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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.397277084543380229193728.1	x^20 + 10x^18 + 43x^16 + 104x^14 + 152x^12 + 130x^10 + 52x^8 - 4x^6 - 7x^4 + 4x^2 + 2	\( 2^{43}\cdot 461^{4} \)	20T369	Trivial (GRH)
20.4.397277084543380229193728.1	x^20 - 10x^18 + 43x^16 - 104x^14 + 152x^12 - 130x^10 + 52x^8 + 4x^6 - 7x^4 - 4x^2 + 2	\( 2^{43}\cdot 461^{4} \)	20T369	Trivial (GRH)
20.8.4391182420642244613154093.1	x^20 - 10x^18 - 2x^17 + 36x^16 - 91x^14 + 5x^13 + 221x^12 + 163x^11 - 156x^10 - 264x^9 - 62x^8 + 22x^7 - 69x^6 - 26x^5 + 47x^4 + 2x^3 - 7x^2 + 10x - 1	\( 13^{13}\cdot 347^{4} \)	20T369	Trivial (GRH)
20.4.5590155758429718017578125.1	x^20 - 5x^19 + 10x^18 - 15x^17 + 20x^16 + 22x^15 - 175x^14 + 395x^13 - 665x^12 + 1050x^11 - 1216x^10 + 780x^9 - 305x^8 + 390x^7 - 545x^6 + 323x^5 - 45x^4 - 25x^3 + 5x + 1	\( 3^{4}\cdot 5^{17}\cdot 67^{6} \)	20T369	Trivial (GRH)
20.0.11562819469661895751953125.1	x^20 - 6x^19 + 26x^18 - 86x^17 + 235x^16 - 547x^15 + 1124x^14 - 2035x^13 + 3199x^12 - 4420x^11 + 5355x^10 - 5560x^9 + 4910x^8 - 3635x^7 + 2135x^6 - 965x^5 + 415x^4 - 240x^3 + 130x^2 - 40x + 5	\( 5^{15}\cdot 269^{6} \)	20T369	Trivial (GRH)
20.8.22313281250000000000000000.1	x^20 - 5x^19 + 10x^18 - 10x^17 + 9x^15 - 15x^14 + 60x^13 - 70x^12 - 15x^11 + 86x^10 - 105x^9 - 5x^8 + 80x^6 + 104x^5 - 80x^4 - 20x^3 - 20x - 4	\( 2^{16}\cdot 5^{23}\cdot 13^{4} \)	20T369	Trivial (GRH)
20.8.40320991273293487548828125.1	x^20 - x^19 - 10x^18 + 11x^17 + 13x^16 - 35x^15 + 15x^14 + 31x^13 - 37x^12 - 7x^11 + 33x^10 - 7x^9 - 37x^8 + 31x^7 + 15x^6 - 35x^5 + 13x^4 + 11x^3 - 10x^2 - x + 1	\( 5^{15}\cdot 6029^{4} \)	20T369	Trivial (GRH)
20.8.43401671403752471923828125.1	x^20 - 2x^19 - 6x^18 + 5x^17 + x^16 - 2x^15 + 12x^14 - 17x^13 - x^12 + 15x^11 - 11x^10 + 15x^9 - x^8 - 17x^7 + 12x^6 - 2x^5 + x^4 + 5x^3 - 6x^2 - 2x + 1	\( 3^{4}\cdot 5^{15}\cdot 23^{4}\cdot 89^{4} \)	20T369	Trivial (GRH)
20.12.390615042633772247314453125.1	x^20 - x^19 - 8x^18 + 16x^17 + x^16 - 86x^15 + 175x^14 + 169x^13 - 704x^12 + 71x^11 + 1178x^10 - 773x^9 - 770x^8 + 1039x^7 - 86x^6 - 417x^5 + 224x^4 - 7x^3 - 30x^2 + 10x - 1	\( 3^{6}\cdot 5^{15}\cdot 23^{4}\cdot 89^{4} \)	20T369	Trivial (GRH)
20.4.5712200000000000000000000000.1	x^20 + 20x^14 - 30x^12 - 10x^10 - 480x^6 - 135x^4 + 250x^2 + 5	\( 2^{24}\cdot 5^{23}\cdot 13^{4} \)	20T369	Trivial (GRH)
20.12.9765376065844306182861328125.1	x^20 - x^19 - 13x^18 + 10x^17 + 37x^16 - 16x^15 + 42x^14 + 22x^13 - 407x^12 - 249x^11 + 806x^10 + 749x^9 - 662x^8 - 887x^7 + 147x^6 + 431x^5 + 67x^4 - 65x^3 - 23x^2 + x + 1	\( 3^{6}\cdot 5^{17}\cdot 23^{4}\cdot 89^{4} \)	20T369	Trivial (GRH)
20.16.10496183922101499053955078125.1	x^20 - 20x^18 - x^17 + 170x^16 + 21x^15 - 799x^14 - 180x^13 + 2258x^12 + 814x^11 - 3884x^10 - 2087x^9 + 3846x^8 + 3012x^7 - 1749x^6 - 2239x^5 - 74x^4 + 630x^3 + 251x^2 + 30x + 1	\( 5^{15}\cdot 61^{4}\cdot 397^{4} \)	20T369	Trivial (GRH)
