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 44 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.93916018045780428800000000000.1	x^20 + 2x^18 + 5x^16 + 12x^14 - 186x^12 - 387x^10 + 185x^8 + 3768x^6 + 9446x^4 - 2550x^2 + 5645	\( 2^{20}\cdot 5^{11}\cdot 1129^{5} \)	20T771	$[2]$ (GRH)
20.4.93916018045780428800000000000.1	x^20 - 2x^18 + 5x^16 - 12x^14 - 186x^12 + 387x^10 + 185x^8 - 3768x^6 + 9446x^4 + 2550x^2 + 5645	\( 2^{20}\cdot 5^{11}\cdot 1129^{5} \)	20T771	Trivial (GRH)
20.0.93916018045780428800000000000.2	x^20 + 13x^18 + 83x^16 + 376x^14 + 1217x^12 + 3054x^10 + 5720x^8 + 8426x^6 + 9369x^4 + 9925x^2 + 5645	\( 2^{20}\cdot 5^{11}\cdot 1129^{5} \)	20T771	$[2]$ (GRH)
20.4.93916018045780428800000000000.2	x^20 - 13x^18 + 83x^16 - 376x^14 + 1217x^12 - 3054x^10 + 5720x^8 - 8426x^6 + 9369x^4 - 9925x^2 + 5645	\( 2^{20}\cdot 5^{11}\cdot 1129^{5} \)	20T771	Trivial (GRH)
20.8.1607575865553562716800000000000.1	x^20 - 7x^19 + 13x^18 + 8x^17 - 57x^16 + 181x^15 - 599x^14 + 1096x^13 - 1057x^12 + 1253x^11 - 2437x^10 + 2358x^9 - 414x^8 - 110x^7 - 220x^6 - 1530x^5 + 4320x^4 - 5000x^3 + 2200x^2 + 500x - 500	\( 2^{16}\cdot 5^{11}\cdot 3469^{5} \)	20T771	$[2]$ (GRH)
20.8.1607575865553562716800000000000.2	x^20 - 5x^19 + 13x^18 - 40x^17 + 37x^16 + 79x^15 - 343x^14 + 894x^13 - 1433x^12 + 677x^11 + 1753x^10 - 5208x^9 + 8464x^8 - 7762x^7 + 1874x^6 + 3358x^5 - 3660x^4 + 1588x^3 - 296x^2 + 4x + 4	\( 2^{16}\cdot 5^{11}\cdot 3469^{5} \)	20T771	Trivial (GRH)
20.8.1607575865553562716800000000000.3	x^20 - 5x^19 + x^18 + 46x^17 - 135x^16 + 57x^15 + 585x^14 - 1494x^13 + 857x^12 + 2779x^11 - 6943x^10 + 6010x^9 + 2194x^8 - 12272x^7 + 16092x^6 - 10924x^5 + 2376x^4 + 2400x^3 - 2240x^2 + 720x - 80	\( 2^{16}\cdot 5^{11}\cdot 3469^{5} \)	20T771	Trivial (GRH)
20.6.4000000000000000000000000000000.1	x^20 + 10x^18 + 20x^16 - 80x^14 - 285x^12 + 26x^10 + 505x^8 - 240x^6 - 40x^4 + 20x^2 - 1	\( -\,2^{32}\cdot 5^{30} \)	20T771	Trivial (GRH)
20.6.4000000000000000000000000000000.2	x^20 - 5x^18 - 10x^16 + 135x^14 - 305x^12 - 24x^10 + 785x^8 - 605x^6 - 170x^4 + 35x^2 - 1	\( -\,2^{32}\cdot 5^{30} \)	20T771	Trivial (GRH)
20.12.25721213848857003468800000000000.1	x^20 - 8x^19 + 6x^18 + 86x^17 - 111x^16 - 470x^15 + 74x^14 + 3420x^13 - 154x^12 - 13418x^11 - 38x^10 + 33924x^9 - 3490x^8 - 42378x^7 - 5382x^6 + 38316x^5 + 4549x^4 - 12394x^3 - 2748x^2 + 482x + 89	\( 2^{20}\cdot 5^{11}\cdot 3469^{5} \)	20T771	Trivial (GRH)
