	Polynomial	Discriminant	Galois group	Class group
16.2.36973431874322432.1	x^16 - 2x^15 + 3x^14 + 6x^13 - 9x^12 + 14x^11 + 6x^10 - 6x^9 + 21x^8 - 6x^7 + 6x^6 + 14x^5 - 9x^4 + 6x^3 + 3x^2 - 2x + 1	\( -\,2^{16}\cdot 47\cdot 331^{4} \)	16T1848	Trivial
16.0.46887413072789504.1	x^16 - x^15 + 2x^14 + 2x^13 - 2x^12 - x^11 + 12x^10 - 20x^9 + 15x^8 - 4x^7 - 4x^5 + 15x^4 - x^3 + 8x^2 + 1	\( 2^{18}\cdot 41\cdot 257^{4} \)	16T1848	Trivial
16.2.63474986914349056.1	x^16 - 6x^15 + 15x^14 - 18x^13 + 5x^12 + 8x^11 + 4x^10 - 22x^9 + 25x^8 - 22x^7 + 4x^6 + 8x^5 + 5x^4 - 18x^3 + 15x^2 - 6x + 1	\( -\,2^{16}\cdot 151\cdot 283^{4} \)	16T1848	Trivial
16.0.118409686025306112.1	x^16 - 2x^15 - 2x^14 + 8x^13 - 10x^12 - 4x^11 + 36x^10 - 16x^9 - 19x^8 - 14x^7 - 3x^6 + 28x^5 + 29x^4 - 6x^2 + 1	\( 2^{16}\cdot 3^{2}\cdot 73\cdot 229^{4} \)	16T1848	Trivial
16.0.202173872163848192.1	x^16 - 2x^15 + x^14 - 6x^13 + 20x^12 - 18x^11 + 10x^10 - 42x^9 + 66x^8 - 16x^7 - 28x^6 + 4x^5 + 19x^4 - 4x^3 - 5x^2 + 1	\( 2^{16}\cdot 257\cdot 331^{4} \)	16T1848	Trivial
16.4.1829424788418854912.1	x^16 - 2x^15 + 2x^14 + 4x^13 - 11x^12 + 4x^11 + 2x^10 - 16x^9 - 8x^8 - 12x^7 + 30x^6 - 30x^5 + 10x^4 + 50x^3 - 50x^2 + 42x - 17	\( 2^{24}\cdot 17\cdot 283^{4} \)	16T1848	Trivial
16.4.1829424788418854912.2	x^16 - 2x^14 - 12x^13 - 12x^12 + 4x^11 + 42x^10 + 72x^9 + 86x^8 + 72x^7 + 42x^6 + 4x^5 - 12x^4 - 12x^3 - 2x^2 + 1	\( 2^{24}\cdot 17\cdot 283^{4} \)	16T1848	Trivial
16.0.3566927848713224192.1	x^16 + 9x^14 + 35x^12 + 76x^10 + 100x^8 + 80x^6 + 36x^4 + 8x^2 + 2	\( 2^{25}\cdot 571^{4} \)	16T1848	Trivial
16.2.6146647162089373696.1	x^16 + 4x^14 + 12x^12 + 22x^10 + 23x^8 + 14x^6 - 2x^4 - 6x^2 - 1	\( -\,2^{28}\cdot 389^{4} \)	16T1848	Trivial
16.6.6146647162089373696.1	x^16 - 4x^14 + 14x^10 - 41x^8 + 54x^6 - 34x^4 + 10x^2 - 1	\( -\,2^{28}\cdot 389^{4} \)	16T1848	Trivial (GRH)
16.2.6146647162089373696.2	x^16 + 4x^14 - 14x^10 - 41x^8 - 54x^6 - 34x^4 - 10x^2 - 1	\( -\,2^{28}\cdot 389^{4} \)	16T1848	Trivial
16.6.6146647162089373696.2	x^16 - 4x^14 + 12x^12 - 22x^10 + 23x^8 - 14x^6 - 2x^4 + 6x^2 - 1	\( -\,2^{28}\cdot 389^{4} \)	16T1848	Trivial (GRH)
16.6.6349180148041908224.1	x^16 - 8x^15 + 30x^14 - 66x^13 + 81x^12 - 34x^11 - 46x^10 + 80x^9 - 46x^8 + 24x^7 - 8x^6 - 42x^5 + 20x^4 + 4x^3 - 8x^2 + 1	\( -\,2^{24}\cdot 59\cdot 283^{4} \)	16T1848	Trivial (GRH)
16.6.6349180148041908224.2	x^16 - 6x^15 + 10x^14 + 12x^13 - 57x^12 + 56x^11 - 46x^10 + 134x^9 - 161x^8 + 70x^7 - 54x^6 + 76x^5 - 31x^4 - 18x^3 + 22x^2 - 10x + 1	\( -\,2^{24}\cdot 59\cdot 283^{4} \)	16T1848	Trivial (GRH)
