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
16.2.3522375537366834603.1	x^16 - 8x^15 + 25x^14 - 35x^13 + 13x^12 + 13x^11 + 5x^10 - 25x^9 - 5x^8 + 27x^7 - 3x^6 - 15x^5 + 3x^4 + 9x^3 + 2x^2 - 7x - 1	\( -\,3^{6}\cdot 7^{4}\cdot 13^{8}\cdot 2467 \)	16T1775	Trivial
16.2.3673508889600000000.1	x^16 - 3x^14 + 3x^12 + 3x^10 - 9x^8 + 10x^6 - 7x^4 + 2x^2 - 1	\( -\,2^{16}\cdot 3^{4}\cdot 5^{8}\cdot 11^{6} \)	16T1775	Trivial
16.4.3935445947722265625.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 70x^12 - 56x^11 + 23x^10 + 17x^9 - 52x^8 + 62x^7 - 48x^6 + 32x^5 - 18x^4 + 5x^3 + 1	\( 3^{6}\cdot 5^{8}\cdot 11^{6}\cdot 29\cdot 269 \)	16T1775	Trivial
16.2.8189935487335530496.1	x^16 - 4x^15 + 8x^14 - 8x^13 + 5x^12 + 8x^11 - 18x^10 + 24x^9 - 31x^8 + 24x^7 - 18x^6 + 8x^5 + 5x^4 - 8x^3 + 8x^2 - 4x + 1	\( -\,2^{32}\cdot 17^{6}\cdot 79 \)	16T1775	Trivial
16.6.8189935487335530496.1	x^16 - 4x^15 + 4x^14 + 6x^12 - 12x^11 - 36x^10 + 92x^9 - 50x^8 + 16x^7 - 74x^6 + 116x^5 - 89x^4 + 36x^3 - 2x^2 - 4x + 1	\( -\,2^{32}\cdot 17^{6}\cdot 79 \)	16T1775	Trivial
16.0.40408597785600000000.1	x^16 - x^14 - 3x^12 + 10x^10 - 4x^8 + 22x^4 - 11x^2 + 11	\( 2^{16}\cdot 3^{4}\cdot 5^{8}\cdot 11^{7} \)	16T1775	Trivial
16.4.40408597785600000000.1	x^16 - 7x^14 + 24x^12 - 52x^10 + 68x^8 - 44x^6 + 11x^4 - 11x^2 + 11	\( 2^{16}\cdot 3^{4}\cdot 5^{8}\cdot 11^{7} \)	16T1775	Trivial (GRH)
16.0.40408597785600000000.2	x^16 - x^14 - 4x^12 - 4x^10 + 8x^8 + 33x^6 + 44x^4 + 33x^2 + 11	\( 2^{16}\cdot 3^{4}\cdot 5^{8}\cdot 11^{7} \)	16T1775	Trivial
16.0.43571104679085755625.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 73x^12 - 74x^11 + 70x^10 - 53x^9 + 19x^8 + 6x^6 - 9x^5 + 9x^4 - 12x^3 + 12x^2 - 6x + 3	\( 3^{14}\cdot 5^{4}\cdot 7^{6}\cdot 229\cdot 541 \)	16T1775	Trivial
16.0.57913064368537337856.1	x^16 - 2x^15 + 4x^14 - 22x^13 + 48x^12 - 56x^11 + 128x^10 - 248x^9 + 184x^8 - 44x^7 + 52x^6 + 66x^5 - 155x^4 - 54x^3 + 84x^2 + 54x + 9	\( 2^{24}\cdot 3^{8}\cdot 13^{6}\cdot 109 \)	16T1775	Trivial (GRH)
16.10.72998530305426171875.1	x^16 - x^15 - 6x^14 + 7x^13 + 6x^12 - 19x^11 + 15x^10 + 16x^9 - 27x^8 + 16x^7 + 15x^6 - 19x^5 + 6x^4 + 7x^3 - 6x^2 - x + 1	\( -\,5^{8}\cdot 11\cdot 13^{4}\cdot 29^{6} \)	16T1775	Trivial (GRH)
16.6.72998530305426171875.1	x^16 - x^15 - 3x^14 + x^13 - 2x^11 + 4x^10 + 5x^9 + x^8 + 5x^7 + 4x^6 - 2x^5 + x^3 - 3x^2 - x + 1	\( -\,5^{8}\cdot 11\cdot 13^{4}\cdot 29^{6} \)	16T1775	Trivial (GRH)
16.0.155420872258478931968.1	x^16 - x^15 + x^14 + 6x^13 - 10x^11 + 10x^10 + 8x^9 - 10x^8 + 18x^7 - 36x^6 + 18x^5 + 57x^4 - 79x^3 + 33x^2 - 4x + 4	\( 2^{28}\cdot 17^{8}\cdot 83 \)	16T1775	Trivial
