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 46 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.198638542271690114596864.1	x^20 - 2x^16 - 2x^12 - 2x^10 + 2x^8 + 2x^4 - 1	\( -\,2^{42}\cdot 461^{4} \)	20T466	Trivial (GRH)
20.2.397277084543380229193728.1	x^20 - 10x^18 + 43x^16 - 104x^14 + 152x^12 - 126x^10 + 32x^8 + 44x^6 - 47x^4 + 16x^2 - 2	\( -\,2^{43}\cdot 461^{4} \)	20T466	Trivial (GRH)
20.0.1589108338173520916774912.1	x^20 + 4x^18 - 4x^17 + 5x^16 - 16x^15 - 2x^14 - 12x^13 + 49x^12 + 24x^11 + 42x^10 - 124x^9 + 23x^8 - 84x^7 + 130x^6 + 4x^5 - 45x^4 - 4x^3 + 20x^2 - 8x + 1	\( 2^{45}\cdot 461^{4} \)	20T466	Trivial
20.0.2325353038190497640742912.1	x^20 - 3x^18 + 6x^16 - 9x^14 + 12x^12 - 15x^10 + 18x^8 - 18x^6 + 15x^4 - 9x^2 + 3	\( 2^{20}\cdot 3^{19}\cdot 11^{4}\cdot 19^{4} \)	20T466	Trivial (GRH)
20.0.3013860906121243338473472.2	x^20 + 9x^16 + 27x^12 + 36x^8 + 33x^4 + 3	\( 2^{20}\cdot 3^{19}\cdot 223^{4} \)	20T466	Trivial (GRH)
20.0.3013860906121243338473472.3	x^20 - 6x^18 + 15x^16 - 18x^14 + 12x^12 - 6x^10 + 6x^8 - 9x^6 + 12x^4 - 9x^2 + 3	\( 2^{20}\cdot 3^{19}\cdot 223^{4} \)	20T466	Trivial (GRH)
20.0.3013860906121243338473472.4	x^20 + 6x^16 + 15x^12 + 21x^8 + 15x^4 + 3	\( 2^{20}\cdot 3^{19}\cdot 223^{4} \)	20T466	Trivial (GRH)
20.0.8065609467643551324045312.1	x^20 + 16x^16 + 48x^12 + 55x^8 + 34x^4 + 3	\( 2^{20}\cdot 3^{11}\cdot 17^{4}\cdot 151^{4} \)	20T466	Trivial (GRH)
20.0.229502363759100519775390625.1	x^20 - 5x^19 + 18x^18 - 37x^17 + 62x^16 - 90x^15 + 187x^14 - 432x^13 + 803x^12 - 1265x^11 + 1710x^10 - 2745x^9 + 4352x^8 - 7446x^7 + 10907x^6 - 12550x^5 + 12853x^4 - 10196x^3 + 8748x^2 - 3165x + 739	\( 5^{12}\cdot 13^{6}\cdot 41^{7} \)	20T466	Trivial (GRH)
20.0.511097690085059595400390625.1	x^20 - 2x^19 - 3x^18 + 16x^17 - 42x^16 + 26x^15 + 192x^14 - 565x^13 + 579x^12 + 362x^11 - 2581x^10 + 5811x^9 - 6521x^8 - 2629x^7 + 24457x^6 - 49129x^5 + 63769x^4 - 63953x^3 + 50935x^2 - 27921x + 8159	\( 5^{10}\cdot 13^{4}\cdot 41^{7}\cdot 97^{2} \)	20T466	Trivial (GRH)
20.4.1147511818795502598876953125.1	x^20 - 4x^19 + 26x^17 - 44x^16 - 37x^15 + 210x^14 - 60x^13 - 328x^12 + 598x^11 + 510x^10 - 957x^9 + 199x^8 + 1589x^7 - 917x^6 - 497x^5 + 3713x^4 + 1100x^3 - 3631x^2 - 1183x + 941	\( 5^{13}\cdot 13^{6}\cdot 41^{7} \)	20T466	Trivial (GRH)
20.6.2095807236189058847283871744.1	x^20 - 4x^18 - 4x^16 + 49x^14 - 137x^12 + 110x^10 + 78x^8 - 128x^6 + 21x^4 + 32x^2 - 1	\( -\,2^{20}\cdot 13^{10}\cdot 347^{4} \)	20T466	Trivial (GRH)
20.6.2095807236189058847283871744.2	x^20 - x^18 - 6x^16 + 10x^14 + 6x^12 - 17x^10 - 6x^8 + 10x^6 + 6x^4 - x^2 - 1	\( -\,2^{20}\cdot 13^{10}\cdot 347^{4} \)	20T466	Trivial (GRH)
20.6.2141929924305725440000000000.1	x^20 - 3x^18 + 13x^14 - 10x^12 - 34x^10 - 16x^8 + 16x^6 + 13x^4 - 4x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3803^{4} \)	20T466	Trivial (GRH)