20.8.25721213848857003468800000000000.1	x^20 - 8x^19 + 17x^18 + 56x^17 - 447x^16 + 1162x^15 - 1166x^14 - 1024x^13 + 4411x^12 - 4938x^11 + 3745x^10 - 5048x^9 + 3425x^8 + 994x^7 - 680x^6 - 72x^5 + 431x^4 - 550x^3 - 115x^2 + 30x + 5	\( 2^{20}\cdot 5^{11}\cdot 3469^{5} \)	20T771	Trivial (GRH)
20.12.25721213848857003468800000000000.2	x^20 - 20x^18 - 6x^17 + 158x^16 + 182x^15 - 758x^14 - 1692x^13 + 2054x^12 + 7146x^11 - 956x^10 - 12796x^9 - 3112x^8 + 7624x^7 - 8568x^6 - 16856x^5 + 164x^4 + 6556x^3 + 920x^2 - 628x - 124	\( 2^{20}\cdot 5^{11}\cdot 3469^{5} \)	20T771	$[2]$ (GRH)
20.10.64000000000000000000000000000000.1	x^20 - 10x^18 + 35x^16 - 40x^14 - 35x^12 + 96x^10 - 5x^8 - 70x^6 + 5x^4 + 20x^2 - 1	\( -\,2^{36}\cdot 5^{30} \)	20T771	Trivial (GRH)
20.2.64000000000000000000000000000000.1	x^20 + 10x^18 + 35x^16 + 40x^14 - 35x^12 - 96x^10 - 5x^8 + 70x^6 + 5x^4 - 20x^2 - 1	\( -\,2^{36}\cdot 5^{30} \)	20T771	Trivial (GRH)
20.6.64000000000000000000000000000000.4	x^20 - 10x^18 + 20x^16 + 80x^14 - 285x^12 - 26x^10 + 505x^8 + 240x^6 - 40x^4 - 20x^2 - 1	\( -\,2^{36}\cdot 5^{30} \)	20T771	Trivial (GRH)
20.6.64000000000000000000000000000000.5	x^20 + 5x^18 - 10x^16 - 135x^14 - 305x^12 + 24x^10 + 785x^8 + 605x^6 - 170x^4 - 35x^2 - 1	\( -\,2^{36}\cdot 5^{30} \)	20T771	Trivial (GRH)
20.10.157276367187500000000000000000000.1	x^20 - 15x^18 + 40x^16 - 35x^14 - 45x^12 + 194x^10 - 30x^8 - 245x^6 + 5x^4 + 60x^2 - 11	\( -\,2^{20}\cdot 5^{30}\cdot 11^{5} \)	20T771	Trivial (GRH)
20.2.157276367187500000000000000000000.1	x^20 + 15x^18 + 40x^16 + 35x^14 - 45x^12 - 194x^10 - 30x^8 + 245x^6 + 5x^4 - 60x^2 - 11	\( -\,2^{20}\cdot 5^{30}\cdot 11^{5} \)	20T771	Trivial (GRH)
20.16.411539421581712055500800000000000.1	x^20 - 4x^19 - 24x^18 + 92x^17 + 190x^16 - 796x^15 - 348x^14 + 3532x^13 - 1896x^12 - 9576x^11 + 7670x^10 + 16000x^9 - 11136x^8 - 14752x^7 + 8316x^6 + 6464x^5 - 3292x^4 - 916x^3 + 540x^2 - 32x - 4	\( 2^{24}\cdot 5^{11}\cdot 3469^{5} \)	20T771	Trivial (GRH)
20.4.411539421581712055500800000000000.1	x^20 - 2x^19 + 18x^18 - 14x^17 + 106x^16 + 48x^15 + 296x^14 + 1290x^13 - 1298x^12 + 11252x^11 - 8586x^10 + 18552x^9 + 50540x^8 - 60716x^7 + 172388x^6 + 43972x^5 - 99956x^4 - 164952x^3 - 76620x^2 - 21984x - 3044	\( 2^{24}\cdot 5^{11}\cdot 3469^{5} \)	20T771	Trivial (GRH)
