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
20.0.54320086096828525390625.1	x^20 - 2x^19 + 6x^18 - 3x^17 + 11x^16 - 4x^15 + 32x^14 - 18x^13 + 52x^12 - 27x^11 + 77x^10 - 50x^9 + 70x^8 - 44x^7 + 53x^6 - 24x^5 + 30x^4 - 27x^3 + 7x^2 - 2x + 1	\( 5^{10}\cdot 13^{4}\cdot 41^{7} \)	20T174	Trivial
20.0.398483526878269003824777.1	x^20 - 3x^19 + 8x^17 + 4x^16 - 26x^15 - 18x^14 + 60x^13 + 63x^12 - 101x^11 - 164x^10 + 111x^9 + 301x^8 - 17x^7 - 322x^6 - 179x^5 + 139x^4 + 177x^3 + 30x^2 + 9	\( 3^{10}\cdot 17^{4}\cdot 97^{7} \)	20T174	Trivial
20.2.826435173591040000000000.1	x^20 - x^18 + 8x^16 - x^14 + 20x^12 + 16x^10 + 24x^8 + 14x^6 + 7x^4 + 2x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 13^{4}\cdot 41^{4} \)	20T174	Trivial
20.0.1485427643260203878707797.1	x^20 + x^16 - 4x^15 + 9x^12 - 21x^11 + 14x^10 + x^8 - 5x^6 + 4x^5 + x^4 - x^3 - x^2 + x + 1	\( 3^{10}\cdot 13^{5}\cdot 19^{4}\cdot 151^{4} \)	20T174	Trivial
20.0.3013860906121243338473472.1	x^20 - 3x^18 + 3x^14 + 3x^10 + 3x^8 + 6x^6 + 15x^4 + 12x^2 + 3	\( 2^{20}\cdot 3^{19}\cdot 223^{4} \)	20T174	Trivial
20.2.5848252104937817609633792.1	x^20 - 4x^19 + 6x^18 + 2x^17 - 10x^16 - 12x^15 + 33x^14 + 26x^13 - 104x^12 - 5x^11 + 245x^10 - 367x^9 + 312x^8 + 134x^7 - 935x^6 + 1425x^5 - 1259x^4 + 739x^3 - 286x^2 + 69x - 9	\( -\,2^{15}\cdot 17^{10}\cdot 97^{4} \)	20T174	Trivial (GRH)
20.0.29950357231036150387578125.1	x^20 - 4x^19 + 12x^18 - 29x^17 + 65x^16 - 95x^15 + 126x^14 - 145x^13 + 71x^12 + 42x^11 - 51x^10 - 67x^9 + 197x^8 - 210x^7 + 151x^6 - 111x^5 + 90x^4 - 57x^3 + 24x^2 - 6x + 1	\( 5^{7}\cdot 13^{4}\cdot 41^{10} \)	20T174	Trivial (GRH)
20.0.90718261713324391265206272.1	x^20 - 3x^18 - 9x^16 + 27x^14 + 27x^12 - 81x^10 + 81x^8 + 243x^6 - 243x^4 - 243x^2 + 243	\( 2^{20}\cdot 3^{15}\cdot 1567^{4} \)	20T174	Trivial (GRH)
20.4.169750269052589141845703125.1	x^20 - 3x^19 - 4x^17 + 33x^16 - 12x^15 - 3x^14 - 223x^13 - 66x^12 + 1678x^11 - 2186x^10 - 678x^9 + 3616x^8 - 2708x^7 - 339x^6 + 243x^5 + 4097x^4 - 6486x^3 + 3604x^2 - 84x - 509	\( 5^{15}\cdot 13^{4}\cdot 41^{7} \)	20T174	Trivial (GRH)
20.6.651260558829045954013671875.1	x^20 - x^18 - 10x^17 + 2x^16 + 6x^15 + 32x^14 - 8x^13 - 21x^12 - 21x^11 + 21x^10 + 23x^9 - 50x^8 - 22x^7 + 17x^6 + 18x^5 - 8x^4 - 5x^3 + 8x^2 - 1	\( -\,5^{10}\cdot 11^{5}\cdot 13^{4}\cdot 347^{4} \)	20T174	Trivial (GRH)
20.6.829440000000000000000000000.1	x^20 - 5x^18 - 35x^16 + 50x^14 + 85x^12 - 119x^10 - 85x^8 + 50x^6 + 35x^4 - 5x^2 - 1	\( -\,2^{32}\cdot 3^{4}\cdot 5^{22} \)	20T174	Trivial (GRH)
20.4.1342499736873772099501953125.1	x^20 - 7x^18 - 7x^17 + 36x^16 + 49x^15 - 98x^14 - 83x^13 + 266x^12 + 126x^11 - 364x^10 - 139x^9 + 229x^8 + 133x^7 - 108x^6 - 56x^5 + 35x^4 + 8x^3 - 10x^2 - x + 1	\( 5^{10}\cdot 29^{5}\cdot 1609^{4} \)	20T174	Trivial (GRH)
20.0.4609814178311274644985033549.1	x^20 - 8x^19 + 29x^18 - 74x^17 + 162x^16 - 211x^15 + 268x^14 - 248x^13 - 66x^12 + 38x^11 - 216x^10 + 477x^9 - 62x^8 + 166x^7 + 14x^6 - 123x^5 + 75x^4 - 54x^3 + 35x^2 - 5x + 1	\( 3^{10}\cdot 61^{7}\cdot 397^{4} \)	20T174	Trivial