20.6.2141929924305725440000000000.2	x^20 - 4x^18 - 13x^16 + 48x^14 + 182x^12 + 134x^10 - 72x^8 - 73x^6 + 16x^4 + 7x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3803^{4} \)	20T466	Trivial (GRH)
20.0.4609814178311274644985033549.2	x^20 - 2x^19 - 10x^18 + 32x^17 - 16x^16 - 15x^15 + 18x^14 - 345x^13 + 1502x^12 - 3447x^11 + 6255x^10 - 10568x^9 + 15833x^8 - 20005x^7 + 21834x^6 - 20890x^5 + 16541x^4 - 9840x^3 + 3985x^2 - 971x + 109	\( 3^{10}\cdot 61^{7}\cdot 397^{4} \)	20T466	Trivial (GRH)
20.4.11414008091096093897705078125.1	x^20 - 8x^19 + 22x^18 - 30x^17 + 67x^16 - 156x^15 + 174x^14 - 336x^13 + 26x^12 + 736x^11 + 3221x^10 - 1154x^9 - 9592x^8 - 8796x^7 + 8344x^6 + 13780x^5 + 4419x^4 + 4599x^3 + 13748x^2 + 10505x + 1829	\( 5^{13}\cdot 13^{4}\cdot 41^{9} \)	20T466	Trivial (GRH)
20.0.262331252425064668558343012352.2	x^20 + 41x^16 + 111x^12 + 101x^8 + 34x^4 + 3	\( 2^{20}\cdot 3^{15}\cdot 11491^{4} \)	20T466	Trivial (GRH)
20.0.262331252425064668558343012352.3	x^20 - 17x^18 + 126x^16 - 524x^14 + 1318x^12 - 2073x^10 + 2277x^8 - 2232x^6 + 1458x^4 + 162x^2 + 27	\( 2^{20}\cdot 3^{15}\cdot 11491^{4} \)	20T466	Trivial (GRH)
20.0.262331252425064668558343012352.4	x^20 - 6x^18 - x^16 + 78x^14 + 21x^12 - 1719x^10 + 6806x^8 - 13104x^6 + 14218x^4 - 8424x^2 + 2187	\( 2^{20}\cdot 3^{15}\cdot 11491^{4} \)	20T466	Trivial (GRH)
20.16.762378983303206514165048828125.1	x^20 - 10x^18 - 18x^17 + 29x^16 + 200x^15 - 193x^14 - 514x^13 + 1508x^12 - 492x^11 - 4848x^10 + 2818x^9 + 7024x^8 - 2667x^7 - 4596x^6 + 755x^5 + 1100x^4 - 143x^3 - 93x^2 + 13x + 1	\( 5^{10}\cdot 61^{7}\cdot 397^{4} \)	20T466	Trivial (GRH)
20.8.762378983303206514165048828125.1	x^20 - 5x^19 + 17x^18 - 68x^17 + 207x^16 - 629x^15 + 1190x^14 - 1544x^13 + 1847x^12 - 1673x^11 + 1655x^10 - 929x^9 - 1293x^8 + 994x^7 + 135x^6 + 252x^5 + 7x^4 - 147x^3 - 91x^2 + 50x - 5	\( 5^{10}\cdot 61^{7}\cdot 397^{4} \)	20T466	Trivial (GRH)
20.16.762378983303206514165048828125.2	x^20 - 5x^19 + 2x^18 + 16x^17 - 59x^16 + 256x^15 - 228x^14 - 916x^13 + 2274x^12 - 1126x^11 - 5587x^10 + 7039x^9 + 8294x^8 - 7709x^7 - 7262x^6 + 2056x^5 + 2236x^4 - 97x^3 - 231x^2 - 10x + 5	\( 5^{10}\cdot 61^{7}\cdot 397^{4} \)	20T466	Trivial (GRH)
20.0.2360981271825582017025087111168.1	x^20 - 3x^18 + 6x^16 - 24x^12 + 63x^10 - 72x^8 + 162x^4 - 243x^2 + 243	\( 2^{20}\cdot 3^{17}\cdot 11491^{4} \)	20T466	$[2]$ (GRH)
20.10.3521934896736480471040000000000.1	x^20 - 5x^18 - 10x^16 + 41x^14 + 64x^12 - 51x^10 - 96x^8 - 8x^6 + 21x^4 + 3x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 61^{4}\cdot 397^{4} \)	20T466	Trivial (GRH)
20.10.3521934896736480471040000000000.2	x^20 - 15x^16 - 4x^14 + 46x^12 + 16x^10 - 46x^8 - 17x^6 + 12x^4 + 3x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 61^{4}\cdot 397^{4} \)	20T466	Trivial (GRH)