20.8.411539421581712055500800000000000.1	x^20 - 8x^19 + 19x^18 + 62x^17 - 569x^16 + 2090x^15 - 5312x^14 + 9874x^13 - 11393x^12 + 302x^11 + 33235x^10 - 91450x^9 + 158821x^8 - 186836x^7 + 113292x^6 + 48668x^5 - 165385x^4 + 133676x^3 - 33935x^2 - 7014x - 89	\( 2^{24}\cdot 5^{11}\cdot 3469^{5} \)	20T771	Trivial (GRH)
20.16.411539421581712055500800000000000.2	x^20 - 6x^19 - 21x^18 + 158x^17 + 99x^16 - 1410x^15 + 372x^14 + 5384x^13 - 2993x^12 - 11122x^11 + 7507x^10 + 13660x^9 - 9569x^8 - 10148x^7 + 6410x^6 + 4228x^5 - 2011x^4 - 742x^3 + 205x^2 - 2x - 1	\( 2^{24}\cdot 5^{11}\cdot 3469^{5} \)	20T771	$[2]$ (GRH)
20.4.411539421581712055500800000000000.2	x^20 - 6x^19 + 13x^18 + 18x^17 - 191x^16 + 714x^15 - 2050x^14 + 5322x^13 - 10739x^12 + 16524x^11 - 21587x^10 + 28024x^9 - 35209x^8 + 65854x^7 - 84758x^6 + 800x^5 + 110721x^4 - 293560x^3 + 314885x^2 - 107400x - 20975	\( 2^{24}\cdot 5^{11}\cdot 3469^{5} \)	20T771	$[2]$ (GRH)
20.8.643030346221425086720000000000000.1	x^20 - 2x^19 + 10x^18 + 22x^17 - 129x^16 + 258x^15 + 34x^14 - 2052x^13 + 3258x^12 + 932x^11 - 9710x^10 + 5342x^9 - 2302x^8 + 12234x^7 + 20642x^6 + 1680x^5 - 13423x^4 - 16766x^3 + 2348x^2 + 3188x + 431	\( 2^{20}\cdot 5^{13}\cdot 3469^{5} \)	20T771	Trivial (GRH)
20.12.1069756574259831337445098876953125.1	x^20 - 33x^18 - 53x^17 + 458x^16 + 1114x^15 - 2937x^14 - 9566x^13 + 10148x^12 + 41938x^11 - 26077x^10 - 91579x^9 + 49188x^8 + 92368x^7 - 47697x^6 - 31838x^5 + 12895x^4 - 7970x^3 + 5579x^2 + 5371x - 1759	\( 5^{15}\cdot 19^{5}\cdot 1699^{5} \)	20T771	Trivial (GRH)
20.8.1069756574259831337445098876953125.1	x^20 - 3x^19 - 10x^18 + 88x^17 - 230x^16 - 47x^15 + 1830x^14 - 7056x^13 + 13375x^12 - 8135x^11 - 39538x^10 + 76702x^9 - 562x^8 - 139480x^7 - 41661x^6 + 317140x^5 - 56704x^4 - 129410x^3 + 49289x^2 + 8361x - 4639	\( 5^{15}\cdot 19^{5}\cdot 1699^{5} \)	20T771	Trivial (GRH)
20.12.1069756574259831337445098876953125.2	x^20 - 4x^19 - 26x^18 + 114x^17 + 109x^16 - 755x^15 + 740x^14 - 199x^13 - 3911x^12 + 13236x^11 - 3883x^10 - 30401x^9 + 21357x^8 + 10118x^7 - 40120x^6 - 11643x^5 + 20529x^4 + 15750x^3 - 3086x^2 - 4576x + 421	\( 5^{15}\cdot 19^{5}\cdot 1699^{5} \)	20T771	Trivial (GRH)