16.6.205723130860746484375.1	x^16 - 5x^15 + 2x^14 + 23x^13 - 30x^12 - 24x^11 + 57x^10 + 14x^9 - 75x^8 + 14x^7 + 57x^6 - 24x^5 - 30x^4 + 23x^3 + 2x^2 - 5x + 1	\( -\,5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 31 \)	16T1775	Trivial (GRH)
16.0.248140790631715831808.1	x^16 - 2x^15 + 3x^14 - 7x^12 + 12x^11 - 3x^10 - 16x^9 + 20x^8 + 4x^7 - 25x^6 + 8x^5 + 29x^4 - 42x^3 + 26x^2 - 8x + 1	\( 2^{28}\cdot 7\cdot 17^{6}\cdot 5471 \)	16T1775	Trivial
16.4.723349073026495703125.1	x^16 - 7x^15 + 23x^14 - 46x^13 + 63x^12 - 57x^11 + 4x^10 + 4x^9 + 437x^8 - 1538x^7 + 2450x^6 - 2184x^5 + 1180x^4 - 423x^3 + 112x^2 - 19x - 1	\( 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 109 \)	16T1775	Trivial (GRH)
16.8.723349073026495703125.1	x^16 - x^15 - 11x^14 - 10x^13 + 17x^12 + 44x^11 + 35x^10 - 6x^9 - 29x^8 - 6x^7 + 35x^6 + 44x^5 + 17x^4 - 10x^3 - 11x^2 - x + 1	\( 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 109 \)	16T1775	Trivial (GRH)
16.4.988798274137136328125.1	x^16 - x^15 - 6x^14 + 15x^13 - 18x^12 + 14x^11 - 10x^10 + 9x^9 - 9x^8 + 9x^7 - 10x^6 + 14x^5 - 18x^4 + 15x^3 - 6x^2 - x + 1	\( 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 149 \)	16T1775	Trivial
16.8.988798274137136328125.1	x^16 - 8x^15 + 39x^14 - 133x^13 + 337x^12 - 657x^11 + 967x^10 - 1029x^9 + 676x^8 - 39x^7 - 419x^6 + 413x^5 - 152x^4 - 25x^3 + 41x^2 - 12x + 1	\( 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 149 \)	16T1775	Trivial (GRH)
16.10.1187885174970116796875.1	x^16 - 7x^15 + 14x^14 + 10x^13 - 88x^12 + 186x^11 - 245x^10 + 134x^9 + 165x^8 - 154x^7 - 306x^6 + 311x^5 + 281x^4 - 506x^3 + 247x^2 - 43x + 1	\( -\,5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 179 \)	16T1775	Trivial (GRH)
16.2.1187885174970116796875.1	x^16 - 7x^15 + 22x^14 - 48x^13 + 91x^12 - 149x^11 + 205x^10 - 248x^9 + 221x^8 - 82x^7 - 30x^6 + 19x^5 - 4x^4 - 7x^3 + 12x^2 - 8x + 1	\( -\,5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 179 \)	16T1775	Trivial
16.6.1187885174970116796875.1	x^16 - x^15 - 4x^14 + 11x^13 - 5x^12 - 7x^11 - 20x^10 + 41x^9 + 58x^8 - 281x^7 + 428x^6 - 261x^5 - 21x^4 + 85x^3 - 18x^2 - 6x + 1	\( -\,5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 179 \)	16T1775	Trivial (GRH)
16.6.1187885174970116796875.2	x^16 - 3x^15 + x^14 + 8x^13 - 3x^12 - 30x^11 + 24x^10 - 31x^9 + 55x^8 + 76x^7 - 53x^6 + 22x^5 - 69x^4 - 61x^3 - 20x^2 - 37x - 11	\( -\,5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 179 \)	16T1775	Trivial (GRH)
16.4.1438214873617795121152.1	x^16 - 2x^14 - 9x^12 - 12x^11 - 4x^10 - 8x^9 + 3x^8 + 12x^7 + 54x^6 + 77x^4 + 12x^3 + 24x^2 + 20x - 7	\( 2^{32}\cdot 17^{6}\cdot 13873 \)	16T1775	Trivial
