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
16.0.210445185730704437.1	x^16 - 3x^15 + 9x^14 - 21x^13 + 39x^12 - 70x^11 + 105x^10 - 142x^9 + 174x^8 - 182x^7 + 183x^6 - 154x^5 + 116x^4 - 65x^3 + 28x^2 - 8x + 1	\( 197\cdot 5717^{4} \)	16T1916	Trivial
16.0.282017913872619144.1	x^16 + 6x^14 - 8x^13 + 11x^12 - 27x^11 + 27x^10 - 30x^9 + 44x^8 - 30x^7 + 27x^6 - 27x^5 + 11x^4 - 8x^3 + 6x^2 + 1	\( 2^{3}\cdot 3\cdot 11\cdot 5717^{4} \)	16T1916	Trivial
16.2.1722506446773758420.1	x^16 - 3x^15 + 5x^14 - 2x^13 - 6x^12 + 23x^11 - 34x^10 + 51x^9 - 50x^8 + 51x^7 - 34x^6 + 23x^5 - 6x^4 - 2x^3 + 5x^2 - 3x + 1	\( -\,2^{2}\cdot 5\cdot 37^{4}\cdot 463^{4} \)	16T1916	Trivial
16.2.2669884992499325551.1	x^16 - 5x^15 + 11x^14 - 17x^13 + 22x^12 - 19x^11 + 11x^10 - 8x^9 + 11x^8 - 28x^7 + 49x^6 - 57x^5 + 61x^4 - 56x^3 + 37x^2 - 13x - 2	\( -\,31\cdot 37^{4}\cdot 463^{4} \)	16T1916	Trivial
16.4.6201023208385530312.1	x^16 - 2x^15 + 3x^14 - 15x^13 + 7x^12 - 31x^11 + 33x^10 - 23x^9 + 58x^8 - 23x^7 + 33x^6 - 31x^5 + 7x^4 - 15x^3 + 3x^2 - 2x + 1	\( 2^{3}\cdot 3^{2}\cdot 37^{4}\cdot 463^{4} \)	16T1916	Trivial
16.4.7923529655159288732.1	x^16 - 4x^15 + 8x^14 - 5x^13 - 15x^12 + 39x^11 - 55x^10 + 52x^9 - 65x^8 + 44x^7 - 35x^6 - 4x^5 - 9x^4 - 17x^3 - 3x^2 - 5x - 1	\( 2^{2}\cdot 23\cdot 37^{4}\cdot 463^{4} \)	16T1916	Trivial
16.4.8698657556207480021.1	x^16 - 3x^15 + 2x^14 + x^12 - 6x^11 + 12x^10 - 16x^9 + 19x^8 - 16x^7 + 12x^6 - 6x^5 + x^4 + 2x^2 - 3x + 1	\( 37^{4}\cdot 101\cdot 463^{4} \)	16T1916	Trivial
16.4.9732161424271735073.1	x^16 + x^14 - 7x^13 - 6x^12 - 13x^11 - 15x^10 + 18x^9 - 22x^8 + 41x^7 + 5x^6 - 27x^5 + 19x^4 - 22x^3 + 12x^2 - 1	\( 37^{4}\cdot 113\cdot 463^{4} \)	16T1916	Trivial
16.6.11282417226368117651.1	x^16 - 2x^15 - 4x^14 + 10x^13 + 5x^12 - 13x^11 - 20x^10 + 24x^9 + 16x^8 - 17x^7 - 7x^6 + 15x^5 + 3x^4 - 14x^3 + 3x^2 + 2x - 1	\( -\,37^{4}\cdot 131\cdot 463^{4} \)	16T1916	Trivial
16.6.39876024242812507423.1	x^16 - 3x^15 + 3x^14 - 3x^13 + x^12 - 4x^11 - 9x^10 + 2x^9 - 14x^8 + 3x^7 + 12x^6 + 14x^5 + 7x^4 - 11x^3 - 6x^2 + 2x + 1	\( -\,37^{4}\cdot 463^{5} \)	16T1916	Trivial
16.0.124270723143146012672.1	x^16 + 11x^14 + 51x^12 + 135x^10 + 229x^8 + 253x^6 + 173x^4 + 61x^2 + 2	\( 2^{17}\cdot 31^{4}\cdot 179^{4} \)	16T1916	Trivial
16.0.4915688588987071074304.1	x^16 - 5x^15 + 9x^14 - 20x^13 + 61x^12 - 69x^11 + 4x^10 - 63x^9 + 202x^8 - 173x^7 + 186x^6 - 243x^5 + 137x^4 - 82x^3 + 65x^2 - x + 3	\( 2^{12}\cdot 4129^{5} \)	16T1916	Trivial
16.8.7953326281161344811008.1	x^16 - 11x^14 + 51x^12 - 135x^10 + 229x^8 - 253x^6 + 173x^4 - 61x^2 + 2	\( 2^{23}\cdot 31^{4}\cdot 179^{4} \)	16T1916	Trivial