20.0.91395200000000000000000000000.1	x^20 + 10x^18 + 35x^16 + 50x^14 + 35x^12 + 55x^10 + 55x^8 - 45x^6 - 35x^4 + 25x^2 + 5	\( 2^{28}\cdot 5^{23}\cdot 13^{4} \)	20T369	$[2, 2]$ (GRH)
20.12.91395200000000000000000000000.1	x^20 - 10x^18 + 35x^16 - 50x^14 + 35x^12 - 55x^10 + 55x^8 + 45x^6 - 35x^4 - 25x^2 + 5	\( 2^{28}\cdot 5^{23}\cdot 13^{4} \)	20T369	Trivial (GRH)
20.4.91395200000000000000000000000.1	x^20 + 10x^18 + 25x^16 - 40x^14 - 230x^12 - 215x^10 + 90x^8 + 130x^6 - 35x^4 - 25x^2 + 5	\( 2^{28}\cdot 5^{23}\cdot 13^{4} \)	20T369	$[2]$ (GRH)
20.0.206635357553265518829345703125.1	x^20 - 9x^19 + 45x^18 - 147x^17 + 416x^16 - 1110x^15 + 2946x^14 - 7181x^13 + 15574x^12 - 29146x^11 + 46749x^10 - 63646x^9 + 73319x^8 - 71062x^7 + 57542x^6 - 38473x^5 + 21130x^4 - 9424x^3 + 3354x^2 - 878x + 139	\( 3^{6}\cdot 5^{15}\cdot 23^{6}\cdot 89^{4} \)	20T369	$[2, 2]$ (GRH)
20.0.267741240538215680000000000000.1	x^20 + 25x^18 + 254x^16 + 1405x^14 + 4674x^12 + 9720x^10 + 12770x^8 + 10400x^6 + 4975x^4 + 1250x^2 + 125	\( 2^{20}\cdot 5^{13}\cdot 3803^{4} \)	20T369	Trivial (GRH)
20.12.267741240538215680000000000000.1	x^20 - 5x^18 - 4x^16 + 5x^14 + 164x^12 - 310x^10 + 50x^6 + 475x^4 - 500x^2 + 125	\( 2^{20}\cdot 5^{13}\cdot 3803^{4} \)	20T369	Trivial (GRH)
20.16.5165883938831637970733642578125.1	x^20 - 7x^19 + 77x^17 + 33x^16 - 765x^15 - 558x^14 + 7153x^13 - 3445x^12 - 27558x^11 + 32442x^10 + 42497x^9 - 80598x^8 - 18979x^7 + 86117x^6 - 10085x^5 - 42210x^4 + 7912x^3 + 9133x^2 - 590x - 499	\( 3^{6}\cdot 5^{17}\cdot 23^{6}\cdot 89^{4} \)	20T369	Trivial (GRH)
20.4.42279623745384992000000000000000.1	x^20 + 15x^18 + 84x^16 + 215x^14 + 224x^12 - 45x^10 - 280x^8 - 180x^6 - 5x^4 + 25x^2 + 5	\( 2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T369	Trivial (GRH)
20.4.45509950993861152000000000000000.1	x^20 + 9x^18 + 10x^16 - 103x^14 - 301x^12 - 90x^10 + 590x^8 + 830x^6 + 420x^4 + 80x^2 + 5	\( 2^{20}\cdot 3^{4}\cdot 5^{15}\cdot 23^{4}\cdot 89^{4} \)	20T369	$[2]$ (GRH)
20.20.150637175656330563226593017578125.1	x^20 - 2x^19 - 39x^18 + 52x^17 + 608x^16 - 536x^15 - 4870x^14 + 3072x^13 + 21921x^12 - 11824x^11 - 57814x^10 + 31441x^9 + 89231x^8 - 53274x^7 - 76707x^6 + 52054x^5 + 31974x^4 - 26170x^3 - 3498x^2 + 5190x - 809	\( 3^{12}\cdot 5^{15}\cdot 23^{6}\cdot 89^{4} \)	20T369	Trivial (GRH)
20.0.1465621300755332525247833251953125.1	x^20 - 3x^19 + 13x^18 - 45x^17 + 181x^16 - 277x^15 + 1527x^14 - 1917x^13 + 6069x^12 - 8567x^11 + 22087x^10 + 8548x^9 + 131627x^8 + 225444x^7 + 530121x^6 + 803419x^5 + 996120x^4 + 1044920x^3 + 674906x^2 + 243078x + 96739	\( 5^{15}\cdot 6029^{6} \)	20T369	$[2, 212]$ (GRH)
20.20.90886347761592416951120000000000000.1	x^20 - 5x^19 - 42x^18 + 206x^17 + 590x^16 - 3005x^15 - 3226x^14 + 19885x^13 + 4258x^12 - 64498x^11 + 17649x^10 + 100553x^9 - 56208x^8 - 68783x^7 + 49465x^6 + 19129x^5 - 14791x^4 - 2945x^3 + 1481x^2 + 290x - 5	\( 2^{16}\cdot 5^{13}\cdot 7^{6}\cdot 23^{4}\cdot 431^{4} \)	20T369	Trivial (GRH)