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 20 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.22178360058837890625.2	x^16 - 2x^15 + 23x^14 - 33x^13 + 198x^12 - 202x^11 + 854x^10 - 564x^9 + 2018x^8 - 627x^7 + 2701x^6 + 20x^5 + 2443x^4 + 86x^3 + 2127x^2 - 403x + 961	\( 3^{8}\cdot 5^{12}\cdot 61^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	Trivial
16.0.23509071529850699776.2	x^16 + 4x^14 - 26x^12 - 24x^11 + 4x^10 + 8x^9 + 178x^8 + 288x^7 - 212x^6 - 688x^5 - 218x^4 + 408x^3 + 396x^2 + 136x + 17	\( 2^{48}\cdot 17^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	Trivial
16.8.268435456000000000000.4	x^16 - 8x^14 - 12x^13 + 12x^12 + 72x^11 + 64x^10 - 96x^9 - 205x^8 - 64x^7 + 132x^6 + 104x^5 - 28x^4 - 48x^3 - 8x^2 + 4x + 1	\( 2^{40}\cdot 5^{12} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	Trivial (GRH)
16.0.5538336400000000000000.2	x^16 + 8x^14 - 30x^13 + 93x^12 - 200x^11 + 481x^10 - 2270x^9 + 1870x^8 - 5230x^7 + 8291x^6 - 19470x^5 + 14203x^4 + 57540x^3 + 150223x^2 + 197210x + 121301	\( 2^{16}\cdot 5^{14}\cdot 61^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	$[2, 2]$ (GRH)
16.8.6710886400000000000000.3	x^16 - 4x^14 - 20x^13 - 28x^12 + 80x^11 + 208x^10 + 60x^9 - 255x^8 - 240x^7 + 112x^6 + 140x^5 - 178x^4 - 240x^3 - 76x^2 + 1	\( 2^{40}\cdot 5^{14} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	Trivial (GRH)
16.0.24073289246567116570624.2	x^16 - 16x^14 + 144x^12 - 880x^10 + 4130x^8 - 14960x^6 + 41616x^4 - 78608x^2 + 83521	\( 2^{58}\cdot 17^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	$[2]$ (GRH)
16.0.24073289246567116570624.3	x^16 + 16x^14 - 24x^13 - 44x^12 - 120x^11 - 136x^10 + 528x^9 + 1078x^8 + 1008x^7 - 800x^6 - 4256x^5 - 5052x^4 - 1168x^3 + 6024x^2 + 8672x + 3554	\( 2^{58}\cdot 17^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	$[2]$
16.0.24073289246567116570624.4	x^16 + 16x^14 - 32x^13 + 108x^12 - 384x^11 + 768x^10 - 1904x^9 + 4188x^8 - 6912x^7 + 13072x^6 - 22432x^5 + 27504x^4 - 28736x^3 + 26080x^2 - 14912x + 3592	\( 2^{58}\cdot 17^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	$[2]$
16.0.24073289246567116570624.5	x^16 - 8x^15 + 32x^14 - 80x^13 + 88x^12 + 96x^11 - 704x^10 + 1048x^9 + 1112x^8 - 2376x^7 + 1368x^6 + 2080x^5 - 2416x^4 - 576x^3 + 2104x^2 - 1496x + 401	\( 2^{58}\cdot 17^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	$[2]$
16.0.96947540496000000000000.1	x^16 + 31x^14 + 450x^12 + 4109x^10 + 26639x^8 + 127379x^6 + 432450x^4 + 923521x^2 + 923521	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 31^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	$[2]$ (GRH)
