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
16.0.36559665392320512.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 266x^12 - 504x^11 + 784x^10 - 1016x^9 + 1109x^8 - 1024x^7 + 804x^6 - 536x^5 + 301x^4 - 138x^3 + 47x^2 - 10x + 1	\( 2^{16}\cdot 3^{8}\cdot 13^{5}\cdot 229 \)	16T1590	Trivial
16.0.138563758754168832.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 270x^12 - 528x^11 + 868x^10 - 1216x^9 + 1473x^8 - 1544x^7 + 1408x^6 - 1104x^5 + 741x^4 - 410x^3 + 183x^2 - 58x + 13	\( 2^{16}\cdot 3^{12}\cdot 7^{4}\cdot 1657 \)	16T1590	Trivial
16.2.320444825600000000.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 260x^12 - 468x^11 + 658x^10 - 716x^9 + 574x^8 - 288x^7 + 8x^6 + 140x^5 - 145x^4 + 84x^3 - 32x^2 + 8x - 1	\( -\,2^{32}\cdot 5^{8}\cdot 191 \)	16T1590	Trivial
16.0.486416793600000000.1	x^16 - 4x^15 + 12x^14 - 30x^13 + 61x^12 - 112x^11 + 193x^10 - 294x^9 + 376x^8 - 402x^7 + 367x^6 - 284x^5 + 181x^4 - 90x^3 + 33x^2 - 8x + 1	\( 2^{20}\cdot 3^{8}\cdot 5^{8}\cdot 181 \)	16T1590	Trivial
16.0.558519956648493056.1	x^16 - 2x^14 + 11x^12 - 8x^11 - 22x^10 + 32x^9 + 14x^8 - 44x^7 + 36x^5 - 6x^4 - 28x^3 + 24x^2 - 8x + 1	\( 2^{32}\cdot 7^{4}\cdot 41\cdot 1321 \)	16T1590	Trivial
16.0.1067670784198828125.1	x^16 - 5x^15 + 13x^14 - 22x^13 + 28x^12 - 40x^11 + 79x^10 - 132x^9 + 140x^8 - 105x^7 + 126x^6 - 194x^5 + 189x^4 - 107x^3 + 36x^2 - 7x + 1	\( 3^{8}\cdot 5^{8}\cdot 19\cdot 29^{4}\cdot 31 \)	16T1590	Trivial
16.0.1067670784198828125.2	x^16 - 4x^15 + 15x^14 - 38x^13 + 82x^12 - 146x^11 + 224x^10 - 284x^9 + 330x^8 - 291x^7 + 259x^6 - 150x^5 + 95x^4 - 41x^3 + 11x^2 - 3x + 1	\( 3^{8}\cdot 5^{8}\cdot 19\cdot 29^{4}\cdot 31 \)	16T1590	Trivial
16.2.4028209561600000000.1	x^16 - 2x^15 + x^14 + 6x^13 - 19x^12 + 20x^11 + 14x^10 - 64x^9 + 68x^8 - 76x^6 + 88x^5 - 44x^4 + 24x^2 - 32x + 16	\( -\,2^{32}\cdot 5^{8}\cdot 7^{4} \)	16T1590	Trivial
16.6.4053375385600000000.1	x^16 - 4x^15 + 4x^14 + 8x^13 - 36x^12 + 68x^11 - 52x^10 - 64x^9 + 230x^8 - 312x^7 + 244x^6 - 80x^5 - 76x^4 + 136x^3 - 96x^2 + 32x - 4	\( -\,2^{36}\cdot 5^{8}\cdot 151 \)	16T1590	Trivial
16.6.5127117209600000000.1	x^16 - 8x^14 - 8x^13 + 8x^12 + 48x^11 + 62x^10 - 24x^9 - 141x^8 - 152x^7 - 26x^6 + 108x^5 + 146x^4 + 100x^3 + 42x^2 + 12x + 1	\( -\,2^{36}\cdot 5^{8}\cdot 191 \)	16T1590	Trivial
16.0.11974482329600000000.1	x^16 + 4x^14 - 10x^13 + 5x^12 - 22x^11 + 29x^10 - 12x^9 + 35x^8 - 22x^7 + 6x^6 - 16x^5 + 3x^2 + 2x + 1	\( 2^{24}\cdot 5^{8}\cdot 7^{4}\cdot 761 \)	16T1590	Trivial