16.4.19778398390148941568.1	x^16 - 2x^15 - 2x^14 + 12x^13 - 21x^12 - 6x^11 + 68x^10 - 78x^9 - 15x^8 + 138x^7 - 160x^6 + 56x^5 + 43x^4 - 58x^3 + 30x^2 - 8x + 1	\( 2^{8}\cdot 23^{5}\cdot 331^{4} \)	16T1848	Trivial (GRH)
16.4.19778398390148941568.2	x^16 - 2x^15 + 5x^14 - 13x^13 + 18x^12 - 30x^11 + 22x^10 - 38x^9 + 61x^8 - 2x^7 + 30x^6 - 20x^5 + 18x^3 - 7x^2 + 5x - 1	\( 2^{8}\cdot 23^{5}\cdot 331^{4} \)	16T1848	Trivial (GRH)
16.0.24643428032230457344.1	x^16 - 2x^15 + 8x^14 - 14x^13 + 32x^12 - 58x^11 + 122x^10 - 226x^9 + 358x^8 - 464x^7 + 470x^6 - 300x^5 + 81x^4 + 62x^3 - 12x^2 + 1	\( 2^{24}\cdot 229\cdot 283^{4} \)	16T1848	Trivial
16.8.24643428032230457344.1	x^16 - 2x^15 - 6x^14 + 4x^13 + 23x^12 + 26x^11 - 76x^10 - 86x^9 + 189x^8 + 6x^7 - 204x^6 + 176x^5 - 17x^4 - 70x^3 + 48x^2 - 12x + 1	\( 2^{24}\cdot 229\cdot 283^{4} \)	16T1848	Trivial (GRH)
16.8.25073880923623129088.1	x^16 - 6x^15 + 10x^14 + 20x^13 - 112x^12 + 158x^11 + 76x^10 - 550x^9 + 708x^8 - 170x^7 - 600x^6 + 902x^5 - 681x^4 + 330x^3 - 100x^2 + 16x - 1	\( 2^{24}\cdot 233\cdot 283^{4} \)	16T1848	Trivial (GRH)
16.0.30006693306684145664.1	x^16 - 4x^15 + 6x^14 - 12x^13 + 17x^12 - 20x^11 + 34x^10 - 6x^9 + 62x^8 + 10x^7 + 130x^6 + 64x^5 + 170x^4 + 96x^3 + 212x^2 + 74x + 127	\( 2^{24}\cdot 149\cdot 331^{4} \)	16T1848	Trivial
16.4.32135775866380681216.1	x^16 - 8x^15 + 32x^14 - 84x^13 + 160x^12 - 232x^11 + 262x^10 - 232x^9 + 155x^8 - 64x^7 - 8x^6 + 42x^5 - 37x^4 + 16x^3 - x^2 - 2x + 1	\( 2^{16}\cdot 53\cdot 359^{4}\cdot 557 \)	16T1848	Trivial
16.8.32853715993814123141.1	x^16 - 8x^15 + 19x^14 + 7x^13 - 85x^12 + 55x^11 + 153x^10 - 149x^9 - 168x^8 + 169x^7 + 132x^6 - 98x^5 - 70x^4 + 28x^3 + 18x^2 - 4x - 1	\( 7537^{4}\cdot 10181 \)	16T1848	Trivial (GRH)
16.4.81774723717298978816.1	x^16 - 8x^15 + 24x^14 - 28x^13 - 8x^12 + 48x^11 - 26x^10 - 24x^9 + 19x^8 + 24x^7 - 28x^6 - 10x^5 + 23x^4 - 4x^3 - 5x^2 + 2x + 1	\( 2^{16}\cdot 43\cdot 359^{4}\cdot 1747 \)	16T1848	Trivial
16.4.143115135058911494144.1	x^16 - 8x^15 + 26x^14 - 42x^13 + 28x^12 + 14x^11 - 40x^10 + 24x^9 + 4x^8 - 6x^7 - 6x^6 + 4x^5 + 3x^4 - 2x^3 - 2x^2 + 2x + 1	\( 2^{16}\cdot 389^{4}\cdot 95369 \)	16T1848	Trivial (GRH)
16.8.163571945145240190976.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 98x^12 + 42x^11 + 212x^10 - 158x^9 - 272x^8 + 210x^7 + 232x^6 - 136x^5 - 123x^4 + 40x^3 + 30x^2 - 4x - 1	\( 2^{16}\cdot 389^{4}\cdot 109001 \)	16T1848	Trivial (GRH)
