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 42 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.87684249573789696.1	x^16 + 5x^14 + 10x^12 + 8x^10 - 2x^6 + 4x^4 + 4x^2 + 1	\( 2^{12}\cdot 3^{8}\cdot 239^{4} \)	16T1665	Trivial
16.0.117236401360736256.1	x^16 + 2x^14 + 6x^12 + 9x^10 - 3x^8 - 10x^6 + 5x^4 + 5x^2 + 1	\( 2^{12}\cdot 3^{8}\cdot 257^{4} \)	16T1665	Trivial
16.0.203831936618070016.3	x^16 - 4x^14 + 11x^12 - 20x^10 + 27x^8 - 26x^6 + 17x^4 - 6x^2 + 1	\( 2^{32}\cdot 83^{4} \)	16T1665	Trivial
16.0.374142420275486976.1	x^16 - 3x^15 + 4x^14 - x^13 + 5x^12 - 6x^11 - 8x^10 + 21x^9 - 2x^8 + 4x^7 + 8x^6 - 16x^5 + 22x^3 + 20x^2 + 7x + 1	\( 2^{8}\cdot 3^{12}\cdot 229^{4} \)	16T1665	Trivial
16.4.641424792100000000.1	x^16 + x^14 + 3x^12 + 3x^10 - 20x^8 - 9x^6 + 15x^4 - 11x^2 + 1	\( 2^{8}\cdot 5^{8}\cdot 283^{4} \)	16T1665	Trivial
16.0.3070625382400000000.1	x^16 + 5x^14 + 9x^12 + 4x^10 + 8x^6 + 16x^4 + 12x^2 + 4	\( 2^{22}\cdot 5^{8}\cdot 37^{4} \)	16T1665	Trivial
16.4.6350601601600000000.3	x^16 + 8x^14 + 24x^12 + 33x^10 + 18x^8 - 4x^6 - 9x^4 - x^2 + 1	\( 2^{12}\cdot 5^{8}\cdot 251^{4} \)	16T1665	Trivial
16.0.49130006118400000000.2	x^16 - 5x^14 + 11x^12 - 12x^10 + 10x^8 - 16x^6 + 24x^4 - 16x^2 + 4	\( 2^{26}\cdot 5^{8}\cdot 37^{4} \)	16T1665	Trivial (GRH)
16.4.101609625625600000000.3	x^16 - 8x^14 + 22x^12 - 17x^10 - 27x^8 + 58x^6 - 33x^4 + 2x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 251^{4} \)	16T1665	Trivial
16.4.101609625625600000000.4	x^16 + 8x^14 + 22x^12 + 17x^10 - 27x^8 - 58x^6 - 33x^4 - 2x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 251^{4} \)	16T1665	Trivial
16.0.406438502502400000000.1	x^16 + 10x^14 + 45x^12 + 121x^10 + 206x^8 + 215x^6 + 129x^4 + 38x^2 + 4	\( 2^{18}\cdot 5^{8}\cdot 251^{4} \)	16T1665	Trivial
16.8.406438502502400000000.1	x^16 - 10x^14 + 45x^12 - 121x^10 + 206x^8 - 215x^6 + 129x^4 - 38x^2 + 4	\( 2^{18}\cdot 5^{8}\cdot 251^{4} \)	16T1665	Trivial (GRH)
16.12.1466774336280100000000.2	x^16 - x^15 - 13x^14 + 10x^13 + 59x^12 - 30x^11 - 115x^10 + 21x^9 + 120x^8 + 21x^7 - 115x^6 - 30x^5 + 59x^4 + 10x^3 - 13x^2 - x + 1	\( 2^{8}\cdot 5^{8}\cdot 19^{4}\cdot 103^{4} \)	16T1665	Trivial (GRH)
16.4.1466774336280100000000.2	x^16 + 9x^14 + 18x^12 - 22x^10 - 59x^8 - 6x^6 + 34x^4 + 15x^2 + 1	\( 2^{8}\cdot 5^{8}\cdot 19^{4}\cdot 103^{4} \)	16T1665	Trivial (GRH)
16.12.1466774336280100000000.3	x^16 - 8x^14 + 16x^12 + 20x^10 - 107x^8 + 128x^6 - 55x^4 + 5x^2 + 1	\( 2^{8}\cdot 5^{8}\cdot 19^{4}\cdot 103^{4} \)	16T1665	Trivial (GRH)
