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 78)

Label	Polynomial	Discriminant	Galois group	Class group
16.4.173722240000000000.1	x^16 - 2x^15 - 3x^14 + 4x^13 + 6x^12 + 8x^11 - 18x^10 - 28x^9 + 30x^8 + 30x^7 - 17x^6 - 22x^5 - 2x^4 + 14x^3 + 3x^2 - 4x - 1	\( 2^{16}\cdot 5^{10}\cdot 521^{2} \)	16T1559	Trivial
16.4.1133799040000000000.1	x^16 - 4x^15 + 7x^14 - 14x^13 + 28x^12 - 58x^11 + 120x^10 - 192x^9 + 261x^8 - 296x^7 + 275x^6 - 226x^5 + 153x^4 - 82x^3 + 33x^2 - 8x + 1	\( 2^{16}\cdot 5^{10}\cdot 11^{6} \)	16T1559	Trivial
16.4.2081789069150390625.1	x^16 - 2x^15 + 3x^14 - 3x^13 - 2x^12 + 16x^11 - 45x^10 + 66x^9 - 54x^8 + 2x^7 + 60x^6 - 92x^5 + 83x^4 - 51x^3 + 22x^2 - 6x + 1	\( 3^{4}\cdot 5^{10}\cdot 29^{4}\cdot 61^{2} \)	16T1559	Trivial
16.4.2081789069150390625.2	x^16 - 3x^15 + 8x^14 - 14x^13 + 17x^12 - 12x^11 - 9x^10 + 33x^9 - 46x^8 + 44x^7 - 21x^6 + 6x^5 + 7x^4 - 12x^3 + 2x^2 - x + 1	\( 3^{4}\cdot 5^{10}\cdot 29^{4}\cdot 61^{2} \)	16T1559	Trivial
16.8.6116053585556640625.1	x^16 - 7x^14 - x^13 + 9x^12 + 15x^11 - x^10 - 8x^9 - 17x^8 - 8x^7 - x^6 + 15x^5 + 9x^4 - x^3 - 7x^2 + 1	\( 5^{10}\cdot 29^{4}\cdot 941^{2} \)	16T1559	Trivial
16.0.17925988595712890625.1	x^16 - x^15 + x^14 + 2x^13 - x^12 + x^11 + 9x^10 - 24x^9 + 48x^8 - 62x^7 + 96x^6 - 113x^5 + 109x^4 - 59x^3 + 24x^2 - 7x + 1	\( 3^{4}\cdot 5^{10}\cdot 29^{4}\cdot 179^{2} \)	16T1559	Trivial
16.4.17925988595712890625.1	x^16 - 2x^15 + 3x^14 + 2x^13 - 14x^12 + 31x^11 - 56x^10 + 66x^9 - 59x^8 + 13x^7 + 58x^6 - 87x^5 + 72x^4 - 35x^3 + 6x^2 - x + 1	\( 3^{4}\cdot 5^{10}\cdot 29^{4}\cdot 179^{2} \)	16T1559	Trivial
16.8.17925988595712890625.1	x^16 - 2x^15 - 7x^14 + 14x^13 + 11x^12 - 42x^11 + 12x^10 + 58x^9 - 52x^8 - 26x^7 + 59x^6 - 13x^5 - 26x^4 + 13x^3 + x^2 - 3x + 1	\( 3^{4}\cdot 5^{10}\cdot 29^{4}\cdot 179^{2} \)	16T1559	Trivial
16.4.17925988595712890625.2	x^16 - x^15 + 4x^14 + 5x^13 + 2x^12 + 24x^11 + 15x^10 + 36x^9 + 5x^8 - 36x^7 + 15x^6 - 24x^5 + 2x^4 - 5x^3 + 4x^2 + x + 1	\( 3^{4}\cdot 5^{10}\cdot 29^{4}\cdot 179^{2} \)	16T1559	Trivial
16.0.29648025000000000000.1	x^16 - 5x^15 + 18x^14 - 50x^13 + 113x^12 - 205x^11 + 311x^10 - 415x^9 + 470x^8 - 405x^7 + 241x^6 - 95x^5 + 33x^4 - 20x^3 + 13x^2 - 5x + 1	\( 2^{12}\cdot 3^{4}\cdot 5^{14}\cdot 11^{4} \)	16T1559	$[2]$
