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 62)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.163216000000000000.2	x^16 - x^14 - 4x^10 + 14x^8 - 19x^6 + 15x^4 - 6x^2 + 1	\( 2^{16}\cdot 5^{12}\cdot 101^{2} \)	16T1385	Trivial
16.0.163216000000000000.3	x^16 - 2x^14 + 3x^10 - x^8 - 3x^6 + 2x^2 + 1	\( 2^{16}\cdot 5^{12}\cdot 101^{2} \)	16T1385	Trivial
16.0.579121000000000000.1	x^16 - 6x^15 + 20x^14 - 49x^13 + 102x^12 - 175x^11 + 258x^10 - 345x^9 + 403x^8 - 403x^7 + 370x^6 - 287x^5 + 186x^4 - 103x^3 + 42x^2 - 10x + 1	\( 2^{12}\cdot 5^{12}\cdot 761^{2} \)	16T1385	Trivial
16.0.25563136000000000000.1	x^16 - 4x^14 + 9x^12 - 8x^10 + 4x^8 + 4x^6 + x^4 + 8x^2 + 1	\( 2^{24}\cdot 5^{12}\cdot 79^{2} \)	16T1385	$[2]$
16.4.25563136000000000000.1	x^16 + 4x^14 + 9x^12 + 8x^10 + 4x^8 - 4x^6 + x^4 - 8x^2 + 1	\( 2^{24}\cdot 5^{12}\cdot 79^{2} \)	16T1385	Trivial
16.8.31966831630052491264.1	x^16 - 8x^15 + 24x^14 - 24x^13 - 46x^12 + 176x^11 - 212x^10 + 8x^9 + 318x^8 - 448x^7 + 248x^6 + 80x^5 - 256x^4 + 224x^3 - 112x^2 + 32x - 4	\( 2^{48}\cdot 337^{2} \)	16T1385	Trivial
16.8.41744722906494140625.1	x^16 - 2x^15 - 4x^14 + 22x^13 - 4x^12 - 71x^11 + 74x^10 + 121x^9 - 178x^8 - 114x^7 + 159x^6 + 14x^5 - 74x^4 + 22x^3 + 11x^2 - 7x + 1	\( 3^{8}\cdot 5^{14}\cdot 1021^{2} \)	16T1385	Trivial (GRH)
16.0.93219557956761760000.2	x^16 - 5x^15 + 9x^14 + 7x^13 - 57x^12 + 96x^11 - 19x^10 - 195x^9 + 408x^8 - 452x^7 + 356x^6 - 263x^5 + 245x^4 - 222x^3 + 152x^2 - 64x + 16	\( 2^{8}\cdot 5^{4}\cdot 17^{12} \)	16T1385	Trivial
16.0.110166016000000000000.1	x^16 + 10x^14 + 37x^12 + 70x^10 + 84x^8 + 70x^6 + 33x^4 + 10x^2 + 1	\( 2^{28}\cdot 5^{12}\cdot 41^{2} \)	16T1385	$[2]$
16.4.110166016000000000000.1	x^16 - 7x^12 - 16x^8 + 40x^6 - 3x^4 + 1	\( 2^{28}\cdot 5^{12}\cdot 41^{2} \)	16T1385	Trivial
16.8.110166016000000000000.1	x^16 - 10x^14 + 37x^12 - 70x^10 + 84x^8 - 70x^6 + 33x^4 - 10x^2 + 1	\( 2^{28}\cdot 5^{12}\cdot 41^{2} \)	16T1385	Trivial (GRH)
16.4.110166016000000000000.2	x^16 - 7x^12 - 16x^8 - 40x^6 - 3x^4 + 1	\( 2^{28}\cdot 5^{12}\cdot 41^{2} \)	16T1385	Trivial
16.0.148254976000000000000.1	x^16 + 2x^14 - 8x^12 - 25x^10 + x^8 + 60x^6 + 88x^4 + 56x^2 + 16	\( 2^{20}\cdot 5^{12}\cdot 761^{2} \)	16T1385	Trivial