16.0.14228997799890218450944.1	x^16 - 3x^15 + 7x^14 - 17x^13 + 21x^12 + 23x^11 - 91x^10 - 7x^9 + 253x^8 - 141x^7 - 263x^6 + 185x^5 + 179x^4 - 167x^3 + 27x^2 + 7x + 2	\( 2^{16}\cdot 31^{4}\cdot 179^{4}\cdot 229 \)	16T1916	Trivial
16.0.19662754355948284297216.1	x^16 - 2x^15 + x^14 - 4x^13 + 19x^12 - 16x^11 + 24x^10 - 92x^9 + 76x^8 - 36x^7 + 248x^6 - 204x^5 + 32x^4 - 260x^3 + 172x^2 + 56x + 292	\( 2^{14}\cdot 4129^{5} \)	16T1916	$[2]$
16.8.52209859404291327213568.1	x^16 - 7x^14 + 7x^12 + 33x^10 - 245x^8 - 181x^6 + 693x^4 - 370x^2 + 37	\( 2^{14}\cdot 37^{5}\cdot 463^{4} \)	16T1916	Trivial
16.6.99307418225498904330240.1	x^16 - 8x^15 + 34x^14 - 98x^13 + 194x^12 - 254x^11 + 156x^10 + 166x^9 - 536x^8 + 642x^7 - 340x^6 - 120x^5 + 351x^4 - 280x^3 + 106x^2 - 14x - 1	\( -\,2^{24}\cdot 3\cdot 5\cdot 4457^{4} \)	16T1916	Trivial
16.6.99307418225498904330240.2	x^16 - 2x^15 - 12x^14 + 28x^13 + 37x^12 - 86x^11 - 116x^10 + 166x^9 + 246x^8 - 160x^7 - 384x^6 + 98x^5 + 346x^4 - 104x^3 - 44x^2 - 18x + 3	\( -\,2^{24}\cdot 3\cdot 5\cdot 4457^{4} \)	16T1916	Trivial
16.12.271440276483030338502656.1	x^16 - 8x^15 + 22x^14 - 14x^13 - 78x^12 + 286x^11 - 412x^10 + 58x^9 + 756x^8 - 1370x^7 + 828x^6 + 628x^5 - 1221x^4 + 636x^3 - 102x^2 - 10x + 3	\( 2^{24}\cdot 41\cdot 4457^{4} \)	16T1916	Trivial
16.4.271440276483030338502656.1	x^16 - 2x^15 - 4x^14 + 12x^13 - 10x^12 - 24x^11 + 36x^10 - 84x^8 + 144x^6 - 192x^5 - 160x^4 + 384x^3 - 256x^2 - 256x + 256	\( 2^{24}\cdot 41\cdot 4457^{4} \)	16T1916	$[2]$
16.8.271440276483030338502656.1	x^16 - 8x^15 + 34x^14 - 98x^13 + 176x^12 - 146x^11 - 180x^10 + 856x^9 - 1489x^8 + 1502x^7 - 704x^6 - 328x^5 + 762x^4 - 538x^3 + 198x^2 - 38x + 3	\( 2^{24}\cdot 41\cdot 4457^{4} \)	16T1916	Trivial
16.8.271440276483030338502656.2	x^16 - 4x^15 - 8x^14 + 36x^13 + 17x^12 - 54x^11 - 144x^10 + 140x^9 - 40x^8 + 246x^7 - 26x^6 + 208x^5 - 288x^4 - 310x^3 + 58x^2 + 22x + 1	\( 2^{24}\cdot 41\cdot 4457^{4} \)	16T1916	Trivial
16.10.681910938481759143067648.1	x^16 - 2x^15 - 18x^14 + 40x^13 + 93x^12 - 172x^11 - 116x^10 + 42x^9 - 192x^8 + 498x^7 + 652x^6 - 358x^5 - 354x^4 + 6x^3 - 2x^2 + 8x - 1	\( -\,2^{24}\cdot 103\cdot 4457^{4} \)	16T1916	Trivial
16.10.681910938481759143067648.2	x^16 - 16x^14 - 38x^13 + 25x^12 + 118x^11 + 156x^10 + 198x^9 - 220x^8 - 516x^7 - 2x^6 + 118x^5 + 11x^4 + 62x^3 + 18x^2 - 6x - 1	\( -\,2^{24}\cdot 103\cdot 4457^{4} \)	16T1916	Trivial
16.14.734874894868691892043776.1	x^16 - 6x^15 + 6x^14 + 38x^13 - 133x^12 + 54x^11 + 524x^10 - 688x^9 - 796x^8 + 1336x^7 + 514x^6 - 984x^5 - 146x^4 + 306x^3 + 12x^2 - 34x + 1	\( -\,2^{24}\cdot 3\cdot 37\cdot 4457^{4} \)	16T1916	Trivial (GRH)