20.12.82943305909096044672939453125.1	x^20 - 7x^18 - 14x^17 + 13x^16 + 62x^15 - 91x^14 - 99x^13 + 327x^12 + 106x^11 - 374x^10 - 207x^9 + 179x^8 + 198x^7 - 77x^6 - 62x^5 + 52x^4 + 7x^3 - 14x^2 + 1	\( 5^{10}\cdot 13^{4}\cdot 29^{5}\cdot 347^{4} \)	20T174	Trivial (GRH)
20.12.115754426025787089002626953125.1	x^20 - x^19 - 10x^18 + 15x^17 + 28x^16 - 90x^15 - 109x^14 + 208x^13 + 418x^12 - 226x^11 - 562x^10 + 249x^9 + 331x^8 - 232x^7 - 151x^6 + 85x^5 + 70x^4 - 6x^3 - 17x^2 - x + 1	\( 5^{10}\cdot 29^{5}\cdot 4903^{4} \)	20T174	Trivial (GRH)
20.0.262331252425064668558343012352.1	x^20 - 2x^18 - 6x^16 + 19x^14 + 10x^12 - 81x^10 + 30x^8 + 171x^6 - 162x^4 - 162x^2 + 243	\( 2^{20}\cdot 3^{15}\cdot 11491^{4} \)	20T174	Trivial
20.10.540934693388277927724326171875.1	x^20 - 2x^19 - 3x^18 + 32x^17 - 12x^16 - 82x^15 - 22x^14 + 280x^13 - 45x^12 - 745x^11 + 323x^10 + 785x^9 + 54x^8 - 652x^7 - 121x^6 + 286x^5 - 20x^4 - 47x^3 + 16x^2 + 4x - 1	\( -\,5^{10}\cdot 11^{5}\cdot 61^{4}\cdot 397^{4} \)	20T174	Trivial (GRH)
20.0.762378983303206514165048828125.1	x^20 - 3x^19 + 11x^18 - 9x^17 + 29x^16 + 26x^15 + 169x^14 - 45x^13 + 1028x^12 + 812x^11 + 2595x^10 + 2965x^9 + 6133x^8 + 7447x^7 + 9309x^6 + 8419x^5 + 6763x^4 + 4568x^3 + 2598x^2 + 900x + 139	\( 5^{10}\cdot 61^{7}\cdot 397^{4} \)	20T174	$[2, 8]$ (GRH)
20.10.2790564977304713540069638671875.1	x^20 - 2x^19 - 3x^18 + 27x^17 - 5x^16 - 81x^15 - 61x^14 + 383x^13 - 88x^12 - 1110x^11 + 817x^10 + 929x^9 - 557x^8 - 384x^7 + 110x^6 + 162x^5 - 69x^4 - 31x^3 + 20x^2 + 2x - 1	\( -\,5^{10}\cdot 11^{5}\cdot 36497^{4} \)	20T174	Trivial (GRH)
20.20.6119366577566395275933837890625.1	x^20 - 33x^18 - 8x^17 + 450x^16 + 197x^15 - 3262x^14 - 1894x^13 + 13516x^12 + 8956x^11 - 32275x^10 - 21581x^9 + 43333x^8 + 24983x^7 - 31327x^6 - 12012x^5 + 10432x^4 + 1475x^3 - 725x^2 - 76x + 1	\( 3^{4}\cdot 5^{14}\cdot 23^{4}\cdot 89^{7} \)	20T174	Trivial (GRH)
20.0.55374574082926437693343023378125.1	x^20 - 6x^19 + 18x^18 - 35x^17 + 3x^16 - 8x^15 + 443x^14 - 1487x^13 + 2989x^12 - 167x^11 - 6369x^10 + 4885x^9 + 19103x^8 - 31548x^7 + 7631x^6 + 30774x^5 - 21536x^4 - 18172x^3 + 51631x^2 - 46426x + 19321	\( 5^{5}\cdot 61^{10}\cdot 397^{4} \)	20T174	$[16]$ (GRH)
20.20.68892413554441036870090126953125.1	x^20 - 2x^19 - 33x^18 + 36x^17 + 367x^16 - 244x^15 - 1859x^14 + 783x^13 + 4843x^12 - 1314x^11 - 6784x^10 + 1267x^9 + 5197x^8 - 702x^7 - 2139x^6 + 204x^5 + 446x^4 - 29x^3 - 40x^2 + 2x + 1	\( 5^{10}\cdot 29^{5}\cdot 61^{4}\cdot 397^{4} \)	20T174	Trivial (GRH)
20.0.1844489348608657807063040000000000.1	x^20 - 8x^19 + 63x^18 - 300x^17 + 1357x^16 - 4724x^15 + 15650x^14 - 43334x^13 + 113629x^12 - 258210x^11 + 553307x^10 - 1047220x^9 + 1852214x^8 - 2909058x^7 + 4222990x^6 - 5414292x^5 + 6184004x^4 - 6044510x^3 + 5034175x^2 - 3157754x + 1126631	\( 2^{20}\cdot 5^{10}\cdot 11^{5}\cdot 5783^{4} \)	20T174	$[2, 2]$ (GRH)
20.0.70600893601130608587973468583100416.1	x^20 + 16x^18 + 56x^16 + 1808x^12 + 12240x^10 + 12656x^8 + 153664x^4 + 307328x^2 + 134456	\( 2^{59}\cdot 7^{5}\cdot 31^{4}\cdot 53^{4} \)	20T174	$[2, 2]$ (GRH)