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 matches 1-50 of 3650)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.569468379011812486801.1	x^20 - 4x^19 + 8x^18 - 12x^17 + 6x^16 + 11x^15 - 13x^14 - 4x^13 + 37x^12 - 63x^11 + 41x^10 + 4x^9 + 12x^8 - 58x^7 + 30x^6 + 7x^5 + 9x^4 - 12x^3 + 1	\( 7^{10}\cdot 17^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.3105926159393528563401.1	x^20 - x^19 - 5x^18 + 22x^16 + x^15 - 38x^14 - 11x^13 + 46x^12 + 11x^11 - 51x^10 + 11x^9 + 46x^8 - 11x^7 - 38x^6 + x^5 + 22x^4 - 5x^2 - x + 1	\( 3^{10}\cdot 47^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.3575694237941010577249.1	x^20 - 4x^19 + 12x^18 - 24x^17 + 40x^16 - 49x^15 + 64x^14 - 95x^13 + 161x^12 - 229x^11 + 304x^10 - 358x^9 + 359x^8 - 288x^7 + 214x^6 - 134x^5 + 67x^4 - 29x^3 + 13x^2 - x + 1	\( 11^{10}\cdot 13^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.10326930237613180030401.1	x^20 - 4x^19 + 12x^17 + 6x^16 - 24x^15 - 29x^14 + 26x^13 + 19x^12 + 33x^11 + 23x^10 - 24x^9 - 32x^8 - 43x^7 + 52x^6 + 54x^5 + 57x^4 + 12x^3 + 24x^2 - x + 1	\( 3^{10}\cdot 53^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.55154187683317729460224.3	x^20 - 11x^18 + 52x^16 - 139x^14 + 241x^12 - 287x^10 + 241x^8 - 139x^6 + 52x^4 - 11x^2 + 1	\( 2^{20}\cdot 47^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.87989866733551025390625.1	x^20 - 10x^19 + 45x^18 - 120x^17 + 200x^16 - 172x^15 - 75x^14 + 475x^13 - 735x^12 + 575x^11 - 30x^10 - 560x^9 + 905x^8 - 975x^7 + 915x^6 - 794x^5 + 595x^4 - 345x^3 + 150x^2 - 45x + 9	\( 3^{10}\cdot 5^{26} \)	$D_{10}$ (as 20T4)	Trivial
20.0.513663400740527822265625.2	x^20 - x^19 + 17x^18 - 6x^17 + 104x^16 - 7x^15 + 366x^14 - 5x^13 + 784x^12 - x^11 + 1015x^10 + x^9 + 784x^8 + 5x^7 + 366x^6 + 7x^5 + 104x^4 + 6x^3 + 17x^2 + x + 1	\( 5^{10}\cdot 47^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.559092234403032700371849.1	x^20 - 2x^19 + x^18 + 8x^17 - 6x^16 - 15x^15 + 88x^14 - 82x^13 + 37x^12 + 161x^11 - 75x^10 - 70x^9 + 457x^8 - 571x^7 + 238x^6 - 333x^5 + 297x^4 - 55x^3 + 4x^2 - 5x + 1	\( 3^{10}\cdot 79^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.1562500000000000000000000.1	x^20 + 5x^18 + 20x^16 + 35x^14 + 215x^12 + 472x^10 + 215x^8 + 35x^6 + 20x^4 + 5x^2 + 1	\( 2^{20}\cdot 5^{26} \)	$D_{10}$ (as 20T4)	Trivial
20.0.5163178154897836475416576.1	x^20 - 2x^19 + 3x^18 - 10x^17 + 29x^16 - 48x^15 + 42x^14 - 40x^13 + 168x^12 - 524x^11 + 872x^10 - 788x^9 + 327x^8 - 10x^7 + 17x^6 + 10x^5 - 117x^4 + 48x^3 + 38x^2 - 16x + 4	\( 2^{30}\cdot 37^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.6522683188340621511158049.1	x^20 - 2x^19 + 3x^18 - 6x^17 + 5x^16 + 13x^15 + 2x^14 + 4x^13 - 32x^12 - 4x^11 + 154x^10 - 23x^9 + 157x^8 - 298x^7 + 29x^6 + 527x^5 + 374x^4 + 114x^3 - 69x^2 + 221x + 289	\( 