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 34 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.2.142966494557221347.1	x^16 - 2x^15 + x^14 + 2x^13 - 3x^12 - 7x^11 + 38x^10 - 84x^9 + 105x^8 - 84x^7 + 38x^6 - 7x^5 - 3x^4 + 2x^3 + x^2 - 2x + 1	\( -\,3^{3}\cdot 19^{6}\cdot 103^{4} \)	16T1758	Trivial
16.2.319040277384290048.1	x^16 - x^15 + 2x^14 - 7x^13 + x^12 + x^11 + x^10 + 13x^9 - 12x^8 - 11x^7 + 5x^6 - 8x^5 - 6x^4 - 8x^3 + 3x^2 - 6x + 1	\( -\,2^{8}\cdot 47^{3}\cdot 331^{4} \)	16T1758	Trivial
16.2.1287945209200830208.1	x^16 - 3x^14 + 6x^12 + 24x^10 + x^8 - 28x^6 - 6x^4 + 21x^2 - 7	\( -\,2^{8}\cdot 7^{3}\cdot 19^{4}\cdot 103^{4} \)	16T1758	Trivial
16.0.1400341099323392000.1	x^16 - 2x^14 + 6x^12 - 5x^10 + 14x^8 - 3x^6 + 16x^4 + 5x^2 + 5	\( 2^{16}\cdot 5^{3}\cdot 643^{4} \)	16T1758	Trivial
16.0.1400341099323392000.2	x^16 - x^12 + 2x^8 + 16x^4 + 5	\( 2^{16}\cdot 5^{3}\cdot 643^{4} \)	16T1758	Trivial
16.0.4395576609545191424.1	x^16 + 6x^12 + 19x^8 + 34x^4 + 29	\( 2^{16}\cdot 29^{3}\cdot 229^{4} \)	16T1758	Trivial
16.0.4395576609545191424.2	x^16 - x^12 + 10x^8 - 16x^4 + 29	\( 2^{16}\cdot 29^{3}\cdot 229^{4} \)	16T1758	Trivial
16.4.4966395213696725133.1	x^16 - 2x^15 - x^14 - 2x^13 + 9x^12 + 15x^11 - 37x^10 + 11x^9 - 14x^8 + 46x^7 - 3x^6 - 54x^5 + 33x^4 + 4x^3 - 9x^2 + 3x - 1	\( 3^{6}\cdot 13^{3}\cdot 1327^{4} \)	16T1758	Trivial
16.4.44697556923270526197.1	x^16 - 2x^15 + 8x^14 - 8x^13 + 22x^12 - 23x^11 + 7x^10 + 12x^9 + 6x^8 + 60x^7 - 29x^6 - 41x^5 + 28x^4 + 13x^3 - 10x^2 - 2x + 1	\( 3^{8}\cdot 13^{3}\cdot 1327^{4} \)	16T1758	Trivial
16.6.51610904535156906267.1	x^16 - 5x^14 + 22x^10 - 24x^8 - 4x^6 + 17x^4 - 3x^2 - 3	\( -\,3^{3}\cdot 19^{8}\cdot 103^{4} \)	16T1758	Trivial
16.2.62545673362377736192.1	x^16 - 14x^12 + 39x^8 - 42x^4 - 43	\( -\,2^{16}\cdot 43^{3}\cdot 331^{4} \)	16T1758	Trivial (GRH)
16.6.104222574532214361963.1	x^16 - 4x^15 + 4x^14 - 2x^13 + 5x^12 + 5x^11 - 16x^10 - 23x^9 + 47x^8 + 37x^7 - 148x^6 + 71x^5 + 128x^4 - 113x^3 - 15x^2 + 25x - 1	\( -\,3^{9}\cdot 19^{6}\cdot 103^{4} \)	16T1758	Trivial
16.4.358487321426788352000.1	x^16 - 2x^15 - 6x^14 + 16x^13 + 15x^12 - 60x^11 - 12x^10 + 138x^9 - 44x^8 - 174x^7 + 130x^6 + 74x^5 - 94x^4 + 18x^3 - 12x^2 + 4x + 1	\( 2^{24}\cdot 5^{3}\cdot 643^{4} \)	16T1758	Trivial (GRH)
16.4.358487321426788352000.2	x^16 - 2x^15 - 2x^14 - 8x^13 + 28x^12 + 8x^11 - 34x^10 - 52x^9 + 102x^8 - 18x^7 - 28x^6 - 20x^5 + 41x^4 - 14x^3 - 2x + 1	\( 2^{24}\cdot 5^{3}\cdot 643^{4} \)	16T1758	Trivial (GRH)
16.8.156223348698028810843269.1	x^16 - 11x^14 - 6x^13 + 21x^12 + 63x^11 + 44x^10 - 95x^9 - 116x^8 - 298x^7 + 179x^6 + 25x^5 + 173x^4 + 315x^3 + 101x^2 + 174x + 89	\( 3^{3}\cdot 19^{6}\cdot 103^{7} \)	16T1758	Trivial (GRH)
16.8.156223348698028810843269.2	x^16 + 9x^14 - 6x^13 - 28x^12 - 16x^11 - 199x^10 - 116x^9 - 146x^8 - 126x^7 + 959x^6 - 538x^5 - 1006x^4 + 1639x^3 + 273x^2 - 694x + 151	\( 3^{3}\cdot 19^{6}\cdot 103^{7} \)	16T1758	Trivial (GRH)
16.0.1700931907332486664814592.1	x^16 - 6x^14 + 23x^12 - 24x^10 - 19x^8 + 126x^6 + 335x^4 - 426x^2 + 147	\( 2^{32}\cdot 3^{3}\cdot 19^{4}\cdot 103^{4} \)	16T1758	$[2]$ (GRH)
