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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.2.27548985049130991616.1	x^16 + x^12 + 12x^8 - 6x^4 - 1	\( -\,2^{32}\cdot 283^{4} \)	16T1666	Trivial (GRH)
16.2.27548985049130991616.2	x^16 - 8x^14 + 27x^12 - 50x^10 + 55x^8 - 36x^6 + 13x^4 - 2x^2 - 1	\( -\,2^{32}\cdot 283^{4} \)	16T1666	Trivial (GRH)
16.2.62359616009735766016.1	x^16 + 12x^12 + 25x^8 + 9x^4 - 1	\( -\,2^{20}\cdot 2777^{4} \)	16T1666	Trivial (GRH)
16.2.62359616009735766016.2	x^16 - 6x^14 + 15x^12 - 17x^10 + 2x^8 + 19x^6 - 25x^4 + 16x^2 - 4	\( -\,2^{20}\cdot 2777^{4} \)	16T1666	Trivial (GRH)
16.0.530732138800906430621.1	x^16 - 2x^15 - 8x^14 + 5x^13 + 10x^12 + 73x^11 + 162x^10 - 366x^9 - 563x^8 + 349x^7 - 469x^6 + 35x^5 + 3051x^4 - 488x^3 - 2022x^2 + 5080x + 4751	\( 29^{5}\cdot 97^{2}\cdot 229^{4} \)	16T1666	Trivial (GRH)
16.6.997753856155772256256.1	x^16 - 2x^14 - 42x^12 - 50x^10 + 5x^8 + 12x^6 + 21x^4 - 2x^2 - 4	\( -\,2^{24}\cdot 2777^{4} \)	16T1666	Trivial (GRH)
16.6.997753856155772256256.2	x^16 - 8x^14 + 27x^12 - 50x^10 + 19x^8 + 108x^6 - 107x^4 - 50x^2 - 4	\( -\,2^{24}\cdot 2777^{4} \)	16T1666	Trivial (GRH)
16.0.446345728731562308152261.1	x^16 - 5x^15 + 8x^14 - 17x^13 + 55x^12 - 92x^11 + 110x^10 - 73x^9 + 238x^8 - 390x^7 - 297x^6 - 500x^5 + 449x^4 + 1071x^3 + 1396x^2 + 876x + 437	\( 29^{7}\cdot 97^{2}\cdot 229^{4} \)	16T1666	$[2]$ (GRH)
16.4.57772777564280173561708544.1	x^16 + 21x^14 + 163x^12 + 888x^10 - 436x^8 - 32800x^6 - 172244x^4 - 111005x^2 + 3307949	\( 2^{16}\cdot 149^{5}\cdot 331^{4} \)	16T1666	Trivial (GRH)
16.4.57772777564280173561708544.2	x^16 - 21x^14 + 163x^12 - 888x^10 - 436x^8 + 32800x^6 - 172244x^4 + 111005x^2 + 3307949	\( 2^{16}\cdot 149^{5}\cdot 331^{4} \)	16T1666	Trivial (GRH)
16.12.2291847513917281950856118272.1	x^16 - 47x^14 + 651x^12 - 1634x^10 - 20614x^8 + 77183x^6 + 124743x^4 - 584284x^2 + 318028	\( 2^{18}\cdot 43^{5}\cdot 2777^{4} \)	16T1666	Trivial (GRH)
16.4.2291847513917281950856118272.1	x^16 + 43x^14 + 693x^12 + 5083x^10 + 15213x^8 - 2001x^6 - 90300x^4 - 86903x^2 + 79507	\( 2^{18}\cdot 43^{5}\cdot 2777^{4} \)	16T1666	$[6]$ (GRH)
16.12.2291847513917281950856118272.2	x^16 - 27x^14 + 223x^12 - 189x^10 - 5506x^8 + 22392x^6 - 12599x^4 - 62866x^2 + 79507	\( 2^{18}\cdot 43^{5}\cdot 2777^{4} \)	16T1666	Trivial (GRH)
16.4.2291847513917281950856118272.2	x^16 + 27x^14 + 223x^12 + 189x^10 - 5506x^8 - 22392x^6 - 12599x^4 + 62866x^2 + 79507	\( 2^{18}\cdot 43^{5}\cdot 2777^{4} \)	16T1666	$[2]$ (GRH)
16.0.9167390055669127803424473088.1	x^16 + 48x^14 + 943x^12 + 9756x^10 + 56971x^8 + 187080x^6 + 325596x^4 + 266256x^2 + 79507	\( 2^{20}\cdot 43^{5}\cdot 2777^{4} \)	16T1666	$[2, 1006]$ (GRH)
16.16.9167390055669127803424473088.1	x^16 - 48x^14 + 943x^12 - 9756x^10 + 56971x^8 - 187080x^6 + 325596x^4 - 266256x^2 + 79507	\( 2^{20}\cdot 43^{5}\cdot 2777^{4} \)	16T1666	Trivial (GRH)
16.8.9167390055669127803424473088.1	x^16 - 28x^14 - 122x^12 + 3224x^10 + 4176x^8 - 71995x^6 - 129645x^4 + 207088x^2 + 318028	\( 2^{20}\cdot 43^{5}\cdot 2777^{4} \)	16T1666	Trivial (GRH)
16.8.9167390055669127803424473088.2	x^16 - 45x^14 + 567x^12 - 1023x^10 - 16116x^8 + 21492x^6 + 218397x^4 + 299538x^2 + 79507	\( 2^{20}\cdot 43^{5}\cdot 2777^{4} \)	16T1666	Trivial (GRH)
16.0.146678240890706044854791569408.1	x^16 + 88x^14 + 3021x^12 + 52742x^10 + 505596x^8 + 2668400x^6 + 7420768x^4 + 9999392x^2 + 5088448	\( 2^{24}\cdot 43^{5}\cdot 2777^{4} \)	16T1666	$[2, 4170]$ (GRH)
16.16.146678240890706044854791569408.1	x^16 - 88x^14 + 3021x^12 - 52742x^10 + 505596x^8 - 2668400x^6 + 7420768x^4 - 9999392x^2 + 5088448	\( 2^{24}\cdot 43^{5}\cdot 2777^{4} \)	16T1666	Trivial (GRH)
16.0.6329643282720100095594349789184.1	x^16 + 128x^14 + 4933x^12 + 68991x^10 + 5054320x^8 + 355678654x^6 + 9123890287x^4 + 96633182650x^2 + 362422200389	\( 2^{16}\cdot 149^{5}\cdot 331^{6} \)	16T1666	$[4, 4]$ (GRH)
16.8.6329643282720100095594349789184.1	x^16 - 62x^14 + 1603x^12 - 118414x^10 + 3522788x^8 - 42372317x^6 + 3452337301x^4 - 73308945256x^2 + 362422200389	\( 2^{16}\cdot 149^{5}\cdot 331^{6} \)	16T1666	Trivial (GRH)
16.0.6329643282720100095594349789184.2	x^16 + 82x^14 + 857x^12 - 98743x^10 - 3623245x^8 - 12750148x^6 + 1981260748x^4 + 48397425166x^2 + 362422200389	\( 2^{16}\cdot 149^{5}\cdot 331^{6} \)	16T1666	$[2, 4]$ (GRH)
16.8.6329643282720100095594349789184.2	x^16 - 186x^14 + 14763x^12 - 700311x^10 + 22756522x^8 - 514980392x^6 + 8166190701x^4 - 82700367874x^2 + 362422200389	\( 2^{16}\cdot 149^{5}\cdot 331^{6} \)	16T1666	Trivial (GRH)