16.4.29648025000000000000.1	x^16 - 3x^15 + 4x^14 - 8x^13 - 2x^12 + 17x^11 - 34x^10 + 46x^9 - 42x^8 - 13x^7 + 44x^6 - 44x^5 - 22x^4 + 39x^3 - 14x^2 - 34x + 1	\( 2^{12}\cdot 3^{4}\cdot 5^{14}\cdot 11^{4} \)	16T1559	Trivial
16.0.29648025000000000000.2	x^16 - 6x^15 + 23x^14 - 67x^13 + 156x^12 - 306x^11 + 520x^10 - 771x^9 + 1004x^8 - 1152x^7 + 1170x^6 - 1043x^5 + 801x^4 - 514x^3 + 257x^2 - 88x + 16	\( 2^{12}\cdot 3^{4}\cdot 5^{14}\cdot 11^{4} \)	16T1559	$[2]$
16.4.29648025000000000000.2	x^16 - 2x^15 + 5x^13 - 5x^12 + 9x^11 - 23x^10 + 15x^9 - 10x^8 + 25x^7 + 7x^6 - 9x^5 - 5x^4 - 25x^3 - 5x^2 - 8x + 1	\( 2^{12}\cdot 3^{4}\cdot 5^{14}\cdot 11^{4} \)	16T1559	Trivial
16.0.52438914916416015625.1	x^16 - 2x^15 - 2x^14 + 2x^13 + 13x^12 - 9x^11 - 20x^10 + 11x^9 + 26x^8 - 3x^7 - 15x^6 + 8x^5 + 18x^4 + 4x^3 - 3x^2 - x + 1	\( 5^{10}\cdot 11^{6}\cdot 1741^{2} \)	16T1559	Trivial
16.0.52438914916416015625.2	x^16 - 5x^15 + 15x^14 - 37x^13 + 70x^12 - 97x^11 + 112x^10 - 143x^9 + 213x^8 - 316x^7 + 409x^6 - 382x^5 + 217x^4 - 90x^3 + 74x^2 - 59x + 19	\( 5^{10}\cdot 11^{6}\cdot 1741^{2} \)	16T1559	Trivial
16.0.95585818240000000000.1	x^16 - x^14 + 2x^12 - 9x^10 - 4x^8 + 10x^6 + 10x^4 + 25x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 11^{4}\cdot 101^{2} \)	16T1559	Trivial
16.0.95585818240000000000.2	x^16 + x^14 + 2x^12 + 9x^10 - 4x^8 - 10x^6 + 10x^4 - 25x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 11^{4}\cdot 101^{2} \)	16T1559	Trivial
16.0.152901339638916015625.1	x^16 - 2x^15 - 8x^13 + 34x^12 - 41x^11 + 29x^10 - 51x^9 + 61x^8 - 13x^7 - 4x^6 - 17x^5 + 9x^4 + x^3 + x + 1	\( 5^{12}\cdot 29^{4}\cdot 941^{2} \)	16T1559	$[2]$
16.0.163410202240000000000.1	x^16 + 4x^14 + 2x^12 - 14x^10 - 19x^8 + 25x^6 + 80x^4 + 75x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 19^{2}\cdot 29^{4} \)	16T1559	Trivial
16.4.163410202240000000000.1	x^16 - 4x^14 + 10x^12 - 22x^10 + 29x^8 - 35x^6 + 40x^4 - 25x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 19^{2}\cdot 29^{4} \)	16T1559	Trivial
16.0.163410202240000000000.2	x^16 + 7x^14 + 18x^12 + 17x^10 - 9x^8 - 20x^6 + 20x^4 + 50x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 19^{2}\cdot 29^{4} \)	16T1559	Trivial
16.4.163410202240000000000.2	x^16 - 3x^14 + 10x^12 - 21x^10 + 39x^8 - 60x^6 + 60x^4 - 50x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 19^{2}\cdot 29^{4} \)	16T1559	Trivial
