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 28 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.51885951292865088442368.1	x^20 - 6x^19 + 20x^18 - 48x^17 + 89x^16 - 134x^15 + 175x^14 - 207x^13 + 237x^12 - 278x^11 + 331x^10 - 386x^9 + 426x^8 - 419x^7 + 372x^6 - 281x^5 + 181x^4 - 95x^3 + 37x^2 - 9x + 1	\( 2^{12}\cdot 3^{10}\cdot 13^{7}\cdot 43^{4} \)	20T658	Trivial (GRH)
20.0.246771190286366549446656.1	x^20 - 4x^19 + 12x^18 - 31x^17 + 68x^16 - 137x^15 + 273x^14 - 514x^13 + 863x^12 - 1242x^11 + 1533x^10 - 1656x^9 + 1603x^8 - 1366x^7 + 993x^6 - 599x^5 + 300x^4 - 119x^3 + 36x^2 - 8x + 1	\( 2^{12}\cdot 3^{15}\cdot 13^{4}\cdot 43^{5} \)	20T658	Trivial
20.2.2631600323952640000000000.1	x^20 - 3x^18 + 6x^16 + 3x^14 - 11x^12 + 12x^10 + 7x^8 - 21x^6 - 2x^4 - 7x^2 - 1	\( -\,2^{32}\cdot 5^{10}\cdot 89^{4} \)	20T658	Trivial (GRH)
20.2.2631600323952640000000000.2	x^20 + 3x^18 + 6x^16 - 3x^14 - 11x^12 - 12x^10 + 7x^8 + 21x^6 - 2x^4 + 7x^2 - 1	\( -\,2^{32}\cdot 5^{10}\cdot 89^{4} \)	20T658	Trivial (GRH)
20.4.452928869330216960000000000.1	x^20 - 3x^19 - 8x^18 + 55x^17 - 109x^16 + 82x^15 + 11x^14 + x^13 - 173x^12 + 238x^11 + 59x^10 - 379x^9 + 178x^8 + 301x^7 - 345x^6 - 30x^5 + 192x^4 - 48x^3 - 48x^2 + 28x - 4	\( 2^{20}\cdot 5^{10}\cdot 89^{7} \)	20T658	Trivial (GRH)
20.6.12543323349925232640000000000.1	x^20 - 11x^18 + 29x^16 + 94x^14 - 559x^12 + 307x^10 + 2271x^8 - 2834x^6 - 2397x^4 + 2549x^2 - 1	\( -\,2^{28}\cdot 3^{4}\cdot 5^{10}\cdot 17^{4}\cdot 29^{4} \)	20T658	Trivial (GRH)
20.6.12543323349925232640000000000.2	x^20 + 11x^18 + 29x^16 - 94x^14 - 559x^12 - 307x^10 + 2271x^8 + 2834x^6 - 2397x^4 - 2549x^2 - 1	\( -\,2^{28}\cdot 3^{4}\cdot 5^{10}\cdot 17^{4}\cdot 29^{4} \)	20T658	Trivial (GRH)
20.10.224453298561466828654636957696.1	x^20 - 8x^18 + 14x^16 + 14x^14 + 21x^12 - 344x^10 + 595x^8 - 98x^6 - 502x^4 + 316x^2 - 1	\( -\,2^{52}\cdot 2657^{4} \)	20T658	Trivial (GRH)
20.2.224453298561466828654636957696.1	x^20 + 8x^18 + 14x^16 - 14x^14 + 21x^12 + 344x^10 + 595x^8 + 98x^6 - 502x^4 - 316x^2 - 1	\( -\,2^{52}\cdot 2657^{4} \)	20T658	$[2]$ (GRH)
20.0.1415402716656928000000000000000.1	x^20 - 6x^19 + 21x^18 - 39x^17 + 157x^16 - 441x^15 + 690x^14 - 1298x^13 + 3509x^12 - 6743x^11 + 9694x^10 - 10821x^9 + 13021x^8 - 13611x^7 + 11130x^6 - 728x^5 + 6223x^4 + 175x^3 + 8131x^2 + 1565x + 2501	\( 2^{20}\cdot 5^{15}\cdot 89^{7} \)	20T658	$[2]$ (GRH)