16.4.1466774336280100000000.3	x^16 + 9x^14 + 22x^12 + 3x^10 - 47x^8 - 41x^6 + 8x^4 + 13x^2 + 1	\( 2^{8}\cdot 5^{8}\cdot 19^{4}\cdot 103^{4} \)	16T1665	Trivial (GRH)
16.8.2719063053560725897216.2	x^16 + 4x^14 - 14x^12 - 48x^10 + 43x^8 + 144x^6 + 2x^4 - 44x^2 + 1	\( 2^{40}\cdot 223^{4} \)	16T1665	Trivial (GRH)
16.8.2719063053560725897216.3	x^16 - 4x^14 - 14x^12 + 48x^10 + 43x^8 - 144x^6 + 2x^4 + 44x^2 + 1	\( 2^{40}\cdot 223^{4} \)	16T1665	Trivial (GRH)
16.0.6503016040038400000000.1	x^16 + 13x^14 + 69x^12 + 206x^10 + 408x^8 + 560x^6 + 528x^4 + 352x^2 + 64	\( 2^{22}\cdot 5^{8}\cdot 251^{4} \)	16T1665	Trivial
16.8.6503016040038400000000.1	x^16 - 13x^14 + 69x^12 - 206x^10 + 408x^8 - 560x^6 + 528x^4 - 352x^2 + 64	\( 2^{22}\cdot 5^{8}\cdot 251^{4} \)	16T1665	Trivial (GRH)
16.4.51371070174496900000000.1	x^16 - 2x^15 + 9x^14 - 9x^13 - 54x^12 + 219x^11 - 518x^10 + 1043x^9 - 1684x^8 + 3053x^7 - 4897x^6 + 7067x^5 - 8004x^4 + 6490x^3 - 3700x^2 + 539x + 271	\( 2^{8}\cdot 5^{8}\cdot 283^{6} \)	16T1665	Trivial (GRH)
16.4.51371070174496900000000.2	x^16 - 3x^15 + 6x^14 + 4x^13 - 14x^12 - 23x^11 + 77x^10 - 169x^9 - 516x^8 + 1055x^7 - 3904x^6 + 3377x^5 - 1410x^4 - 1529x^3 + 1435x^2 - 312x - 11	\( 2^{8}\cdot 5^{8}\cdot 283^{6} \)	16T1665	Trivial (GRH)
16.8.53909686445544769140625.1	x^16 - 7x^15 + 21x^14 - 13x^13 - 93x^12 + 292x^11 - 306x^10 - 200x^9 + 898x^8 - 862x^7 - 368x^6 + 1340x^5 - 535x^4 - 761x^3 + 681x^2 + 595x + 101	\( 5^{8}\cdot 19^{4}\cdot 97^{2}\cdot 103^{4} \)	16T1665	Trivial (GRH)
16.12.332163245093145255346176.1	x^16 - 10x^14 + 27x^12 + 12x^10 - 108x^8 + 26x^6 + 95x^4 - 28x^2 + 1	\( 2^{28}\cdot 3^{8}\cdot 659^{4} \)	16T1665	Trivial (GRH)
16.4.332163245093145255346176.1	x^16 + 10x^14 + 27x^12 - 12x^10 - 108x^8 - 26x^6 + 95x^4 + 28x^2 + 1	\( 2^{28}\cdot 3^{8}\cdot 659^{4} \)	16T1665	$[2]$ (GRH)
16.12.363186685016078400000000.1	x^16 - 20x^14 + 116x^12 - 204x^10 - 12x^8 + 318x^6 - 234x^4 + 27x^2 + 9	\( 2^{12}\cdot 3^{14}\cdot 5^{8}\cdot 83^{4} \)	16T1665	Trivial (GRH)
16.4.363186685016078400000000.1	x^16 + 7x^14 - 16x^12 - 87x^10 + 12x^8 + 276x^6 + 279x^4 + 90x^2 + 9	\( 2^{12}\cdot 3^{14}\cdot 5^{8}\cdot 83^{4} \)	16T1665	Trivial (GRH)
16.8.363186685016078400000000.1	x^16 - 3x^14 - 27x^12 + 94x^10 + 57x^8 - 279x^6 - 50x^4 + 54x^2 + 9	\( 2^{12}\cdot 3^{14}\cdot 5^{8}\cdot 83^{4} \)	16T1665	Trivial (GRH)
16.0.856618051132000300957696.1	x^16 - 4x^14 - 2x^12 - 20x^10 + 207x^8 + 468x^6 + 1902x^4 + 1888x^2 + 3481	\( 2^{24}\cdot 19^{4}\cdot 59^{2}\cdot 103^{4} \)	16T1665	$[2]$ (GRH)