20.10.4305926880688359795034353497883.1	x^20 - 4x^19 - 10x^18 + 54x^17 - 55x^16 + 296x^15 - 1529x^14 + 2175x^13 + 2079x^12 - 9305x^11 + 8524x^10 + 3223x^9 - 11868x^8 + 7423x^7 + 846x^6 - 2398x^5 + 279x^4 + 97x^3 + 354x^2 - 122x - 61	\( -\,3^{5}\cdot 61^{10}\cdot 397^{4} \)	20T466	Trivial (GRH)
20.10.8455924749076998400000000000000.1	x^20 - x^18 - 20x^16 + 30x^14 + 58x^12 - 59x^10 - 58x^8 + 30x^6 + 20x^4 - x^2 - 1	\( -\,2^{20}\cdot 5^{14}\cdot 6029^{4} \)	20T466	Trivial (GRH)
20.0.26696074417804819521986853076992.1	x^20 - 27x^18 + 324x^16 - 2187x^14 + 8964x^12 - 22572x^10 + 34452x^8 - 30132x^6 + 14175x^4 - 2916x^2 + 243	\( 2^{20}\cdot 3^{15}\cdot 36497^{4} \)	20T466	$[2]$ (GRH)
20.8.30596832887831976379669189453125.1	x^20 - x^19 - x^18 - 3x^17 - 117x^16 + 324x^15 + 544x^14 - 1944x^13 + 338x^12 + 1805x^11 - 3500x^10 + 3845x^9 - 784x^8 + 3698x^7 + 4586x^6 - 296x^5 - 8168x^4 - 9711x^3 + 4982x^2 + 2316x - 1069	\( 3^{4}\cdot 5^{15}\cdot 23^{4}\cdot 89^{7} \)	20T466	$[2]$ (GRH)
20.10.42279623745384992000000000000000.1	x^20 - 9x^18 - 25x^16 + 228x^14 + 324x^12 - 555x^10 - 800x^8 + 200x^6 + 380x^4 + 10x^2 - 5	\( -\,2^{20}\cdot 5^{15}\cdot 6029^{4} \)	20T466	Trivial (GRH)
20.10.45509950993861152000000000000000.1	x^20 - 5x^18 - 46x^16 + 85x^14 + 739x^12 + 530x^10 - 1280x^8 - 685x^6 + 605x^4 - 5	\( -\,2^{20}\cdot 3^{4}\cdot 5^{15}\cdot 23^{4}\cdot 89^{4} \)	20T466	Trivial (GRH)
20.12.152984164439159881898345947265625.1	x^20 - 3x^19 - 33x^18 + 57x^17 + 387x^16 - 315x^15 - 1867x^14 + 753x^13 + 3353x^12 - 4272x^11 - 3517x^10 + 15328x^9 + 3673x^8 - 15652x^7 + 24753x^6 + 18740x^5 - 24733x^4 + 12707x^3 + 23592x^2 - 9768x - 8059	\( 3^{4}\cdot 5^{16}\cdot 23^{4}\cdot 89^{7} \)	20T466	$[2]$ (GRH)
20.12.275371495990487787417022705078125.1	x^20 - 2x^19 + 3x^18 + 11x^17 - 141x^16 + 208x^15 + 197x^14 - 552x^13 + 1636x^12 - 1338x^11 - 4694x^10 + 102x^9 + 6436x^8 + 8747x^7 - 3535x^6 - 10420x^5 - 495x^4 + 2849x^3 + 143x^2 - 116x - 1	\( 3^{6}\cdot 5^{15}\cdot 23^{4}\cdot 89^{7} \)	20T466	$[2]$ (GRH)
20.4.1844489348608657807063040000000000.1	x^20 + 5x^18 - 150x^16 + 1750x^14 - 80x^12 - 56377x^10 - 880x^8 + 211750x^6 - 199650x^4 + 73205x^2 + 161051	\( 2^{20}\cdot 5^{10}\cdot 11^{5}\cdot 5783^{4} \)	20T466	Trivial (GRH)
20.8.1844489348608657807063040000000000.1	x^20 - 5x^18 - 150x^16 - 1750x^14 - 80x^12 + 56377x^10 - 880x^8 - 211750x^6 - 199650x^4 - 73205x^2 + 161051	\( 2^{20}\cdot 5^{10}\cdot 11^{5}\cdot 5783^{4} \)	20T466	Trivial (GRH)
20.4.2382434322822520356765777587890625.1	x^20 - 5x^19 + 13x^18 - 33x^17 - 3x^16 - 644x^15 + 1679x^14 - 7955x^13 + 3033x^12 + 9864x^11 - 112213x^10 + 227014x^9 - 433032x^8 + 484980x^7 - 485421x^6 + 332544x^5 - 155528x^4 + 45122x^3 + 3946x^2 - 9272x + 3721	\( 5^{15}\cdot 61^{7}\cdot 397^{4} \)	20T466	$[2, 12]$ (GRH)