16.8.2963025166336000000000000.5	x^16 - 8x^15 + 18x^14 - 45x^12 + 28x^11 - 56x^10 + 400x^9 - 296x^8 - 600x^7 + 1336x^6 - 1004x^5 - 960x^4 + 380x^3 - 978x^2 - 656x + 41	\( 2^{32}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	Trivial (GRH)
16.8.2963025166336000000000000.6	x^16 - 4x^15 + 6x^14 + 36x^13 - 221x^12 + 456x^11 - 266x^10 - 1088x^9 + 1584x^8 + 4432x^7 - 9896x^6 + 1660x^5 + 7687x^4 - 5972x^3 + 1140x^2 + 480x - 199	\( 2^{32}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	Trivial (GRH)
16.0.20723941878730254150390625.5	x^16 - x^15 + 32x^14 - 50x^13 + 405x^12 - 754x^11 + 2716x^10 - 4745x^9 + 9704x^8 - 12185x^7 + 12899x^6 - 5082x^5 - 10935x^4 + 17395x^3 - 6502x^2 - 14598x + 12401	\( 5^{12}\cdot 13^{8}\cdot 101^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	$[2, 2]$ (GRH)
16.0.20723941878730254150390625.6	x^16 - 3x^15 + 7x^14 + 13x^13 - 28x^12 - 140x^11 + 328x^10 + 154x^9 - 3755x^8 - 7864x^7 + 20608x^6 + 104525x^5 + 188102x^4 + 187062x^3 + 109982x^2 + 36288x + 5281	\( 5^{12}\cdot 13^{8}\cdot 101^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	$[2, 2]$ (GRH)
16.0.758534442582016000000000000.2	x^16 + 40x^14 - 24x^13 + 632x^12 - 840x^11 + 5176x^10 - 9716x^9 + 28019x^8 - 50784x^7 + 109376x^6 - 170828x^5 + 270644x^4 - 318432x^3 + 344084x^2 - 294108x + 212321	\( 2^{40}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	$[2, 2, 2, 92]$ (GRH)
16.16.758534442582016000000000000.2	x^16 - 52x^14 - 24x^13 + 1022x^12 + 976x^11 - 9504x^10 - 13752x^9 + 40510x^8 + 82048x^7 - 53392x^6 - 193432x^5 - 55468x^4 + 130176x^3 + 107488x^2 + 24528x + 316	\( 2^{40}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	Trivial (GRH)
16.8.758534442582016000000000000.2	x^16 - 12x^14 - 24x^13 - 198x^12 - 344x^11 + 56x^10 + 2188x^9 + 11965x^8 + 20768x^7 + 21828x^6 + 37508x^5 + 49932x^4 + 31296x^3 - 22752x^2 - 41292x + 1321	\( 2^{40}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	$[2]$ (GRH)
16.8.758534442582016000000000000.3	x^16 + 4x^14 - 24x^13 - 238x^12 + 488x^11 - 72x^10 + 940x^9 + 1737x^8 - 12064x^7 + 25292x^6 - 13884x^5 - 53904x^4 + 92752x^3 - 60008x^2 - 1716x + 9721	\( 2^{40}\cdot 5^{12}\cdot 41^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	$[2]$ (GRH)
16.0.10455582754471936000000000000.1	x^16 - 4x^15 + 52x^14 - 204x^13 + 1478x^12 - 5224x^11 + 25196x^10 - 69432x^9 + 224498x^8 - 402184x^7 + 874144x^6 - 743520x^5 + 1448468x^4 + 35312x^3 + 1960928x^2 + 899376x + 1069756	\( 2^{40}\cdot 5^{12}\cdot 79^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	$[2, 2, 2, 2, 170]$ (GRH)
16.16.10455582754471936000000000000.1	x^16 - 4x^15 - 64x^14 + 296x^13 + 1154x^12 - 6084x^11 - 8176x^10 + 48352x^9 + 38794x^8 - 179028x^7 - 143096x^6 + 282880x^5 + 264382x^4 - 123492x^3 - 138960x^2 - 5400x + 3321	\( 2^{40}\cdot 5^{12}\cdot 79^{4} \)	$C_2^4:C_2^2.C_2$ (as 16T317)	Trivial (GRH)