16.4.20427938201600000000.1	x^16 - 4x^15 + 6x^14 - 12x^13 + 36x^12 - 76x^11 + 106x^10 - 128x^9 + 161x^8 - 156x^7 + 118x^6 - 84x^5 + 46x^4 - 20x^3 + 8x^2 - 1	\( 2^{36}\cdot 5^{8}\cdot 761 \)	16T1590	Trivial
16.4.20427938201600000000.2	x^16 - 4x^15 + 6x^14 - 12x^13 + 32x^12 - 56x^11 + 66x^10 - 48x^9 + 42x^8 - 92x^7 + 46x^6 + 76x^5 - 48x^4 - 32x^3 + 10x^2 + 8x + 1	\( 2^{36}\cdot 5^{8}\cdot 761 \)	16T1590	Trivial
16.4.103508711833600000000.1	x^16 - 2x^14 - 4x^13 - 3x^12 - 4x^11 - 24x^10 - 8x^9 + 3x^8 - 16x^7 - 28x^6 - 16x^5 + 5x^4 - 20x^3 - 22x^2 - 12x - 1	\( 2^{40}\cdot 5^{8}\cdot 241 \)	16T1590	Trivial
16.12.228295483029373059072.1	x^16 - 14x^14 + 71x^12 - 4x^11 - 168x^10 + 20x^9 + 200x^8 - 36x^7 - 128x^6 + 36x^5 + 48x^4 - 20x^3 - 10x^2 + 4x + 1	\( 2^{32}\cdot 3^{8}\cdot 17^{4}\cdot 97 \)	16T1590	Trivial
16.4.228295483029373059072.1	x^16 - 8x^15 + 26x^14 - 36x^13 - 21x^12 + 184x^11 - 366x^10 + 380x^9 - 142x^8 - 196x^7 + 400x^6 - 384x^5 + 246x^4 - 112x^3 + 36x^2 - 8x + 1	\( 2^{32}\cdot 3^{8}\cdot 17^{4}\cdot 97 \)	16T1590	Trivial
16.8.454237404378030931968.1	x^16 - 2x^14 - 4x^13 - 9x^12 + 12x^11 + 2x^10 - 24x^9 + 58x^8 + 20x^7 - 72x^6 + 40x^5 + 70x^4 - 20x^3 - 24x^2 + 1	\( 2^{32}\cdot 3^{8}\cdot 17^{4}\cdot 193 \)	16T1590	Trivial
16.8.454237404378030931968.2	x^16 - 10x^14 - 4x^13 + 35x^12 + 16x^11 - 82x^10 - 64x^9 + 104x^8 + 120x^7 - 106x^6 - 156x^5 + 102x^4 + 224x^3 + 112x^2 + 20x + 1	\( 2^{32}\cdot 3^{8}\cdot 17^{4}\cdot 193 \)	16T1590	Trivial
16.4.506646779980412878848.1	x^16 + 4x^12 - 12x^11 - 30x^10 + 3x^8 + 12x^7 - 54x^6 - 60x^5 + 220x^4 + 60x^3 - 24x^2 - 24x - 2	\( 2^{36}\cdot 3^{12}\cdot 13873 \)	16T1590	Trivial
16.0.611603342950400000000.1	x^16 + 12x^14 + 54x^12 + 128x^10 + 227x^8 + 496x^6 + 1054x^4 + 1060x^2 + 89	\( 2^{44}\cdot 5^{8}\cdot 89 \)	16T1590	Trivial
16.8.611603342950400000000.1	x^16 - 12x^14 + 54x^12 - 128x^10 + 227x^8 - 496x^6 + 1054x^4 - 1060x^2 + 89	\( 2^{44}\cdot 5^{8}\cdot 89 \)	16T1590	Trivial (GRH)
16.8.8300381085614374649856.1	x^16 - 8x^15 + 16x^14 + 28x^13 - 124x^12 + 16x^11 + 334x^10 - 196x^9 - 461x^8 + 336x^7 + 358x^6 - 228x^5 - 164x^4 + 52x^3 + 40x^2 - 2	\( 2^{36}\cdot 3^{12}\cdot 227281 \)	16T1590	Trivial
16.12.58443643655519503122432.1	x^16 - 12x^14 - 12x^13 + 30x^12 + 152x^11 + 92x^10 - 436x^9 - 790x^8 + 1540x^6 + 1580x^5 - 342x^4 - 1544x^3 - 1020x^2 - 268x - 23	\( 2^{40}\cdot 3^{8}\cdot 17^{4}\cdot 97 \)	16T1590	Trivial (GRH)
16.8.58443643655519503122432.1	x^16 - 8x^14 - 12x^13 + 46x^12 + 72x^11 - 124x^10 - 180x^9 - 39x^8 + 672x^7 - 356x^6 + 84x^5 - 236x^4 - 336x^3 + 704x^2 - 336x + 49	\( 2^{40}\cdot 3^{8}\cdot 17^{4}\cdot 97 \)	16T1590	Trivial