16.4.1438214873617795121152.2	x^16 - 8x^15 + 32x^14 - 84x^13 + 158x^12 - 220x^11 + 224x^10 - 152x^9 + 38x^8 + 56x^7 - 90x^6 + 72x^5 - 33x^4 + 4x^3 + 6x^2 - 4x + 1	\( 2^{32}\cdot 17^{6}\cdot 13873 \)	16T1775	Trivial (GRH)
16.0.6946827684441348898816.1	x^16 - 4x^15 + 12x^14 - 28x^13 + 47x^12 - 44x^11 - 14x^10 + 156x^9 - 313x^8 + 380x^7 - 226x^6 - 116x^5 + 487x^4 - 636x^3 + 538x^2 - 280x + 89	\( 2^{32}\cdot 17^{6}\cdot 113\cdot 593 \)	16T1775	$[2]$
16.8.6946827684441348898816.1	x^16 - 8x^15 + 16x^14 + 28x^13 - 122x^12 + 4x^11 + 344x^10 - 136x^9 - 554x^8 + 216x^7 + 582x^6 - 96x^5 - 377x^4 - 68x^3 + 102x^2 + 68x + 17	\( 2^{32}\cdot 17^{6}\cdot 113\cdot 593 \)	16T1775	Trivial (GRH)
16.10.8832822166956566796875.1	x^16 - 7x^15 + 12x^14 + 28x^13 - 133x^12 + 127x^11 + 248x^10 - 703x^9 + 365x^8 + 686x^7 - 1004x^6 + 311x^5 + 159x^4 - 208x^3 + 226x^2 - 108x + 1	\( -\,5^{8}\cdot 11^{3}\cdot 13^{4}\cdot 29^{6} \)	16T1775	Trivial (GRH)
16.0.15268631500129927430144.1	x^16 - 4x^15 + 16x^14 - 44x^13 + 119x^12 - 268x^11 + 548x^10 - 992x^9 + 1708x^8 - 2628x^7 + 3654x^6 - 4416x^5 + 5076x^4 - 5332x^3 + 4534x^2 - 2284x + 553	\( 2^{32}\cdot 17^{6}\cdot 31\cdot 4751 \)	16T1775	$[2]$
16.8.15268631500129927430144.1	x^16 - 8x^15 + 24x^14 - 28x^13 - 10x^12 + 60x^11 - 52x^10 - 4x^9 + 32x^8 - 16x^7 - 2x^6 + 4x^5 + 3x^4 - 8x^3 + 4x + 1	\( 2^{32}\cdot 17^{6}\cdot 31\cdot 4751 \)	16T1775	Trivial (GRH)
16.2.36561172319257600000000.1	x^16 - x^14 - 8x^12 - 3x^10 - 18x^8 - 3x^6 - 8x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} \)	16T1775	$[2]$ (GRH)
16.6.36561172319257600000000.1	x^16 + 9x^14 + 30x^12 + 11x^10 - 147x^8 - 311x^6 - 173x^4 + 42x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} \)	16T1775	Trivial (GRH)
16.4.46899612929336430624768.1	x^16 - 2x^14 - 6x^13 + 4x^12 + 6x^11 - 8x^10 - 48x^9 + 28x^8 + 6x^7 + 22x^6 - 24x^5 + 127x^4 + 66x^3 + 88x^2 - 11	\( 2^{16}\cdot 3^{14}\cdot 11^{6}\cdot 84457 \)	16T1775	Trivial (GRH)
16.4.46899612929336430624768.2	x^16 - 8x^15 + 26x^14 - 42x^13 + 26x^12 + 26x^11 - 68x^10 + 54x^9 - 8x^8 - 6x^7 - 8x^6 + 4x^5 + 5x^4 - 4x^2 + 2x + 1	\( 2^{16}\cdot 3^{14}\cdot 11^{6}\cdot 84457 \)	16T1775	Trivial (GRH)
16.10.434911971099673600000000.1	x^16 - x^14 - 29x^12 + 19x^10 + 177x^8 + 57x^6 - 94x^4 + 20x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} \)	16T1775	Trivial (GRH)
16.14.434911971099673600000000.1	x^16 - 7x^14 - x^12 + 117x^10 - 343x^8 + 384x^6 - 181x^4 + 30x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} \)	16T1775	Trivial (GRH)
16.2.434911971099673600000000.1	x^16 + 17x^14 + 104x^12 + 288x^10 + 332x^8 + 21x^6 - 181x^4 - 30x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} \)	16T1775	$[4]$ (GRH)
