Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 17 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.1008403552400000000000000.1	x^16 + 3x^14 - 10x^13 + 8x^12 + 6x^10 + 60x^9 + 135x^8 + 120x^7 + 161x^6 + 210x^5 + 153x^4 + 50x^3 + 48x^2 + 10x + 1	\( 2^{16}\cdot 5^{14}\cdot 1361^{3} \)	16T1354	$[8]$ (GRH)
16.8.1008403552400000000000000.1	x^16 - 10x^14 - 10x^13 - 20x^12 - 70x^11 + 200x^9 + 260x^8 - 150x^7 - 550x^6 - 100x^5 + 475x^4 + 350x^3 - 400x^2 + 25	\( 2^{16}\cdot 5^{14}\cdot 1361^{3} \)	16T1354	Trivial (GRH)
16.0.1008403552400000000000000.2	x^16 - 2x^15 + 15x^14 - 30x^13 + 70x^12 - 76x^11 + 72x^10 - 140x^9 + 45x^8 + 140x^7 + 72x^6 + 76x^5 + 70x^4 + 30x^3 + 15x^2 + 2x + 1	\( 2^{16}\cdot 5^{14}\cdot 1361^{3} \)	16T1354	$[8]$ (GRH)
16.8.1008403552400000000000000.2	x^16 - 4x^15 + 10x^14 - 30x^13 + 20x^12 + 58x^11 - 142x^10 + 120x^9 + 225x^8 - 130x^7 - 132x^6 - 62x^5 + 85x^4 + 80x^3 - 25x^2 - 14x + 1	\( 2^{16}\cdot 5^{14}\cdot 1361^{3} \)	16T1354	Trivial (GRH)
16.4.5800246632584641733722112.1	x^16 - 28x^12 - 112x^10 - 178x^8 - 128x^6 - 12x^4 + 48x^2 + 17	\( 2^{70}\cdot 17^{3} \)	16T1354	Trivial (GRH)
16.4.5800246632584641733722112.2	x^16 - 28x^12 + 112x^10 - 178x^8 + 128x^6 - 12x^4 - 48x^2 + 17	\( 2^{70}\cdot 17^{3} \)	16T1354	Trivial (GRH)
16.10.7358939853847283935546875.1	x^16 - 2x^15 - 11x^14 - 2x^13 - 82x^12 + 348x^11 + 1316x^10 - 2056x^9 - 3997x^8 + 2193x^7 - 201x^6 + 6619x^5 + 7738x^4 - 6414x^3 + 2491x^2 - 5631x + 2371	\( -\,3^{8}\cdot 5^{14}\cdot 179^{5} \)	16T1354	Trivial (GRH)
16.2.7358939853847283935546875.1	x^16 - 2x^15 + 15x^14 - 25x^13 + 55x^12 - 161x^11 - 93x^10 - 1435x^9 - 2520x^8 - 7600x^7 - 14958x^6 - 27119x^5 - 30590x^4 - 21985x^3 - 6870x^2 + 4027x + 3001	\( -\,3^{8}\cdot 5^{14}\cdot 179^{5} \)	16T1354	$[2, 2]$ (GRH)
16.6.7358939853847283935546875.1	x^16 - 4x^15 + 10x^14 + 20x^13 - 125x^12 + 83x^11 + 433x^10 - 1840x^9 + 1755x^8 + 4880x^7 - 14637x^6 + 19148x^5 + 1025x^4 - 43515x^3 + 64680x^2 - 69144x + 39511	\( -\,3^{8}\cdot 5^{14}\cdot 179^{5} \)	16T1354	Trivial (GRH)
16.6.7358939853847283935546875.2	x^16 - 3x^15 + 16x^14 - 17x^13 - 24x^12 + 261x^11 - 876x^10 + 614x^9 - 68x^8 - 7841x^7 + 5959x^6 + 2021x^5 - 11234x^4 + 23063x^3 + 85241x^2 + 92597x + 33571	\( -\,3^{8}\cdot 5^{14}\cdot 179^{5} \)	16T1354	Trivial (GRH)
16.10.23842965126465199951171875.1	x^16 - 5x^15 - 10x^14 + 50x^13 + 29x^12 + 110x^11 + 120x^10 - 2370x^9 - 3524x^8 + 3450x^7 + 22485x^6 + 27140x^5 - 48826x^4 - 86560x^3 + 6155x^2 + 23515x - 2789	\( -\,3^{12}\cdot 5^{12}\cdot 179^{5} \)	16T1354	Trivial (GRH)
16.2.23842965126465199951171875.1	x^16 - 8x^15 + 40x^14 - 119x^13 + 183x^12 + 106x^11 - 1631x^10 + 4629x^9 - 9140x^8 + 10263x^7 - 12907x^6 + 11631x^5 - 31738x^4 + 42761x^3 - 84733x^2 + 75162x - 72329	\( -\,3^{12}\cdot 5^{12}\cdot 179^{5} \)	16T1354	$[2, 2]$ (GRH)
16.0.11020639142936576000000000000.1	x^16 - 40x^14 + 1146x^12 - 23000x^10 + 337476x^8 - 3819820x^6 + 27412511x^4 - 96297440x^2 + 124666421	\( 2^{32}\cdot 5^{12}\cdot 101^{5} \)	16T1354	$[4]$ (GRH)
16.0.11020639142936576000000000000.2	x^16 - 4x^14 + 161x^12 - 564x^10 - 13764x^8 + 317140x^6 + 4394510x^4 + 18361800x^2 + 25757525	\( 2^{32}\cdot 5^{12}\cdot 101^{5} \)	16T1354	$[4]$ (GRH)
16.0.6896992068684009105950840251291271168.1	x^16 - 8x^15 + 512x^14 - 3440x^13 + 106852x^12 - 627488x^11 + 11853904x^10 - 63644240x^9 + 761253712x^8 - 3866300704x^7 + 28876699048x^6 - 136494175840x^5 + 631426271688x^4 - 2392471589872x^3 + 6956085731328x^2 - 12251031213824x + 12753433956482	\( 2^{62}\cdot 113^{3}\cdot 1009^{4} \)	16T1354	$[2, 2, 2, 2, 1539044]$ (GRH)
16.16.6896992068684009105950840251291271168.1	x^16 - 8x^15 - 352x^14 + 2592x^13 + 50132x^12 - 324544x^11 - 3800032x^10 + 20439024x^9 + 166409360x^8 - 700013280x^7 - 4199520744x^6 + 13083333328x^5 + 56738103992x^4 - 125162855440x^3 - 336014595440x^2 + 496411645008x + 448136625922	\( 2^{62}\cdot 113^{3}\cdot 1009^{4} \)	16T1354	Trivial (GRH)
16.16.6896992068684009105950840251291271168.2	x^16 - 8x^15 - 624x^14 + 3888x^13 + 153884x^12 - 652752x^11 - 18836896x^10 + 41048896x^9 + 1164628660x^8 - 369211456x^7 - 32677192552x^6 - 29700370768x^5 + 365137419440x^4 + 614616142256x^3 - 995680684832x^2 - 1808592898624x + 433872087934	\( 2^{62}\cdot 113^{3}\cdot 1009^{4} \)	16T1354	Trivial (GRH)