16.0.163410202240000000000.3	x^16 - 6x^14 + 12x^12 + 11x^10 - 74x^8 + 85x^6 + 40x^4 - 75x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 19^{2}\cdot 29^{4} \)	16T1559	Trivial
16.4.163410202240000000000.3	x^16 + 9x^12 - 15x^10 + 19x^8 - 80x^6 + 60x^4 + 25	\( 2^{16}\cdot 5^{10}\cdot 19^{2}\cdot 29^{4} \)	16T1559	Trivial
16.0.760921191040000000000.1	x^16 + 11x^14 + 45x^12 + 88x^10 + 99x^8 + 110x^6 + 140x^4 + 100x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 41^{2} \)	16T1559	Trivial
16.8.760921191040000000000.1	x^16 - 11x^14 + 45x^12 - 88x^10 + 99x^8 - 110x^6 + 140x^4 - 100x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 41^{2} \)	16T1559	Trivial
16.0.760921191040000000000.2	x^16 + 3x^14 + 8x^12 + 18x^10 + 41x^8 + 140x^6 + 210x^4 + 125x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 41^{2} \)	16T1559	$[2]$
16.8.760921191040000000000.2	x^16 - 3x^14 + 8x^12 - 18x^10 + 41x^8 - 140x^6 + 210x^4 - 125x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 41^{2} \)	16T1559	Trivial
16.4.920103418270301814784.1	x^16 - 4x^12 + 40x^10 - 88x^8 + 112x^6 - 88x^4 + 16x^2 + 4	\( 2^{56}\cdot 113^{2} \)	16T1559	Trivial
16.4.920103418270301814784.2	x^16 - 4x^12 - 40x^10 - 88x^8 - 112x^6 - 88x^4 - 16x^2 + 4	\( 2^{56}\cdot 113^{2} \)	16T1559	Trivial
16.8.5143601065453134765625.1	x^16 - 2x^15 - 14x^14 + 33x^13 + 33x^12 - 75x^11 - 67x^10 + 17x^9 + 115x^8 + 82x^7 + 7x^6 - 61x^5 - 97x^4 - 17x^3 - 39x^2 + 4x + 1	\( 5^{10}\cdot 29^{6}\cdot 941^{2} \)	16T1559	Trivial
16.0.8183508897293437763584.1	x^16 + 8x^14 + 8x^12 - 16x^10 + 18x^8 + 72x^6 + 56x^4 + 16x^2 + 1	\( 2^{56}\cdot 337^{2} \)	16T1559	$[2]$
16.8.8183508897293437763584.1	x^16 - 8x^14 + 8x^12 + 16x^10 + 18x^8 - 72x^6 + 56x^4 - 16x^2 + 1	\( 2^{56}\cdot 337^{2} \)	16T1559	Trivial (GRH)
16.0.8183508897293437763584.2	x^16 + 8x^14 + 20x^12 + 40x^10 + 182x^8 + 472x^6 + 468x^4 + 120x^2 + 1	\( 2^{56}\cdot 337^{2} \)	16T1559	$[2]$
16.8.8183508897293437763584.2	x^16 - 8x^14 + 20x^12 - 40x^10 + 182x^8 - 472x^6 + 468x^4 - 120x^2 + 1	\( 2^{56}\cdot 337^{2} \)	16T1559	Trivial (GRH)
16.0.14503673933440000000000.1	x^16 + 13x^14 + 65x^12 + 171x^10 + 279x^8 + 320x^6 + 260x^4 + 125x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 179^{2} \)	16T1559	Trivial
16.12.14503673933440000000000.1	x^16 - 13x^14 + 65x^12 - 171x^10 + 279x^8 - 320x^6 + 260x^4 - 125x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 179^{2} \)	16T1559	Trivial (GRH)