16.4.334692732183837890625.1	x^16 - x^15 - 8x^14 + 12x^13 + 15x^12 - 37x^11 - 13x^10 + 66x^9 + 31x^8 - 110x^7 - 20x^6 + 135x^5 - 30x^4 - 80x^3 - 15x^2 - 30x - 5	\( 3^{8}\cdot 5^{14}\cdot 7^{4}\cdot 59^{2} \)	16T1385	Trivial
16.0.365421456000000000000.1	x^16 + 10x^14 + 38x^12 + 70x^10 + 69x^8 + 45x^6 + 27x^4 + 10x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1385	$[2]$
16.0.365421456000000000000.2	x^16 + 3x^14 + 7x^12 + 5x^10 + 11x^8 + 10x^6 + 3x^4 + 4x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1385	$[2]$
16.12.365421456000000000000.3	x^16 - 10x^14 + 38x^12 - 70x^10 + 69x^8 - 45x^6 + 27x^4 - 10x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1385	Trivial (GRH)
16.0.390615696000000000000.3	x^16 + 6x^14 + 13x^12 + 15x^10 + 11x^8 + 2x^4 + 12x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 61^{2} \)	16T1385	$[2]$
16.8.390615696000000000000.4	x^16 - 6x^14 + 13x^12 - 30x^10 + 56x^8 - 75x^6 + 47x^4 - 12x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 61^{2} \)	16T1385	Trivial (GRH)
16.4.409010176000000000000.1	x^16 - 4x^15 + 2x^14 + 4x^13 - 19x^12 + 40x^11 - 62x^10 + 80x^9 - 88x^8 + 80x^7 - 62x^6 + 40x^5 - 19x^4 + 4x^3 + 2x^2 - 4x + 1	\( 2^{28}\cdot 5^{12}\cdot 79^{2} \)	16T1385	Trivial (GRH)
16.8.409010176000000000000.1	x^16 - 6x^15 + 5x^14 + 24x^13 - 21x^12 - 88x^11 + 101x^10 + 128x^9 - 214x^8 - 44x^7 + 199x^6 - 44x^5 - 81x^4 + 38x^3 + 10x^2 - 8x + 1	\( 2^{28}\cdot 5^{12}\cdot 79^{2} \)	16T1385	Trivial (GRH)
16.4.1491512927308188160000.1	x^16 - 3x^15 - x^14 + 4x^13 + 6x^12 - 15x^11 + 5x^10 + 38x^9 - 21x^8 - 19x^7 - 45x^6 + 42x^5 - 72x^4 + 162x^3 - 30x^2 + 64x - 13	\( 2^{12}\cdot 5^{4}\cdot 17^{12} \)	16T1385	Trivial
16.0.3363536016000000000000.1	x^16 + 7x^14 + 16x^12 + 16x^10 + 24x^8 + 53x^6 + 49x^4 + 14x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 179^{2} \)	16T1385	$[2]$
16.12.3363536016000000000000.1	x^16 - 7x^14 + 16x^12 - 16x^10 + 24x^8 - 53x^6 + 49x^4 - 14x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 179^{2} \)	16T1385	Trivial (GRH)
16.4.3363536016000000000000.1	x^16 + 4x^14 + 4x^12 - 17x^10 - 66x^8 - 79x^6 - 29x^4 + 2x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 179^{2} \)	16T1385	Trivial (GRH)
16.8.3363536016000000000000.1	x^16 - 4x^14 + 4x^12 + 17x^10 - 66x^8 + 79x^6 - 29x^4 - 2x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 179^{2} \)	16T1385	Trivial (GRH)