16.14.734874894868691892043776.2	x^16 - 22x^14 - 2x^13 + 190x^12 + 30x^11 - 834x^10 - 148x^9 + 2015x^8 + 278x^7 - 2670x^6 - 92x^5 + 1742x^4 - 194x^3 - 388x^2 + 94x + 1	\( -\,2^{24}\cdot 3\cdot 37\cdot 4457^{4} \)	16T1916	Trivial (GRH)
16.12.748115883965425079287808.1	x^16 - 4x^15 - 14x^14 + 40x^13 + 88x^12 - 92x^11 - 232x^10 + 28x^9 + 257x^8 + 28x^7 - 232x^6 - 92x^5 + 88x^4 + 40x^3 - 14x^2 - 4x + 1	\( 2^{24}\cdot 113\cdot 4457^{4} \)	16T1916	Trivial
16.4.748115883965425079287808.1	x^16 - 2x^15 - 6x^14 - 2x^13 + 44x^12 + 30x^11 - 154x^10 - 22x^9 + 232x^8 + 284x^7 - 12x^6 - 256x^5 - 303x^4 + 226x^3 + 2x^2 + 48x - 29	\( 2^{24}\cdot 113\cdot 4457^{4} \)	16T1916	$[2]$ (GRH)
16.2.761119510147092815740928.1	x^16 - 8x^15 + 42x^14 - 154x^13 + 430x^12 - 942x^11 + 1598x^10 - 2072x^9 + 1819x^8 - 630x^7 - 1086x^6 + 2336x^5 - 2472x^4 + 1694x^3 - 772x^2 + 216x - 29	\( -\,2^{16}\cdot 19^{4}\cdot 23^{5}\cdot 61^{4} \)	16T1916	Trivial
16.8.1224791491447819820072960.1	x^16 - 4x^15 - 2x^14 + 16x^13 - 6x^12 + 36x^11 - 6x^10 - 224x^9 - 64x^8 - 68x^7 + 10x^6 + 936x^5 + 1822x^4 + 1172x^3 - 2162x^2 - 3720x - 1465	\( 2^{24}\cdot 5\cdot 37\cdot 4457^{4} \)	16T1916	Trivial
16.8.1224791491447819820072960.2	x^16 - 2x^15 - 16x^14 + 4x^13 + 101x^12 + 122x^11 - 376x^10 - 556x^9 + 968x^8 + 322x^7 - 1256x^6 + 1166x^5 + 580x^4 - 1176x^3 + 128x^2 + 276x - 81	\( 2^{24}\cdot 5\cdot 37\cdot 4457^{4} \)	16T1916	Trivial
16.2.33886364277853175796465664.1	x^16 + 10x^14 - 38x^12 - 570x^10 - 1808x^8 - 2338x^6 - 1450x^4 - 430x^2 - 49	\( -\,2^{26}\cdot 19^{4}\cdot 23^{4}\cdot 61^{4} \)	16T1916	$[4]$
16.16.2914889170947674938335821824.1	x^16 - 6x^15 - 26x^14 + 178x^13 + 264x^12 - 1964x^11 - 1820x^10 + 10656x^9 + 9976x^8 - 28424x^7 - 34170x^6 + 25796x^5 + 49494x^4 + 15832x^3 - 1908x^2 - 248x + 11	\( 2^{18}\cdot 19^{6}\cdot 23^{4}\cdot 61^{5} \)	16T1916	Trivial (GRH)
16.0.8268272883796174894337622016.1	x^16 + 32x^14 + 412x^12 + 2788x^10 + 10874x^8 + 25176x^6 + 34004x^4 + 24644x^2 + 7381	\( 2^{28}\cdot 19^{4}\cdot 23^{4}\cdot 61^{5} \)	16T1916	$[288]$ (GRH)
16.16.8268272883796174894337622016.1	x^16 - 32x^14 + 412x^12 - 2788x^10 + 10874x^8 - 25176x^6 + 34004x^4 - 24644x^2 + 7381	\( 2^{28}\cdot 19^{4}\cdot 23^{4}\cdot 61^{5} \)	16T1916	Trivial (GRH)
16.0.68342443055127758111009406976.1	x^16 + 16x^14 - 12x^13 + 190x^12 - 216x^11 + 1546x^10 - 2500x^9 + 10092x^8 - 15972x^7 + 47784x^6 - 79524x^5 + 176004x^4 - 196144x^3 + 302016x^2 - 211640x + 408916	\( 2^{22}\cdot 19^{4}\cdot 23^{6}\cdot 61^{5} \)	16T1916	$[2, 282]$ (GRH)