16.4.14503673933440000000000.1	x^16 + 8x^14 + 9x^12 - 33x^10 - 59x^8 - 150x^6 - 105x^4 + 125x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 179^{2} \)	16T1559	Trivial
16.8.14503673933440000000000.1	x^16 - x^14 - 10x^12 + 12x^10 - 31x^8 + 65x^6 + 15x^4 - 75x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 179^{2} \)	16T1559	Trivial
16.0.14503673933440000000000.2	x^16 + 11x^14 + 51x^12 + 161x^10 + 431x^8 + 790x^6 + 755x^4 + 300x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 179^{2} \)	16T1559	$[3]$
16.12.14503673933440000000000.2	x^16 - 11x^14 + 51x^12 - 161x^10 + 431x^8 - 790x^6 + 755x^4 - 300x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 179^{2} \)	16T1559	Trivial (GRH)
16.4.14503673933440000000000.2	x^16 + 5x^14 - 14x^12 - 70x^10 + 44x^8 + 165x^6 + 65x^4 + 50x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 179^{2} \)	16T1559	Trivial
16.8.14503673933440000000000.2	x^16 - 8x^14 + 9x^12 + 33x^10 - 59x^8 + 150x^6 - 105x^4 - 125x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 179^{2} \)	16T1559	Trivial
16.4.14503673933440000000000.3	x^16 + x^14 - 10x^12 - 12x^10 - 31x^8 - 65x^6 + 15x^4 + 75x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 179^{2} \)	16T1559	Trivial
16.8.14503673933440000000000.3	x^16 - 12x^14 + 54x^12 - 103x^10 + 6x^8 + 365x^6 - 705x^4 + 450x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 179^{2} \)	16T1559	Trivial
16.0.25601344017640000000000.1	x^16 + 10x^14 + 31x^12 + 85x^10 + 164x^8 + 245x^6 + 295x^4 + 175x^2 + 25	\( 2^{12}\cdot 5^{10}\cdot 89^{4}\cdot 101^{2} \)	16T1559	Trivial
16.8.25601344017640000000000.1	x^16 - 10x^14 + 31x^12 - 85x^10 + 164x^8 - 245x^6 + 295x^4 - 175x^2 + 25	\( 2^{12}\cdot 5^{10}\cdot 89^{4}\cdot 101^{2} \)	16T1559	Trivial (GRH)
16.4.27109425949418759765625.1	x^16 - 4x^15 + 10x^14 - 14x^13 - 2x^12 + 10x^11 - 32x^10 - 12x^9 - 63x^8 - 14x^7 - 58x^6 - 10x^5 - 27x^4 - 8x^3 - 5x^2 - 2x + 1	\( 3^{4}\cdot 5^{10}\cdot 29^{4}\cdot 6961^{2} \)	16T1559	Trivial
16.0.70071868016127643746304.1	x^16 + 4x^14 + 18x^12 - 4x^10 + 117x^8 - 88x^6 + 60x^4 + 4	\( 2^{50}\cdot 7^{6}\cdot 23^{2} \)	16T1559	$[2]$
16.4.146833965391572509765625.1	x^16 - 6x^15 + 3x^14 + 33x^13 - 179x^11 - 42x^10 + 619x^9 + 160x^8 - 1393x^7 - 12x^6 + 1601x^5 - 519x^4 - 320x^3 + 540x^2 - 530x + 55	\( 3^{4}\cdot 5^{12}\cdot 41^{4}\cdot 1621^{2} \)	16T1559	Trivial