3^{10}\cdot 101^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.7935691828389105528301401.1	x^20 - 2x^19 + x^18 - 8x^17 + 26x^16 - 35x^15 + 108x^14 - 230x^13 + 359x^12 - 619x^11 + 1059x^10 - 1756x^9 + 2561x^8 - 3379x^7 + 4120x^6 - 4105x^5 + 3313x^4 - 1833x^3 + 828x^2 - 351x + 81	\( 3^{10}\cdot 103^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.9928207061616528930635776.1	x^20 - 2x^18 - 17x^16 - 3x^14 + 85x^12 + 208x^10 + 439x^8 - 195x^6 + 229x^4 - 17x^2 + 1	\( 2^{20}\cdot 79^{10} \)	$D_{10}$ (as 20T4)	$[3]$
20.0.10912062142819279835644801.1	x^20 - 2x^19 + x^18 - 6x^17 + 24x^16 - 30x^15 + 45x^14 - 135x^13 + 139x^12 - 125x^11 + 397x^10 - 546x^9 + 111x^8 - 276x^7 + 936x^6 - 162x^5 + 382x^4 - 179x^3 + 205x^2 - 60x + 9	\( 11^{10}\cdot 29^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.14857952975500019812957201.1	x^20 - x^19 - 16x^18 + 3x^17 + 137x^16 + 5x^15 - 615x^14 - 107x^13 + 1852x^12 + 161x^11 - 4157x^10 + 322x^9 + 7408x^8 - 856x^7 - 9840x^6 + 160x^5 + 8768x^4 + 384x^3 - 4096x^2 - 512x + 1024	\( 7^{10}\cdot 47^{10} \)	$D_{10}$ (as 20T4)	Trivial (GRH)
20.0.23205152438409568951730176.1	x^20 + 12x^18 + 57x^16 + 144x^14 + 236x^12 + 270x^10 + 109x^8 - 108x^6 + 73x^4 - 14x^2 + 4	\( 2^{30}\cdot 43^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.33626538312268515533112249.1	x^20 - 6x^19 + 13x^18 - 6x^17 - 18x^16 - 18x^15 + 296x^14 - 939x^13 + 1648x^12 - 1689x^11 + 727x^10 + 537x^9 - 1049x^8 + 546x^7 + 156x^6 - 315x^5 + 354x^4 - 399x^3 + 14x^2 + 147x + 49	\( 3^{10}\cdot 7^{10}\cdot 17^{10} \)	$D_{10}$ (as 20T4)	$[2]$
20.0.33626538312268515533112249.2	x^20 - 6x^19 + 18x^18 - 32x^17 + 41x^16 + x^15 - 113x^14 + 222x^13 - 194x^12 - 14x^11 + 723x^10 - 446x^9 + 1142x^8 + 574x^7 + 89x^6 + 2241x^5 + 424x^4 + 340x^3 + 629x^2 + 289	\( 3^{10}\cdot 7^{10}\cdot 17^{10} \)	$D_{10}$ (as 20T4)	$[2]$
20.0.56477888187717354967269376.2	x^20 - 22x^18 + 208x^16 - 1112x^14 + 3856x^12 - 9184x^10 + 15424x^8 - 17792x^6 + 13312x^4 - 5632x^2 + 1024	\( 2^{30}\cdot 47^{10} \)	$D_{10}$ (as 20T4)	Trivial (GRH)
20.0.56477888187717354967269376.3	x^20 + 22x^18 + 208x^16 + 1112x^14 + 3856x^12 + 9184x^10 + 15424x^8 + 17792x^6 + 13312x^4 + 5632x^2 + 1024	\( 2^{30}\cdot 47^{10} \)	$D_{10}$ (as 20T4)	$[4]$
20.0.64453982490130814650341801.1	x^20 - 5x^19 + 7x^18 - 6x^17 + 38x^16 - 98x^15 + 84x^14 - 82x^13 + 358x^12 - 752x^11 + 849x^10 - 748x^9 + 1133x^8 - 2523x^7 + 3679x^6 - 2392x^5 - 407x^4 + 1206x^3 - 198x^2 + 81	\( 3^{10}\cdot 127^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.87887174756230199195247249.1	x^20 - 4x^19 + 12x^18 - 8x^17 - 9x^16 + 50x^15 - 20x^14 - 38x^13 - 16x^12 - 126x^11 + 236x^10 - 176x^9 - 237x^8 + 434x^7 - 428x^6 - 58x^5 + 1629x^4 - 66x^3 - 160x^2 - 8x + 16	\( 3^{10}\cdot 131^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.92463633619402804697265625.1	x^20 - 6x^19 + 17x^18 - 34x^17 + 72x^16 - 142x^15 + 230x^14 - 374x^13 + 667x^12 - 926x^11 + 1464x^10 - 4142x^9 + 10155x^8 - 17489x^7 + 24262x^6 - 26479x^5 + 20704x^4 - 10840x^3 + 3907x^2 - 1407x + 441	\( 5^{10}\cdot 79^{10} \)	$D_{10}$ (as 20T4)	$[4]$