20.4.2382434322822520356765777587890625.2	x^20 - 12x^18 - 40x^17 - 74x^16 + 205x^15 - 136x^14 - 430x^13 + 699x^12 + 6830x^11 + 8362x^10 - 560x^9 + 51809x^8 + 161485x^7 + 152131x^6 - 22055x^5 - 47929x^4 + 45950x^3 + 146950x^2 + 215710x + 153355	\( 5^{15}\cdot 61^{7}\cdot 397^{4} \)	20T466	$[2, 2]$ (GRH)
20.0.70600893601130608587973468583100416.2	x^20 + 144x^16 + 1936x^14 + 10368x^12 + 77336x^10 + 557816x^8 + 2173248x^6 + 4360216x^4 + 4302592x^2 + 1647086	\( 2^{59}\cdot 7^{5}\cdot 31^{4}\cdot 53^{4} \)	20T466	$[2]$ (GRH)
20.0.145671521378968039543605010986328125.1	x^20 + 44x^18 - 37x^17 + 769x^16 - 1799x^15 + 8136x^14 - 27411x^13 + 76643x^12 - 217497x^11 + 553045x^10 - 1184443x^9 + 2527476x^8 - 4505558x^7 + 7673064x^6 - 12834474x^5 + 19281736x^4 - 24949939x^3 + 27457237x^2 - 17683985x + 5729201	\( 3^{6}\cdot 5^{15}\cdot 23^{6}\cdot 89^{7} \)	20T466	$[2, 2, 1156]$ (GRH)
20.20.728357606894840197718025054931640625.1	x^20 - 3x^19 - 69x^18 + 171x^17 + 2045x^16 - 3905x^15 - 34113x^14 + 45691x^13 + 350741x^12 - 282690x^11 - 2282540x^10 + 761812x^9 + 9278956x^8 + 631491x^7 - 22303995x^6 - 9053970x^5 + 27746442x^4 + 19787211x^3 - 11465334x^2 - 13744080x - 3231351	\( 3^{6}\cdot 5^{16}\cdot 23^{6}\cdot 89^{7} \)	20T466	$[2]$ (GRH)
20.0.22027144683070052721556702905834143744.1	x^20 + 35x^18 - 67x^16 - 7693x^14 + 196025x^12 + 9512779x^10 + 152718262x^8 + 1265444251x^6 + 5621322256x^4 + 12383187719x^2 + 10510100501	\( 2^{20}\cdot 13^{10}\cdot 101^{5}\cdot 347^{4} \)	20T466	$[2, 2]$ (GRH)
20.12.22027144683070052721556702905834143744.1	x^20 - 35x^18 - 67x^16 + 7693x^14 + 196025x^12 - 9512779x^10 + 152718262x^8 - 1265444251x^6 + 5621322256x^4 - 12383187719x^2 + 10510100501	\( 2^{20}\cdot 13^{10}\cdot 101^{5}\cdot 347^{4} \)	20T466	Trivial (GRH)
20.8.97339589945843039759666267763507200000.1	x^20 - 6x^19 - 20x^18 + 126x^17 - 648x^16 - 3954x^15 + 7804x^14 + 52536x^13 + 27931x^12 - 275092x^11 - 810376x^10 - 399580x^9 + 2087755x^8 + 2499778x^7 - 2288088x^6 - 3024628x^5 + 1984585x^4 + 1671184x^3 - 844676x^2 - 497984x - 56371	\( 2^{30}\cdot 5^{5}\cdot 11^{10}\cdot 5783^{4} \)	20T466	$[2]$ (GRH)
20.20.106194539085267700827288053009033203125.1	x^20 - 6x^19 - 100x^18 + 346x^17 + 4397x^16 - 5261x^15 - 95841x^14 - 17208x^13 + 1073576x^12 + 980401x^11 - 6508432x^10 - 8437350x^9 + 22267576x^8 + 31881165x^7 - 45043233x^6 - 57268807x^5 + 55942237x^4 + 41395457x^3 - 36231332x^2 - 871060x + 980269	\( 3^{12}\cdot 5^{15}\cdot 23^{6}\cdot 89^{7} \)	20T466	$[2]$ (GRH)
20.12.105374376135245356088725314843202362306199552.1	x^20 - 141x^18 + 8100x^16 - 247742x^14 + 4407877x^12 - 46066504x^10 + 269167585x^8 - 796090326x^6 + 1098047444x^4 - 636927538x^2 + 3007693	\( 2^{20}\cdot 13^{7}\cdot 101^{10}\cdot 347^{4} \)	20T466	$[2]$ (GRH)