16.4.3363536016000000000000.2	x^16 + 2x^14 - 9x^12 - 34x^10 - 61x^8 - 17x^6 + 19x^4 + 9x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 179^{2} \)	16T1385	Trivial (GRH)
16.8.3363536016000000000000.2	x^16 - 9x^14 + 19x^12 - 8x^10 - 16x^8 + 29x^6 - 9x^4 - 7x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 179^{2} \)	16T1385	Trivial (GRH)
16.0.3439118736000000000000.1	x^16 + 9x^14 + 33x^12 + 65x^10 + 76x^8 + 60x^6 + 37x^4 + 13x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 181^{2} \)	16T1385	$[2]$
16.8.3439118736000000000000.3	x^16 - 9x^14 + 33x^12 - 65x^10 + 76x^8 - 60x^6 + 37x^4 - 13x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 181^{2} \)	16T1385	Trivial (GRH)
16.0.6544162816000000000000.1	x^16 + 2x^14 + 11x^12 + 26x^10 + 24x^8 + 8x^6 - x^4 + 4x^2 + 1	\( 2^{32}\cdot 5^{12}\cdot 79^{2} \)	16T1385	$[2]$
16.4.6544162816000000000000.1	x^16 - 2x^14 + 11x^12 - 26x^10 + 24x^8 - 8x^6 - x^4 - 4x^2 + 1	\( 2^{32}\cdot 5^{12}\cdot 79^{2} \)	16T1385	Trivial (GRH)
16.0.7587106816000000000000.1	x^16 + 2x^14 + 14x^12 - 12x^10 + 51x^8 - 100x^6 + 110x^4 - 50x^2 + 25	\( 2^{24}\cdot 5^{12}\cdot 1361^{2} \)	16T1385	$[4]$
16.0.7587106816000000000000.2	x^16 - 2x^14 + 14x^12 + 12x^10 + 51x^8 + 100x^6 + 110x^4 + 50x^2 + 25	\( 2^{24}\cdot 5^{12}\cdot 1361^{2} \)	16T1385	$[4]$
16.4.29599137936000000000000.1	x^16 - 12x^12 - 81x^8 - 135x^6 + 432x^4 + 405x^2 + 81	\( 2^{16}\cdot 3^{12}\cdot 5^{12}\cdot 59^{2} \)	16T1385	Trivial (GRH)
16.0.37953273856000000000000.1	x^16 + 8x^14 + 21x^12 + 84x^10 + 224x^8 + 212x^6 + 89x^4 + 16x^2 + 1	\( 2^{28}\cdot 5^{12}\cdot 761^{2} \)	16T1385	$[2]$ (GRH)
16.8.37953273856000000000000.1	x^16 - 2x^14 - 19x^12 + 14x^10 + 124x^8 - 78x^6 + 49x^4 - 14x^2 + 1	\( 2^{28}\cdot 5^{12}\cdot 761^{2} \)	16T1385	Trivial (GRH)
16.8.51572772974449630642176.1	x^16 - 8x^14 - 8x^13 + 16x^12 + 40x^11 - 24x^10 - 48x^9 + 70x^8 + 32x^7 - 88x^6 - 88x^5 + 120x^4 + 216x^3 - 88x^2 - 112x + 31	\( 2^{58}\cdot 3^{4}\cdot 47^{2} \)	16T1385	Trivial (GRH)
16.4.121393709056000000000000.1	x^16 + 8x^14 + 22x^12 - 140x^10 - 249x^8 + 620x^6 - 402x^4 + 84x^2 + 1	\( 2^{28}\cdot 5^{12}\cdot 1361^{2} \)	16T1385	Trivial (GRH)
16.4.121393709056000000000000.2	x^16 - 8x^14 + 22x^12 + 140x^10 - 249x^8 - 620x^6 - 402x^4 - 84x^2 + 1	\( 2^{28}\cdot 5^{12}\cdot 1361^{2} \)	16T1385	Trivial (GRH)