16.12.58443643655519503122432.2	x^16 - 8x^14 + 10x^12 + 68x^10 - 213x^8 + 100x^6 + 286x^4 - 340x^2 + 97	\( 2^{40}\cdot 3^{8}\cdot 17^{4}\cdot 97 \)	16T1590	Trivial
16.6.94234855709081600000000.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 254x^12 - 432x^11 + 532x^10 - 416x^9 + 70x^8 + 324x^7 - 478x^6 + 320x^5 - 39x^4 - 116x^3 + 88x^2 - 24x - 9	\( -\,2^{32}\cdot 5^{8}\cdot 19^{4}\cdot 431 \)	16T1590	Trivial (GRH)
16.6.139984420202086400000000.1	x^16 - 8x^15 + 34x^14 - 98x^13 + 197x^12 - 272x^11 + 191x^10 + 156x^9 - 719x^8 + 1236x^7 - 1391x^6 + 1110x^5 - 605x^4 + 196x^3 - 12x^2 - 16x + 4	\( -\,2^{24}\cdot 5^{8}\cdot 41^{4}\cdot 7559 \)	16T1590	Trivial (GRH)
16.10.303774876408217600000000.1	x^16 - 4x^14 - 12x^12 + 50x^10 - 16x^8 - 56x^6 + 43x^4 - 6x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 29^{4} \)	16T1590	Trivial (GRH)
16.14.303774876408217600000000.1	x^16 - 12x^14 + 40x^12 - 10x^10 - 126x^8 + 184x^6 - 93x^4 + 18x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 29^{4} \)	16T1590	Trivial (GRH)
16.2.303774876408217600000000.1	x^16 + 12x^14 + 40x^12 + 10x^10 - 126x^8 - 184x^6 - 93x^4 - 18x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 29^{4} \)	16T1590	Trivial
16.6.303774876408217600000000.1	x^16 + 6x^14 - 15x^12 - 80x^10 - 61x^8 + 48x^6 + 63x^4 + 14x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 29^{4} \)	16T1590	Trivial
16.10.303774876408217600000000.2	x^16 - 12x^14 + 42x^12 - 20x^10 - 103x^8 + 104x^6 + 16x^4 - 28x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 29^{4} \)	16T1590	Trivial (GRH)
16.14.303774876408217600000000.2	x^16 - 10x^14 + 11x^12 + 104x^10 - 287x^8 + 272x^6 - 109x^4 + 18x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 29^{4} \)	16T1590	Trivial (GRH)
16.2.303774876408217600000000.2	x^16 + 10x^14 + 11x^12 - 104x^10 - 287x^8 - 272x^6 - 109x^4 - 18x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 29^{4} \)	16T1590	Trivial
16.6.303774876408217600000000.2	x^16 + 4x^14 - 8x^12 - 38x^10 + 2x^8 + 72x^6 + 45x^4 + 2x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 29^{4} \)	16T1590	Trivial
16.10.303774876408217600000000.3	x^16 - 10x^14 + 19x^12 + 52x^10 - 112x^8 - 46x^6 + 44x^4 + 4x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 29^{4} \)	16T1590	Trivial (GRH)
16.6.303774876408217600000000.3	x^16 + 10x^14 + 19x^12 - 52x^10 - 112x^8 + 46x^6 + 44x^4 - 4x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 29^{4} \)	16T1590	Trivial
16.10.303774876408217600000000.4	x^16 + 2x^14 - 17x^12 - 16x^10 + 67x^8 + 36x^6 - 55x^4 + 14x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 29^{4} \)	16T1590	Trivial (GRH)