16.0.1700931907332486664814592.2	x^16 - 8x^14 + 55x^12 - 100x^10 + 18x^8 + 246x^6 + 14x^4 - 240x^2 + 147	\( 2^{32}\cdot 3^{3}\cdot 19^{4}\cdot 103^{4} \)	16T1758	$[2]$ (GRH)
16.0.255247314189656912262660096.1	x^16 + 39x^14 + 601x^12 + 4708x^10 + 20159x^8 + 47380x^6 + 57165x^4 + 28737x^2 + 2781	\( 2^{16}\cdot 3^{5}\cdot 19^{4}\cdot 103^{7} \)	16T1758	$[2, 264]$ (GRH)
16.12.255247314189656912262660096.1	x^16 - 9x^14 - 70x^12 + 850x^10 - 324x^8 - 17613x^6 + 58401x^4 - 66744x^2 + 25029	\( 2^{16}\cdot 3^{5}\cdot 19^{4}\cdot 103^{7} \)	16T1758	Trivial (GRH)
16.16.255247314189656912262660096.1	x^16 - 39x^14 + 601x^12 - 4708x^10 + 20159x^8 - 47380x^6 + 57165x^4 - 28737x^2 + 2781	\( 2^{16}\cdot 3^{5}\cdot 19^{4}\cdot 103^{7} \)	16T1758	Trivial (GRH)
16.4.255247314189656912262660096.1	x^16 + x^14 - 204x^12 - 884x^10 + 2818x^8 + 20291x^6 + 32754x^4 + 17613x^2 + 2781	\( 2^{16}\cdot 3^{5}\cdot 19^{4}\cdot 103^{7} \)	16T1758	Trivial (GRH)
16.8.255247314189656912262660096.1	x^16 - 8x^14 - 95x^12 + 185x^10 + 1956x^8 - 721x^6 - 10506x^4 + 2781	\( 2^{16}\cdot 3^{5}\cdot 19^{4}\cdot 103^{7} \)	16T1758	Trivial (GRH)
16.0.255247314189656912262660096.2	x^16 + 36x^14 + 531x^12 + 4134x^10 + 18127x^8 + 43775x^6 + 51603x^4 + 21321x^2 + 2781	\( 2^{16}\cdot 3^{5}\cdot 19^{4}\cdot 103^{7} \)	16T1758	$[2, 160]$ (GRH)
16.12.255247314189656912262660096.2	x^16 - x^14 - 204x^12 + 884x^10 + 2818x^8 - 20291x^6 + 32754x^4 - 17613x^2 + 2781	\( 2^{16}\cdot 3^{5}\cdot 19^{4}\cdot 103^{7} \)	16T1758	Trivial (GRH)
16.16.255247314189656912262660096.2	x^16 - 36x^14 + 531x^12 - 4134x^10 + 18127x^8 - 43775x^6 + 51603x^4 - 21321x^2 + 2781	\( 2^{16}\cdot 3^{5}\cdot 19^{4}\cdot 103^{7} \)	16T1758	Trivial (GRH)
16.4.255247314189656912262660096.2	x^16 + 9x^14 - 70x^12 - 850x^10 - 324x^8 + 17613x^6 + 58401x^4 + 66744x^2 + 25029	\( 2^{16}\cdot 3^{5}\cdot 19^{4}\cdot 103^{7} \)	16T1758	Trivial (GRH)
16.8.255247314189656912262660096.2	x^16 + 16x^14 - 71x^12 - 1231x^10 + 2580x^8 + 5768x^6 - 11124x^4 + 927x^2 + 2781	\( 2^{16}\cdot 3^{5}\cdot 19^{4}\cdot 103^{7} \)	16T1758	Trivial (GRH)
16.0.285106224166483496040464384.1	x^16 + 69x^14 + 1898x^12 + 28749x^10 + 273330x^8 + 1718888x^6 + 7012424x^4 + 16521865x^2 + 16324589	\( 2^{16}\cdot 149^{3}\cdot 331^{6} \)	16T1758	$[2, 2]$ (GRH)
16.8.285106224166483496040464384.1	x^16 - 51x^14 + 1058x^12 - 13095x^10 + 132210x^8 - 1129107x^6 + 6195754x^4 - 16965736x^2 + 16324589	\( 2^{16}\cdot 149^{3}\cdot 331^{6} \)	16T1758	Trivial (GRH)
16.0.285106224166483496040464384.2	x^16 + 51x^14 + 1058x^12 + 13095x^10 + 132210x^8 + 1129107x^6 + 6195754x^4 + 16965736x^2 + 16324589	\( 2^{16}\cdot 149^{3}\cdot 331^{6} \)	16T1758	$[2, 2]$ (GRH)
16.8.285106224166483496040464384.2	x^16 - 5x^14 - 150x^12 - 126x^10 + 7522x^8 - 21486x^6 + 2174095x^4 - 17409607x^2 + 16324589	\( 2^{16}\cdot 149^{3}\cdot 331^{6} \)	16T1758	Trivial (GRH)
16.4.285106224166483496040464384.3	x^16 - 46x^14 + 707x^12 - 4773x^10 - 5325x^8 + 308278x^6 - 1761300x^4 + 1479570x^2 + 16324589	\( 2^{16}\cdot 149^{3}\cdot 331^{6} \)	16T1758	Trivial (GRH)
16.4.285106224166483496040464384.4	x^16 + 5x^14 - 122x^12 - 1137x^10 + 8858x^8 + 185816x^6 - 1246560x^4 - 3994839x^2 + 16324589	\( 2^{16}\cdot 149^{3}\cdot 331^{6} \)	16T1758	Trivial (GRH)