16.6.434911971099673600000000.1	x^16 + x^14 - 22x^12 - 25x^10 + 107x^8 + 123x^6 - 11x^4 - 24x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} \)	16T1775	Trivial (GRH)
16.10.434911971099673600000000.2	x^16 - 7x^14 - x^12 + 72x^10 - 63x^8 - 136x^6 + 189x^4 - 55x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} \)	16T1775	Trivial (GRH)
16.14.434911971099673600000000.2	x^16 - 15x^14 + 84x^12 - 218x^10 + 258x^8 - 101x^6 - 26x^4 + 19x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} \)	16T1775	Trivial (GRH)
16.6.434911971099673600000000.2	x^16 - 5x^14 - 24x^12 + 64x^10 + 218x^8 + 192x^6 + 61x^4 + 3x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} \)	16T1775	$[2]$ (GRH)
16.10.434911971099673600000000.3	x^16 - 10x^14 + 21x^12 + 61x^10 - 197x^8 - 72x^6 + 296x^4 + 32x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} \)	16T1775	Trivial (GRH)
16.8.1799619495159615883203125.1	x^16 - 8x^15 + 29x^14 - 63x^13 + 80x^12 - 25x^11 - 110x^10 + 231x^9 - 199x^8 - 7x^7 + 198x^6 - 207x^5 + 62x^4 + 57x^3 - 62x^2 + 23x + 1	\( 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 271181 \)	16T1775	Trivial (GRH)
16.12.1833066094499556601953125.1	x^16 - 8x^15 + 21x^14 - 7x^13 - 67x^12 + 129x^11 - 44x^10 - 176x^9 + 280x^8 - 75x^7 - 199x^6 + 221x^5 - 40x^4 - 84x^3 + 39x^2 + 9x - 1	\( 5^{8}\cdot 11\cdot 13^{4}\cdot 29^{6}\cdot 25111 \)	16T1775	Trivial (GRH)
16.12.4784031682096409600000000.1	x^16 - 15x^14 + 87x^12 - 240x^10 + 298x^8 - 75x^6 - 133x^4 + 65x^2 + 11	\( 2^{16}\cdot 5^{8}\cdot 11\cdot 13^{4}\cdot 29^{6} \)	16T1775	Trivial (GRH)
16.0.156133397624782822400000000.1	x^16 + 23x^14 + 217x^12 + 1085x^10 + 3107x^8 + 5149x^6 + 4736x^4 + 2152x^2 + 359	\( 2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 359 \)	16T1775	$[2, 92]$ (GRH)
16.16.755767196072963272539453125.1	x^16 - 8x^15 + 5x^14 + 105x^13 - 193x^12 - 571x^11 + 1390x^10 + 1740x^9 - 4792x^8 - 3559x^7 + 8955x^6 + 5505x^5 - 8638x^4 - 5868x^3 + 3007x^2 + 2921x + 529	\( 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 149\cdot 839\cdot 911 \)	16T1775	Trivial (GRH)
16.0.874607973881443609600000000.1	x^16 + 25x^14 + 262x^12 + 1495x^10 + 5048x^8 + 10260x^6 + 12192x^4 + 7735x^2 + 2011	\( 2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6}\cdot 2011 \)	16T1775	$[2, 308]$ (GRH)
16.2.2396072989114866073600000000.1	x^16 - 2x^14 - 51x^12 - 54x^10 - 657x^8 - 3190x^6 - 1817x^4 - 9888x^2 - 11881	\( -\,2^{32}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} \)	16T1775	$[2, 2]$ (GRH)
16.6.2396072989114866073600000000.1	x^16 - 2x^14 - 7x^12 + 52x^10 - 129x^8 - 910x^6 + 343x^4 + 7048x^2 - 121	\( -\,2^{32}\cdot 5^{8}\cdot 7^{4}\cdot 29^{6} \)	16T1775	$[2]$ (GRH)