16.4.246762676390430427509.1	x^16 - 8x^15 + 27x^14 - 49x^13 + 48x^12 - 15x^11 - 21x^10 + 28x^9 - 12x^8 + x^7 - x^6 + x^4 + x^3 - 2x^2 + x + 1	\( 47\cdot 1627\cdot 7537^{4} \)	16T1848	Trivial (GRH)
16.4.466783216447679942912.1	x^16 - x^15 - 4x^14 + 3x^13 + 2x^12 - 6x^10 + 2x^9 + 5x^8 + 2x^7 - 6x^6 + 2x^4 + 3x^3 - 4x^2 - x + 1	\( 2^{8}\cdot 17\cdot 18097^{4} \)	16T1848	Trivial (GRH)
16.8.466783216447679942912.1	x^16 - 8x^15 + 24x^14 - 16x^13 - 113x^12 + 440x^11 - 840x^10 + 980x^9 - 648x^8 + 56x^7 + 354x^6 - 376x^5 + 184x^4 - 28x^3 - 16x^2 + 8x - 1	\( 2^{8}\cdot 17\cdot 18097^{4} \)	16T1848	Trivial
16.6.921365448100612734976.1	x^16 - 6x^15 + 8x^14 + 20x^13 - 65x^12 + 22x^11 + 100x^10 - 64x^9 - 101x^8 + 28x^7 + 191x^6 - 188x^5 + 34x^4 + 38x^3 - 26x^2 + 8x - 1	\( -\,2^{16}\cdot 10889^{4} \)	16T1848	Trivial
16.6.921365448100612734976.2	x^16 + 2x^14 - 18x^13 + 4x^12 - 66x^11 + 44x^10 - 2x^9 + 139x^8 - 68x^7 - 109x^6 + 36x^5 + 49x^4 - 10x^3 - 17x^2 + 8x - 1	\( -\,2^{16}\cdot 10889^{4} \)	16T1848	Trivial
16.4.1015939941680244581632.1	x^16 - 8x^15 + 37x^14 - 119x^13 + 283x^12 - 515x^11 + 713x^10 - 727x^9 + 483x^8 - 89x^7 - 216x^6 + 286x^5 - 169x^4 + 36x^3 + 20x^2 - 16x + 4	\( 2^{8}\cdot 37\cdot 18097^{4} \)	16T1848	Trivial
16.8.1015939941680244581632.1	x^16 - x^15 - 10x^14 + 7x^13 + 24x^12 + 6x^11 - 53x^10 + 8x^9 + 56x^8 - 78x^7 + 52x^6 - 23x^5 + 22x^4 - 7x^3 - 13x^2 + 9x - 1	\( 2^{8}\cdot 37\cdot 18097^{4} \)	16T1848	Trivial
16.0.2681463488418637938688.1	x^16 - 7x^15 + 25x^14 - 70x^13 + 176x^12 - 394x^11 + 782x^10 - 1392x^9 + 2224x^8 - 3084x^7 + 3556x^6 - 3288x^5 + 2368x^4 - 1288x^3 + 504x^2 - 128x + 16	\( 2^{20}\cdot 43\cdot 2777^{4} \)	16T1848	Trivial
16.0.2681463488418637938688.2	x^16 - x^15 + 10x^14 + 15x^13 + 32x^12 + 57x^11 + 86x^10 + 97x^9 + 94x^8 + 97x^7 + 86x^6 + 57x^5 + 32x^4 + 15x^3 + 10x^2 - x + 1	\( 2^{20}\cdot 43\cdot 2777^{4} \)	16T1848	Trivial
16.10.3487145205226785455872.1	x^16 - x^15 - 10x^14 + 13x^13 + 28x^12 - 16x^11 - 159x^10 + 116x^9 + 452x^8 - 725x^7 + 188x^6 + 262x^5 - 149x^4 - 20x^3 + 22x^2 - 1	\( -\,2^{8}\cdot 127\cdot 18097^{4} \)	16T1848	Trivial (GRH)
16.12.4310880293075632413952.1	x^16 - 6x^15 + 7x^14 + 17x^13 - 38x^12 + 24x^11 - 8x^10 - 122x^9 + 241x^8 + 124x^7 - 412x^6 - 12x^5 + 262x^4 - 32x^3 - 53x^2 + 7x + 1	\( 2^{8}\cdot 157\cdot 18097^{4} \)	16T1848	Trivial (GRH)
16.10.5244446725970992299776.1	x^16 - 7x^15 + 12x^14 + 17x^13 - 78x^12 + 96x^11 - 40x^10 - 58x^9 + 115x^8 - 58x^7 - 40x^6 + 96x^5 - 78x^4 + 17x^3 + 12x^2 - 7x + 1	\( -\,2^{8}\cdot 191\cdot 18097^{4} \)	16T1848	Trivial (GRH)