20.0.140919846138714198689972224.1	x^20 - 2x^18 - 17x^16 - 15x^14 + 129x^12 + 300x^10 + 763x^8 + 1393x^6 + 1021x^4 + 135x^2 + 81	\( 2^{20}\cdot 103^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.151523839718807162587890625.1	x^20 - 2x^19 + x^18 - 7x^17 + 30x^16 - 31x^15 + 85x^14 - 294x^13 + 401x^12 - 247x^11 + 505x^10 - 849x^9 + 449x^8 + 956x^7 - 1284x^6 + 17x^5 + 680x^4 - 347x^3 - 256x^2 - 168x + 441	\( 5^{10}\cdot 83^{10} \)	$D_{10}$ (as 20T4)	$[3]$
20.0.211141169056178733575976201.1	x^20 - 2x^19 + 3x^18 + 3x^17 + 27x^16 - 54x^15 + 168x^14 + 16x^13 + 165x^12 - 233x^11 + 1651x^10 - 1477x^9 + 2362x^8 - 964x^7 + 1188x^6 + 1161x^5 + 2680x^4 + 2012x^3 + 1952x^2 + 1056x + 352	\( 3^{10}\cdot 11^{10}\cdot 13^{10} \)	$D_{10}$ (as 20T4)	$[4]$
20.0.211141169056178733575976201.2	x^20 - 6x^19 + 13x^18 - 6x^17 - 16x^16 - 30x^15 + 338x^14 - 1062x^13 + 1939x^12 - 2190x^11 + 1354x^10 - 174x^9 + 53x^8 - 1311x^7 + 2270x^6 - 1533x^5 + 324x^4 + 180x^3 - 225x^2 - 375x + 625	\( 3^{10}\cdot 11^{10}\cdot 13^{10} \)	$D_{10}$ (as 20T4)	$[2, 2]$
20.0.380289177849714310556640625.1	x^20 - 10x^19 + 47x^18 - 138x^17 + 247x^16 - 140x^15 - 632x^14 + 2386x^13 - 4378x^12 + 4350x^11 + 269x^10 - 9513x^9 + 18621x^8 - 21290x^7 + 15762x^6 - 6851x^5 + 779x^4 + 910x^3 - 371x^2 - 49x + 49	\( 5^{10}\cdot 7^{10}\cdot 13^{10} \)	$D_{10}$ (as 20T4)	$[4]$
20.0.380289177849714310556640625.2	x^20 - 10x^19 + 49x^18 - 154x^17 + 352x^16 - 658x^15 + 1097x^14 - 1685x^13 + 2301x^12 - 2747x^11 + 2931x^10 - 2708x^9 + 2371x^8 - 1380x^7 + 1802x^6 - 312x^5 + 1202x^4 + 189x^3 + 469x^2 + 110x + 121	\( 5^{10}\cdot 7^{10}\cdot 13^{10} \)	$D_{10}$ (as 20T4)	$[4]$
20.0.380289177849714310556640625.3	x^20 - 6x^19 + 19x^18 - 50x^17 + 141x^16 - 391x^15 + 904x^14 - 1750x^13 + 3286x^12 - 6246x^11 + 10834x^10 - 16150x^9 + 20781x^8 - 23886x^7 + 26369x^6 - 28225x^5 + 26886x^4 - 21221x^3 + 12949x^2 - 5575x + 1355	\( 5^{10}\cdot 7^{10}\cdot 13^{10} \)	$D_{10}$ (as 20T4)	$[4]$
20.0.420920921862125396728515625.1	x^20 + 5x^18 + 15x^16 + 85x^14 + 450x^12 + 1090x^10 + 1275x^8 + 1125x^6 + 575x^4 - 625x^2 + 100	\( 5^{26}\cdot 7^{10} \)	$D_{10}$ (as 20T4)	Trivial (GRH)
20.0.597130874990690290159845376.1	x^20 - 7x^18 + 18x^16 + 9x^14 - 104x^12 + 144x^10 + 114x^8 - 472x^6 + 592x^4 - 175x^2 + 49	\( 2^{20}\cdot 7^{10}\cdot 17^{10} \)	$D_{10}$ (as 20T4)	$[4]$
20.0.597130874990690290159845376.2	x^20 - 11x^18 + 40x^16 - 49x^14 - 125x^12 + 829x^10 - 500x^8 - 784x^6 + 2560x^4 - 2816x^2 + 1024	\( 2^{20}\cdot 7^{10}\cdot 17^{10} \)	$D_{10}$ (as 20T4)	$[2, 2]$