20.8.1069756574259831337445098876953125.2	x^20 - 2x^19 + 5x^18 + 60x^17 - 119x^16 - 84x^15 + 2577x^14 - 5921x^13 - 1119x^12 + 49587x^11 - 117590x^10 + 81686x^9 + 173576x^8 - 472480x^7 + 308850x^6 + 64335x^5 - 296334x^4 + 118979x^3 + 120463x^2 - 3930x - 4889	\( 5^{15}\cdot 19^{5}\cdot 1699^{5} \)	20T771	Trivial (GRH)
20.12.6584630745307392888012800000000000.1	x^20 - 8x^19 + 28x^18 - 56x^17 - 88x^16 + 838x^15 - 1630x^14 + 1708x^13 - 370x^12 - 10284x^11 + 31022x^10 - 56488x^9 + 24668x^8 + 97080x^7 - 6948x^6 + 118692x^5 - 886104x^4 + 575880x^3 + 504812x^2 - 353496x - 20956	\( 2^{28}\cdot 5^{11}\cdot 3469^{5} \)	20T771	Trivial (GRH)
20.16.6584630745307392888012800000000000.1	x^20 - 4x^19 - 35x^18 + 182x^17 + 383x^16 - 3196x^15 - 76x^14 + 27220x^13 - 29329x^12 - 109758x^11 + 229495x^10 + 116204x^9 - 676839x^8 + 461710x^7 + 493490x^6 - 1000694x^5 + 689579x^4 - 232870x^3 + 36309x^2 - 1684x - 29	\( 2^{28}\cdot 5^{11}\cdot 3469^{5} \)	20T771	Trivial (GRH)
20.4.6584630745307392888012800000000000.1	x^20 - 2x^19 + 12x^18 - 60x^17 + 130x^16 - 502x^15 + 1414x^14 - 4464x^13 + 11592x^12 - 23992x^11 + 62318x^10 - 111748x^9 + 191596x^8 - 416468x^7 + 663196x^6 - 682180x^5 + 424256x^4 - 76360x^3 - 65940x^2 + 55560x - 15380	\( 2^{28}\cdot 5^{11}\cdot 3469^{5} \)	20T771	$[2]$ (GRH)
20.12.6584630745307392888012800000000000.2	x^20 - 4x^19 - 9x^18 + 46x^17 - 93x^16 - 358x^15 + 1366x^14 + 3416x^13 - 535x^12 + 9002x^11 + 39897x^10 - 63890x^9 - 379411x^8 - 327670x^7 + 565752x^6 + 1165256x^5 + 259669x^4 - 793320x^3 - 509915x^2 + 54050x + 69775	\( 2^{28}\cdot 5^{11}\cdot 3469^{5} \)	20T771	Trivial (GRH)
20.16.6584630745307392888012800000000000.2	x^20 - 22x^18 + 13x^16 + 2312x^14 - 11774x^12 - 28580x^10 + 276498x^8 - 570872x^6 + 463389x^4 - 154710x^2 + 17345	\( 2^{28}\cdot 5^{11}\cdot 3469^{5} \)	20T771	$[2]$ (GRH)
20.4.6584630745307392888012800000000000.2	x^20 - 8x^19 + 12x^18 + 66x^17 - 468x^16 + 1834x^15 - 5296x^14 + 12292x^13 - 23702x^12 + 36028x^11 - 41810x^10 + 25800x^9 + 48952x^8 - 186004x^7 + 363896x^6 - 630084x^5 + 821652x^4 - 761240x^3 + 716304x^2 - 516048x + 154804	\( 2^{28}\cdot 5^{11}\cdot 3469^{5} \)	20T771	$[2]$ (GRH)
20.12.6584630745307392888012800000000000.3	x^20 + 2x^18 - 263x^16 + 840x^14 + 7642x^12 - 14024x^10 - 34594x^8 + 80288x^6 - 22531x^4 - 34690x^2 + 17345	\( 2^{28}\cdot 5^{11}\cdot 3469^{5} \)	20T771	Trivial (GRH)