16.8.1008851902822440000000000.5	x^16 + 16x^14 + 5x^12 - 412x^10 + 344x^8 + 205x^6 - 190x^4 - 25x^2 + 25	\( 2^{12}\cdot 3^{12}\cdot 5^{10}\cdot 83^{4} \)	16T1665	Trivial (GRH)
16.8.1008851902822440000000000.6	x^16 - 11x^14 + 2x^12 + 161x^10 + 71x^8 - 530x^6 - 355x^4 + 500x^2 + 400	\( 2^{12}\cdot 3^{12}\cdot 5^{10}\cdot 83^{4} \)	16T1665	Trivial (GRH)
16.0.3095345822428295086473216.1	x^16 - 4x^14 - 4x^12 + 44x^10 + 102x^8 - 684x^6 + 2540x^4 - 3804x^2 + 7569	\( 2^{26}\cdot 3^{2}\cdot 8461^{4} \)	16T1665	$[12]$ (GRH)
16.12.16141630445159040000000000.1	x^16 - 20x^14 + 134x^12 - 335x^10 + 109x^8 + 650x^6 - 505x^4 - 250x^2 + 25	\( 2^{16}\cdot 3^{12}\cdot 5^{10}\cdot 83^{4} \)	16T1665	Trivial (GRH)
16.4.16141630445159040000000000.1	x^16 + 20x^14 + 134x^12 + 335x^10 + 109x^8 - 650x^6 - 505x^4 + 250x^2 + 25	\( 2^{16}\cdot 3^{12}\cdot 5^{10}\cdot 83^{4} \)	16T1665	$[2]$ (GRH)
16.12.16141630445159040000000000.2	x^16 - 11x^14 + 17x^12 + 166x^10 - 569x^8 - 220x^6 + 2855x^4 - 3100x^2 + 400	\( 2^{16}\cdot 3^{12}\cdot 5^{10}\cdot 83^{4} \)	16T1665	Trivial (GRH)
16.4.16141630445159040000000000.2	x^16 + 11x^14 + 17x^12 - 166x^10 - 569x^8 + 220x^6 + 2855x^4 + 3100x^2 + 400	\( 2^{16}\cdot 3^{12}\cdot 5^{10}\cdot 83^{4} \)	16T1665	$[2, 2]$ (GRH)
16.16.108517832495346918400000000.1	x^16 - 35x^14 + 391x^12 - 2067x^10 + 5870x^8 - 9271x^6 + 7839x^4 - 3026x^2 + 289	\( 2^{16}\cdot 5^{8}\cdot 17^{2}\cdot 19^{4}\cdot 103^{4} \)	16T1665	Trivial (GRH)
16.16.9063517887843869971686400000000.1	x^16 - 137x^14 + 7159x^12 - 182393x^10 + 2442050x^8 - 17357629x^6 + 61889061x^4 - 92290705x^2 + 24137569	\( 2^{16}\cdot 5^{8}\cdot 17^{6}\cdot 19^{4}\cdot 103^{4} \)	16T1665	Trivial (GRH)
16.0.14142152448626105752806400000000.1	x^16 + 130x^14 + 6838x^12 + 186090x^10 + 2778300x^8 + 22225440x^6 + 85958071x^4 + 122433150x^2 + 37662769	\( 2^{16}\cdot 5^{8}\cdot 17^{2}\cdot 19^{8}\cdot 103^{4} \)	16T1665	$[2, 2, 4, 3868]$ (GRH)
16.8.415606912264471900087321600000000.1	x^16 + 31x^14 - 3533x^12 - 36902x^10 + 2503791x^8 + 22902790x^6 - 424623514x^4 - 4016433294x^2 + 1106826361	\( 2^{16}\cdot 5^{8}\cdot 17^{2}\cdot 19^{6}\cdot 103^{6} \)	16T1665	$[2]$ (GRH)
16.8.415606912264471900087321600000000.2	x^16 + 5x^14 - 2833x^12 + 3782x^10 + 1658203x^8 - 9258928x^6 - 209128592x^4 + 1233880672x^2 + 1106826361	\( 2^{16}\cdot 5^{8}\cdot 17^{2}\cdot 19^{6}\cdot 103^{6} \)	16T1665	$[2, 2]$ (GRH)
16.0.12213777651561724066555110400000000.1	x^16 + 356x^14 + 49410x^12 + 3419732x^10 + 125045630x^8 + 2344543474x^6 + 19807098481x^4 + 51865194328x^2 + 32527204609	\( 2^{16}\cdot 5^{8}\cdot 17^{2}\cdot 19^{4}\cdot 103^{8} \)	16T1665	$[2, 2, 2, 300472]$ (GRH)