20.0.1855196648776568668160000000000.1	x^20 - 2x^19 + 26x^18 - 74x^17 + 360x^16 - 954x^15 + 2868x^14 - 6062x^13 + 12571x^12 - 19956x^11 + 27438x^10 - 25448x^9 + 14807x^8 - 770x^7 - 2304x^6 + 30x^5 + 2776x^4 + 506x^3 + 38364x^2 - 50222x + 63041	\( 2^{32}\cdot 5^{10}\cdot 89^{7} \)	20T658	$[4]$ (GRH)
20.4.3587649573964648540160000000000.1	x^20 - x^19 + 9x^18 - 22x^17 + 83x^16 - 35x^15 - 157x^14 + 1172x^13 - 1273x^12 + 1905x^11 + 2841x^10 + 218x^9 - 920x^8 + 8504x^7 + 10096x^6 + 640x^5 - 4544x^4 - 4480x^3 - 2048x^2 + 512x + 1024	\( 2^{20}\cdot 5^{10}\cdot 89^{9} \)	20T658	Trivial (GRH)
20.10.5297130689384517848057641959424.1	x^20 - 6x^18 - 9x^16 + 172x^14 - 628x^12 + 1268x^10 - 1712x^8 + 1424x^6 - 600x^4 + 96x^2 - 4	\( -\,2^{54}\cdot 41^{4}\cdot 101^{4} \)	20T658	Trivial (GRH)
20.2.5297130689384517848057641959424.1	x^20 + 6x^18 - 9x^16 - 172x^14 - 628x^12 - 1268x^10 - 1712x^8 - 1424x^6 - 600x^4 - 96x^2 - 4	\( -\,2^{54}\cdot 41^{4}\cdot 101^{4} \)	20T658	Trivial (GRH)
20.0.19696131789411483760640000000000.1	x^20 + x^18 - 36x^16 - 78x^14 + 407x^12 + 2071x^10 + 3845x^8 + 3531x^6 + 1542x^4 + 244x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 11^{9}\cdot 13^{8} \)	20T658	$[2]$ (GRH)
20.12.19696131789411483760640000000000.1	x^20 - x^18 - 36x^16 + 78x^14 + 407x^12 - 2071x^10 + 3845x^8 - 3531x^6 + 1542x^4 - 244x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 11^{9}\cdot 13^{8} \)	20T658	Trivial (GRH)
20.20.291196495384907705490560000000000.1	x^20 - 3x^19 - 37x^18 + 97x^17 + 548x^16 - 1245x^15 - 4161x^14 + 8051x^13 + 17285x^12 - 27300x^11 - 39010x^10 + 45384x^9 + 45218x^8 - 30246x^7 - 23634x^6 + 5754x^5 + 3797x^4 - 465x^3 - 173x^2 + 17x + 1	\( 2^{16}\cdot 5^{10}\cdot 13^{4}\cdot 29^{7}\cdot 31^{4} \)	20T658	Trivial (GRH)
20.10.355694566977399050976640000000000.1	x^20 - x^19 - 13x^18 - 48x^17 - 145x^16 - 99x^15 + 297x^14 + 1664x^13 + 3268x^12 + 1172x^11 - 3388x^10 - 7530x^9 + 1523x^8 + 13537x^7 - 4037x^6 - 10258x^5 + 5897x^4 + 1851x^3 - 2335x^2 + 672x - 64	\( -\,2^{16}\cdot 5^{10}\cdot 13^{4}\cdot 29^{4}\cdot 31^{7} \)	20T658	Trivial (GRH)
20.0.2383231946518789535037440000000000.1	x^20 + 3x^18 - 58x^16 - 89x^14 + 963x^12 - 103x^10 - 5603x^8 + 16172x^6 + 36971x^4 + 18271x^2 + 1331	\( 2^{20}\cdot 5^{10}\cdot 11^{11}\cdot 13^{8} \)	20T658	$[2]$ (GRH)
20.12.2383231946518789535037440000000000.1	x^20 - 3x^18 - 58x^16 + 89x^14 + 963x^12 + 103x^10 - 5603x^8 - 16172x^6 + 36971x^4 - 18271x^2 + 1331	\( 2^{20}\cdot 5^{10}\cdot 11^{11}\cdot 13^{8} \)	20T658	Trivial (GRH)