16.4.142097995473827886268416.1	x^16 - 4x^15 + 14x^14 - 24x^13 + 29x^12 - 32x^11 - 2x^10 - 68x^9 - 102x^8 - 44x^7 - 94x^6 - 51x^4 - 6x^2 - 4x + 1	\( 2^{46}\cdot 3^{4}\cdot 4993^{2} \)	16T1385	Trivial (GRH)
16.8.1193372717056000000000000.1	x^16 - 6x^15 - 2x^14 + 76x^13 - 120x^12 - 230x^11 + 814x^10 - 338x^9 - 1619x^8 + 2522x^7 + 554x^6 - 5022x^5 + 4448x^4 + 604x^3 - 2816x^2 + 1134x - 19	\( 2^{24}\cdot 5^{12}\cdot 13^{4}\cdot 101^{2} \)	16T1385	Trivial (GRH)
16.8.1193372717056000000000000.2	x^16 - 22x^14 - 2x^13 + 133x^12 + 38x^11 - 30x^10 - 70x^9 - 1159x^8 - 1068x^7 + 100x^6 + 304x^5 + 2760x^4 + 6000x^3 + 4592x^2 + 1248x + 16	\( 2^{24}\cdot 5^{12}\cdot 13^{4}\cdot 101^{2} \)	16T1385	Trivial (GRH)
16.0.7772780323046872376672256.1	x^16 + 8x^14 - 32x^13 - 20x^12 - 80x^11 + 296x^10 + 704x^9 + 110x^8 - 2688x^7 - 4488x^6 - 608x^5 + 7948x^4 + 13328x^3 + 10872x^2 + 4736x + 881	\( 2^{58}\cdot 3^{4}\cdot 577^{2} \)	16T1385	$[2]$ (GRH)
16.8.7772780323046872376672256.1	x^16 - 16x^14 - 32x^13 + 40x^12 + 272x^11 + 432x^10 + 176x^9 - 784x^8 - 1696x^7 - 2176x^6 - 1504x^5 + 1328x^4 + 2816x^3 + 4608x^2 - 128x - 248	\( 2^{58}\cdot 3^{4}\cdot 577^{2} \)	16T1385	Trivial (GRH)
16.4.11509937633380058787741696.1	x^16 - 4x^15 - 2x^14 + 16x^13 - 3x^12 - 24x^11 + 14x^10 + 68x^9 - 102x^8 - 108x^7 + 210x^6 + 8x^5 - 83x^4 - 8x^3 + 10x^2 + 4x + 1	\( 2^{46}\cdot 3^{8}\cdot 4993^{2} \)	16T1385	Trivial (GRH)
16.16.29834317926400000000000000.1	x^16 - 4x^15 - 30x^14 + 130x^13 + 330x^12 - 1642x^11 - 1552x^10 + 10190x^9 + 2225x^8 - 32570x^7 + 4258x^6 + 52348x^5 - 13380x^4 - 39980x^3 + 10300x^2 + 11376x - 2404	\( 2^{24}\cdot 5^{14}\cdot 13^{4}\cdot 101^{2} \)	16T1385	Trivial (GRH)
16.0.31037260546487147588222976.1	x^16 + 24x^14 + 212x^12 - 64x^11 + 680x^10 - 352x^9 + 714x^8 + 864x^7 - 776x^6 - 256x^5 + 1372x^4 - 160x^3 - 984x^2 + 96x + 353	\( 2^{58}\cdot 3^{4}\cdot 1153^{2} \)	16T1385	$[16]$ (GRH)
16.16.31037260546487147588222976.1	x^16 - 32x^14 + 352x^12 - 64x^11 - 1712x^10 + 544x^9 + 3716x^8 - 928x^7 - 3840x^6 + 224x^5 + 1728x^4 + 256x^3 - 224x^2 - 64x - 4	\( 2^{58}\cdot 3^{4}\cdot 1153^{2} \)	16T1385	Trivial (GRH)
16.0.114713585069001347360475625.1	x^16 - x^15 + 3x^14 + 8x^13 + 14x^12 + 25x^11 + 54x^10 + 28x^9 + 77x^8 - 28x^7 + 54x^6 - 25x^5 + 14x^4 - 8x^3 + 3x^2 + x + 1	\( 5^{4}\cdot 17^{12}\cdot 17749^{2} \)	16T1385	$[15]$ (GRH)