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 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.31874096343147504926018949.1	x^20 - 5x^19 + 19x^18 - 48x^17 + 108x^16 - 180x^15 + 243x^14 - 219x^13 + 153x^12 - 50x^11 - 377x^10 + 973x^9 - 1023x^8 + 222x^7 + 1050x^6 - 1107x^5 - 396x^4 + 696x^3 + 268x^2 - 434x + 109	\( 3^{19}\cdot 223^{7} \)	$C_4:S_5$ (as 20T120)	Trivial (GRH)
20.0.622079687467809991455078125.1	x^20 - 2x^19 + 3x^18 - 8x^17 + 40x^16 - 113x^15 + 202x^14 - 191x^13 + 125x^12 + 120x^11 + 121x^10 + 85x^9 + 442x^8 + 372x^7 - 275x^6 + 625x^5 + 728x^4 - 188x^3 - 9x^2 + 280x + 101	\( 5^{14}\cdot 269^{7} \)	$C_4:S_5$ (as 20T120)	Trivial (GRH)
20.6.83510262074750967216189850187.1	x^20 - 3x^19 + 6x^18 + 13x^17 - 83x^16 + 158x^15 - 36x^14 - 663x^13 + 1656x^12 - 1364x^11 - 1727x^10 + 5936x^9 - 7493x^8 + 4040x^7 + 876x^6 - 10785x^5 + 18605x^4 - 12047x^3 + 2869x^2 + x - 61	\( -\,13^{10}\cdot 347^{7} \)	$C_4:S_5$ (as 20T120)	Trivial (GRH)
20.0.332890802464111776751903153461.1	x^20 - 4x^19 + 15x^18 - 49x^17 + 175x^16 - 486x^15 + 1452x^14 - 3417x^13 + 8985x^12 - 18018x^11 + 45207x^10 - 78273x^9 + 180504x^8 - 213489x^7 + 632475x^6 - 266436x^5 + 1865295x^4 + 184761x^3 + 2473983x^2 + 309501x + 656181	\( 3^{15}\cdot 1567^{7} \)	$C_4:S_5$ (as 20T120)	Trivial (GRH)
20.6.671088640000000000000000000000.1	x^20 - 5x^18 + 25x^16 - 64x^15 - 110x^14 + 320x^13 + 325x^12 - 600x^11 - 383x^10 + 920x^9 - 535x^8 - 2080x^7 + 1920x^6 + 2744x^5 - 2415x^4 - 1520x^3 + 1435x^2 + 280x - 229	\( -\,2^{48}\cdot 5^{22} \)	$C_4:S_5$ (as 20T120)	Trivial (GRH)
20.4.652297830366246329600000000000000.1	x^20 + 16x^18 + 82x^16 - 273x^14 - 5955x^12 - 40649x^10 - 241677x^8 - 759789x^6 - 1826779x^4 - 11939565x^2 + 19465109	\( 2^{20}\cdot 5^{14}\cdot 269^{7} \)	$C_4:S_5$ (as 20T120)	Trivial (GRH)
20.0.2421769784649371094992432861328125.1	x^20 - 4x^19 + 23x^18 - 86x^17 + 286x^16 - 841x^15 + 1894x^14 - 3550x^13 + 5536x^12 - 4335x^11 + 6012x^10 + 9176x^9 + 14031x^8 + 28625x^7 + 71096x^6 + 45116x^5 + 93564x^4 + 66361x^3 + 5468x^2 + 9565x + 10555	\( 5^{13}\cdot 269^{10} \)	$C_4:S_5$ (as 20T120)	Trivial (GRH)
20.0.1767246164450779958943837335205078125.1	x^20 - 3x^19 + 49x^18 - 231x^17 + 1502x^16 - 7304x^15 + 33532x^14 - 137685x^13 + 515016x^12 - 1709342x^11 + 5124144x^10 - 13137281x^9 + 30194239x^8 - 57126905x^7 + 97213725x^6 - 130092378x^5 + 155067625x^4 - 134835408x^3 + 98000344x^2 - 43507098x + 11369359	\( 5^{14}\cdot 6029^{7} \)	$C_4:S_5$ (as 20T120)	$[16350]$ (GRH)
20.4.2539409673708498945302785280000000000000.1	x^20 - 26x^18 + 317x^16 - 2060x^14 + 8246x^12 - 29112x^10 + 83890x^8 - 172403x^6 + 222565x^4 - 152710x^2 + 26645	\( 2^{20}\cdot 5^{13}\cdot 269^{10} \)	$C_4:S_5$ (as 20T120)	Trivial (GRH)
20.20.1853091914135141046229493177600000000000000.1	x^20 - 255x^18 + 26780x^16 - 1503545x^14 + 49256545x^12 - 970837684x^10 + 11493603485x^8 - 79010543635x^6 + 291125849965x^4 - 485802259965x^2 + 219147162389	\( 2^{20}\cdot 5^{14}\cdot 6029^{7} \)	$C_4:S_5$ (as 20T120)	Trivial (GRH)
20.0.77457396436446494932074374685797656495361328125.1	x^20 - 10x^19 + 155x^18 - 1090x^17 + 9450x^16 - 48809x^15 + 299040x^14 - 1149425x^13 + 5365250x^12 - 14618695x^11 + 54147603x^10 - 87675235x^9 + 296502290x^8 - 159474145x^7 + 1055587375x^6 + 2898777x^5 + 3651466705x^4 - 1661558095x^3 + 7205970510x^2 - 5223386330x + 5105600303	\( 5^{13}\cdot 6029^{10} \)	$C_4:S_5$ (as 20T120)	$[16350]$ (GRH)
20.20.81219966925743319869894819510534963457280000000000000.1	x^20 - 283x^18 + 30002x^16 - 1524616x^14 + 40234241x^12 - 571963368x^10 + 4239133720x^8 - 13873345570x^6 + 9682058280x^4 - 983215875x^2 + 25878125	\( 2^{20}\cdot 5^{13}\cdot 6029^{10} \)	$C_4:S_5$ (as 20T120)	Trivial (GRH)