16.10.5244446725970992299776.2	x^16 - 8x^15 + 34x^14 - 98x^13 + 171x^12 - 116x^11 - 138x^10 + 371x^9 - 286x^8 - 70x^7 + 275x^6 - 130x^5 - 52x^4 + 61x^3 - 4x^2 - 11x - 1	\( -\,2^{8}\cdot 191\cdot 18097^{4} \)	16T1848	Trivial (GRH)
16.12.5409193743540761691392.1	x^16 - x^15 - 17x^14 + 21x^13 + 83x^12 - 140x^11 - 100x^10 + 351x^9 - 213x^8 - 240x^7 + 506x^6 - 177x^5 - 228x^4 + 196x^3 - 42x^2 - 2x + 1	\( 2^{8}\cdot 197\cdot 18097^{4} \)	16T1848	Trivial (GRH)
16.8.5409193743540761691392.1	x^16 - 7x^15 + 24x^14 - 50x^13 + 63x^12 - 42x^11 + 10x^10 + 5x^9 - 74x^8 + 78x^7 + 14x^6 + 203x^5 - 333x^4 - 49x^3 + 260x^2 - 111x + 9	\( 2^{8}\cdot 197\cdot 18097^{4} \)	16T1848	Trivial
16.8.5409193743540761691392.2	x^16 - 7x^15 + 10x^14 + 36x^13 - 118x^12 + 9x^11 + 339x^10 - 298x^9 - 343x^8 + 498x^7 + 90x^6 - 208x^5 - 60x^4 - 64x^3 + 120x^2 + 48x - 16	\( 2^{8}\cdot 197\cdot 18097^{4} \)	16T1848	Trivial
16.10.27205187892436187283456.1	x^16 - 6x^14 - 2x^12 + 54x^10 - 71x^8 - 34x^6 + 100x^4 - 40x^2 - 1	\( -\,2^{16}\cdot 3^{4}\cdot 8461^{4} \)	16T1848	Trivial (GRH)
16.14.27205187892436187283456.1	x^16 - 10x^14 + 26x^12 + 26x^10 - 211x^8 + 330x^6 - 208x^4 + 48x^2 - 1	\( -\,2^{16}\cdot 3^{4}\cdot 8461^{4} \)	16T1848	Trivial (GRH)
16.6.27205187892436187283456.1	x^16 + 7x^14 + x^12 - 44x^10 - 8x^8 + 48x^6 + 3x^4 - 11x^2 - 1	\( -\,2^{16}\cdot 3^{4}\cdot 8461^{4} \)	16T1848	Trivial (GRH)
16.6.58967388678439215038464.1	x^16 + x^14 - 26x^12 - 33x^10 + 155x^8 + 268x^6 + 107x^4 + 7x^2 - 1	\( -\,2^{22}\cdot 10889^{4} \)	16T1848	Trivial (GRH)
16.14.112467297327629238009856.1	x^16 - 5x^14 - 14x^12 + 128x^10 - 277x^8 + 256x^6 - 108x^4 + 19x^2 - 1	\( -\,2^{20}\cdot 18097^{4} \)	16T1848	Trivial (GRH)
16.2.112467297327629238009856.1	x^16 + 5x^14 - 14x^12 - 128x^10 - 277x^8 - 256x^6 - 108x^4 - 19x^2 - 1	\( -\,2^{20}\cdot 18097^{4} \)	16T1848	$[2]$
16.2.235869554713756860153856.1	x^16 + 15x^14 + 85x^12 + 234x^10 + 325x^8 + 203x^6 + 28x^4 - 13x^2 - 1	\( -\,2^{24}\cdot 10889^{4} \)	16T1848	$[6]$ (GRH)
16.16.27281804073354933341058304.1	x^16 - 8x^15 + 11x^14 + 63x^13 - 172x^12 - 151x^11 + 759x^10 + 44x^9 - 1629x^8 + 301x^7 + 1901x^6 - 388x^5 - 1172x^4 + 137x^3 + 310x^2 - 7x - 17	\( 2^{8}\cdot 18097^{4}\cdot 993589 \)	16T1848	Trivial (GRH)
16.16.29738494307011366943002624.1	x^16 - 8x^15 + 12x^14 + 56x^13 - 163x^12 - 114x^11 + 673x^10 - 32x^9 - 1362x^8 + 382x^7 + 1483x^6 - 444x^5 - 841x^4 + 170x^3 + 207x^2 - 20x - 16	\( 2^{12}\cdot 19\cdot 53^{4}\cdot 293^{4}\cdot 6571 \)	16T1848	Trivial (GRH)