20.0.7352664362157151362137165437861888.1	x^20 - 2x^19 + 27x^18 - 36x^17 + 400x^16 - 644x^15 + 5074x^14 - 9716x^13 + 46637x^12 - 83518x^11 + 264779x^10 - 393960x^9 + 860486x^8 - 985804x^7 + 1459328x^6 - 1102432x^5 + 964740x^4 - 29968x^3 + 11056x^2 - 47936x + 378944	\( 2^{34}\cdot 97^{5}\cdot 2657^{4} \)	20T658	$[3, 3]$ (GRH)
20.0.7352664362157151362137165437861888.2	x^20 - 2x^19 + 27x^18 - 24x^17 + 178x^16 + 28x^15 + 154x^14 + 628x^13 + 4865x^12 - 20062x^11 + 88787x^10 - 190644x^9 + 455792x^8 - 742204x^7 + 1196960x^6 - 1410472x^5 + 1632084x^4 - 1455424x^3 + 1246000x^2 - 689984x + 303728	\( 2^{34}\cdot 97^{5}\cdot 2657^{4} \)	20T658	$[3]$ (GRH)
20.10.21301994921006951430400000000000000.1	x^20 + 12x^18 - 29x^16 - 475x^14 + 566x^12 + 3625x^10 - 1521x^8 - 6085x^6 + 1844x^4 - 38x^2 - 1	\( -\,2^{20}\cdot 5^{14}\cdot 11^{8}\cdot 353^{4} \)	20T658	Trivial (GRH)
20.0.234321944131076465734400000000000000.1	x^20 + 27x^18 + 290x^16 + 1652x^14 + 5528x^12 + 11250x^10 + 13821x^8 + 9740x^6 + 3476x^4 + 459x^2 + 11	\( 2^{20}\cdot 5^{14}\cdot 11^{9}\cdot 353^{4} \)	20T658	$[2, 734]$ (GRH)
20.20.244896252618707380317560960000000000.1	x^20 - 7x^19 - 18x^18 + 218x^17 - 78x^16 - 2417x^15 + 3322x^14 + 11758x^13 - 24607x^12 - 22722x^11 + 78290x^10 - 4842x^9 - 110376x^8 + 70104x^7 + 45466x^6 - 63952x^5 + 18689x^4 + 3143x^3 - 2100x^2 + 86x + 41	\( 2^{16}\cdot 5^{10}\cdot 13^{4}\cdot 29^{9}\cdot 31^{4} \)	20T658	Trivial (GRH)
20.12.1882282076712230748707114352092643328.1	x^20 - 20x^18 - 64x^17 - 536x^16 - 392x^15 + 10482x^14 + 20284x^13 - 55312x^12 - 110868x^11 + 83872x^10 + 12360x^9 + 204210x^8 + 998784x^7 - 1491372x^6 - 2227824x^5 + 3432132x^4 + 1329696x^3 - 2991816x^2 + 314928x + 472392	\( 2^{42}\cdot 97^{5}\cdot 2657^{4} \)	20T658	Trivial (GRH)
20.12.1882282076712230748707114352092643328.2	x^20 - 82x^18 - 28x^17 + 2776x^16 + 1984x^15 - 50192x^14 - 54664x^13 + 518589x^12 + 757984x^11 - 2987314x^10 - 5559644x^9 + 8443210x^8 + 20741056x^7 - 7190628x^6 - 34973776x^5 - 8943656x^4 + 18959776x^3 + 11528688x^2 + 845536x - 385724	\( 2^{42}\cdot 97^{5}\cdot 2657^{4} \)	20T658	Trivial (GRH)
20.0.28352955239860252353862400000000000000.1	x^20 + 56x^18 + 1198x^16 + 12323x^14 + 64301x^12 + 175867x^10 + 255321x^8 + 200233x^6 + 83413x^4 + 17061x^2 + 1331	\( 2^{20}\cdot 5^{14}\cdot 11^{11}\cdot 353^{4} \)	20T658	$[2, 6536]$ (GRH)