16.6.303774876408217600000000.4	x^16 - 2x^14 - 17x^12 + 16x^10 + 67x^8 - 36x^6 - 55x^4 - 14x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 29^{4} \)	16T1590	Trivial
16.10.303774876408217600000000.5	x^16 - 4x^14 - 12x^12 + 60x^10 - 13x^8 - 112x^6 + 34x^4 + 16x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 29^{4} \)	16T1590	Trivial (GRH)
16.10.303774876408217600000000.6	x^16 - 6x^14 - 15x^12 + 80x^10 - 61x^8 - 48x^6 + 63x^4 - 14x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 29^{4} \)	16T1590	Trivial (GRH)
16.4.378471464046259599310848.1	x^16 - 8x^15 + 40x^14 - 140x^13 + 366x^12 - 740x^11 + 1160x^10 - 1400x^9 + 1262x^8 - 784x^7 + 254x^6 + 56x^5 - 105x^4 + 44x^3 - 2x^2 - 4x + 1	\( 2^{32}\cdot 3^{8}\cdot 7^{2}\cdot 41^{4}\cdot 97 \)	16T1590	$[2]$
16.12.449626777045509882249216.1	x^16 - 8x^15 + 20x^14 - 80x^12 + 116x^11 + 18x^10 - 200x^9 + 176x^8 + 56x^7 - 188x^6 + 72x^5 + 53x^4 - 44x^3 + 8x + 1	\( 2^{32}\cdot 3^{8}\cdot 17^{4}\cdot 73\cdot 2617 \)	16T1590	Trivial (GRH)
16.8.738109270943334400000000.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 60x^12 + 4x^11 - 122x^10 + 192x^9 - 127x^8 - 28x^7 + 122x^6 - 88x^5 + 12x^4 + 20x^3 - 10x^2 + 1	\( 2^{32}\cdot 5^{8}\cdot 11^{4}\cdot 151\cdot 199 \)	16T1590	Trivial (GRH)
16.8.923149009479270400000000.1	x^16 - 8x^15 + 26x^14 - 42x^13 + 15x^12 + 92x^11 - 235x^10 + 284x^9 - 160x^8 - 52x^7 + 167x^6 - 120x^5 + 21x^4 + 24x^3 - 15x^2 + 2x + 1	\( 2^{24}\cdot 5^{8}\cdot 41^{4}\cdot 79\cdot 631 \)	16T1590	Trivial (GRH)
16.0.1470751850469785600000000.1	x^16 - 6x^14 + 25x^12 - 74x^10 + 150x^8 - 202x^6 + 183x^4 - 114x^2 + 41	\( 2^{40}\cdot 5^{8}\cdot 17^{4}\cdot 41 \)	16T1590	Trivial
16.0.14961572775812992799342592.1	x^16 + 24x^14 + 242x^12 + 1328x^10 + 4281x^8 + 8108x^6 + 8376x^4 + 3704x^2 + 97	\( 2^{48}\cdot 3^{8}\cdot 17^{4}\cdot 97 \)	16T1590	$[2, 38]$
16.0.28554109096925593600000000.1	x^16 - 14x^14 + 95x^12 - 406x^10 + 1175x^8 - 2308x^6 + 2958x^4 - 2256x^2 + 796	\( 2^{42}\cdot 5^{8}\cdot 17^{4}\cdot 199 \)	16T1590	Trivial (GRH)
16.16.88818327543670374400000000.1	x^16 - 8x^15 + 10x^14 + 70x^13 - 181x^12 - 188x^11 + 845x^10 + 120x^9 - 1892x^8 + 204x^7 + 2311x^6 - 252x^5 - 1511x^4 - 32x^3 + 417x^2 + 86x + 1	\( 2^{24}\cdot 5^{8}\cdot 41^{4}\cdot 4796089 \)	16T1590	Trivial (GRH)
16.4.97434031449807257600000000.1	x^16 - 8x^14 - 20x^13 + 38x^12 + 220x^11 - 22x^10 - 1308x^9 - 1259x^8 + 3912x^7 + 6910x^6 - 4988x^5 - 20302x^4 - 12284x^3 + 5978x^2 + 6324x - 2151	\( 2^{36}\cdot 5^{8}\cdot 41\cdot 97^{4} \)	16T1590	Trivial (GRH)