20.0.10288485539542801387520000000000000.1	x^20 - 6x^19 + 31x^18 - 126x^17 + 585x^16 - 2104x^15 + 6984x^14 - 20704x^13 + 60785x^12 - 160826x^11 + 383571x^10 - 820556x^9 + 1669105x^8 - 3136304x^7 + 5344064x^6 - 7735664x^5 + 9191895x^4 - 8447796x^3 + 5304891x^2 - 2161426x + 543131	\( 2^{24}\cdot 5^{13}\cdot 3469^{5} \)	20T771	$[2, 2, 188]$ (GRH)
20.10.12888021157371923168000000000000000.1	x^20 - 40x^18 + 545x^16 - 2275x^14 - 9000x^12 + 72500x^10 + 152625x^8 - 2170625x^6 + 7590000x^4 - 10371875x^2 - 10371875	\( -\,2^{20}\cdot 5^{15}\cdot 3319^{5} \)	20T771	Trivial (GRH)
20.2.12888021157371923168000000000000000.1	x^20 - 5x^18 - 245x^16 + 25x^14 + 24025x^12 + 109000x^10 - 686500x^8 - 7156250x^6 - 21549375x^4 - 25518750x^2 - 10371875	\( -\,2^{20}\cdot 5^{15}\cdot 3319^{5} \)	20T771	$[2]$ (GRH)
20.10.12888021157371923168000000000000000.2	x^20 - 30x^18 + 300x^16 - 2925x^14 + 40300x^12 - 194875x^10 - 132500x^8 - 688125x^6 + 7807500x^4 - 10371875	\( -\,2^{20}\cdot 5^{15}\cdot 3319^{5} \)	20T771	Trivial (GRH)
20.2.12888021157371923168000000000000000.2	x^20 + 30x^18 + 340x^16 + 3800x^14 + 36350x^12 + 189125x^10 + 759625x^8 + 1132500x^6 - 8078125x^4 - 20743750x^2 - 10371875	\( -\,2^{20}\cdot 5^{15}\cdot 3319^{5} \)	20T771	Trivial (GRH)
20.0.105354091924918286208204800000000000.1	x^20 + 50x^18 + 1073x^16 + 12924x^14 + 95854x^12 + 451496x^10 + 1341646x^8 + 2405876x^6 + 2340241x^4 + 936630x^2 + 17345	\( 2^{32}\cdot 5^{11}\cdot 3469^{5} \)	20T771	$[2, 1232]$ (GRH)
20.12.105354091924918286208204800000000000.1	x^20 - 23x^18 + 173x^16 - 276x^14 - 2023x^12 + 6181x^10 + 8225x^8 - 27296x^6 - 18131x^4 + 34005x^2 + 17345	\( 2^{32}\cdot 5^{11}\cdot 3469^{5} \)	20T771	$[2]$ (GRH)
20.20.105354091924918286208204800000000000.1	x^20 - 50x^18 + 1073x^16 - 12924x^14 + 95854x^12 - 451496x^10 + 1341646x^8 - 2405876x^6 + 2340241x^4 - 936630x^2 + 17345	\( 2^{32}\cdot 5^{11}\cdot 3469^{5} \)	20T771	Trivial (GRH)
20.20.164615768632684822200320000000000000.1	x^20 - 2x^19 - 54x^18 + 150x^17 + 1012x^16 - 3730x^15 - 7068x^14 + 39644x^13 + 5066x^12 - 196456x^11 + 139610x^10 + 455972x^9 - 593080x^8 - 412196x^7 + 933912x^6 - 31268x^5 - 604764x^4 + 223160x^3 + 115660x^2 - 76600x + 10900	\( 2^{28}\cdot 5^{13}\cdot 3469^{5} \)	20T771	Trivial (GRH)