20.0.765946119106374437095604224.1	x^20 - 4x^18 - 4x^17 + 20x^16 - 28x^15 - 42x^14 + 160x^13 + 242x^12 - 148x^11 + 140x^10 + 352x^9 - 1375x^8 + 168x^7 + 3214x^6 - 2152x^5 - 5308x^4 + 3888x^3 + 4816x^2 - 5440x + 1600	\( 2^{30}\cdot 61^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.1144556201520286695842381824.1	x^20 - 11x^18 + 56x^16 - 150x^14 + 146x^12 + 174x^10 - 199x^8 - 1235x^6 + 2266x^4 - 396x^2 + 81	\( 2^{20}\cdot 127^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.1312418339203244062978515625.1	x^20 - 8x^19 + 44x^18 - 188x^17 + 649x^16 - 1890x^15 + 4683x^14 - 9996x^13 + 18417x^12 - 28542x^11 + 36198x^10 - 38148x^9 + 35494x^8 - 28955x^7 + 20732x^6 - 11735x^5 + 6277x^4 - 2889x^3 + 1269x^2 - 243x + 81	\( 5^{10}\cdot 103^{10} \)	$D_{10}$ (as 20T4)	$[3]$
20.0.1364286026444870446587635449.1	x^20 + 29x^18 + 373x^16 + 2732x^14 + 12704x^12 + 38962x^10 + 76742x^8 + 94643x^6 + 51635x^4 + 41965x^2 + 27889	\( 11^{10}\cdot 47^{10} \)	$D_{10}$ (as 20T4)	Trivial (GRH)
20.0.1560676423939251085562085376.1	x^20 + 8x^18 + 2x^16 - 32x^14 + 195x^12 - 484x^10 + 874x^8 - 1028x^6 + 1769x^4 - 324x^2 + 16	\( 2^{20}\cdot 131^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.1570539027548129147161113769.1	x^20 - 10x^19 + 47x^18 - 138x^17 + 264x^16 - 276x^15 - 89x^14 + 965x^13 - 1963x^12 + 2145x^11 - 714x^10 - 2046x^9 + 5062x^8 - 7225x^7 + 8630x^6 - 9087x^5 + 8019x^4 - 5370x^3 + 3430x^2 - 1645x + 947	\( 7^{10}\cdot 11^{18} \)	$D_{10}$ (as 20T4)	$[5]$
20.0.1600000000000000000000000000.1	x^20 - 10x^18 + 55x^16 - 160x^14 + 525x^12 - 390x^10 + 725x^8 - 500x^6 + 575x^4 + 250x^2 + 225	\( 2^{30}\cdot 5^{26} \)	$D_{10}$ (as 20T4)	Trivial (GRH)
20.0.1994081282499911259959052849.1	x^20 - 14x^18 + 99x^16 - 355x^14 + 823x^12 - 1103x^10 + 2806x^8 + 5547x^6 + 1536x^4 + 128x^2 + 64	\( 3^{10}\cdot 179^{10} \)	$D_{10}$ (as 20T4)	Trivial
20.0.2674553644040763237187428049.1	x^20 - 6x^19 + 11x^18 + 8x^17 - 45x^16 - 100x^15 + 917x^14 - 2570x^13 + 3808x^12 - 2840x^11 + 591x^10 - 746x^9 + 5829x^8 - 12332x^7 + 9220x^6 + 11228x^5 - 23849x^4 - 2776x^3 + 32929x^2 - 25596x + 6399	\( 7^{10}\cdot 79^{10} \)	$D_{10}$ (as 20T4)	Trivial (GRH)
20.0.3256799628512228606896766976.1	x^20 + 33x^18 + 468x^16 + 3753x^14 + 19521x^12 + 69741x^10 + 175689x^8 + 303993x^6 + 341172x^4 + 216513x^2 + 59049	\( 2^{20}\cdot 3^{10}\cdot 47^{10} \)	$D_{10}$ (as 20T4)	$[2, 2]$ (GRH)
20.0.3749387161243233107049447424.1	x^20 - 11x^18 + 60x^16 - 211x^14 + 613x^12 - 1523x^10 + 2633x^8 - 1847x^6 + 564x^4 + 253x^2 + 121	\( 2^{20}\cdot 11^{10}\cdot 13^{10} \)	$D_{10}$ (as 20T4)	$[2]$
20.0.3749387161243233107049447424.2	x^20 - 12x^18 + 60x^16 - 233x^14 + 744x^12 - 1557x^10 + 4367x^8 - 2480x^6 + 5299x^4 - 1925x^2 + 625	\( 2^{20}\cdot 11^{10}\cdot 13^{10} \)	$D_{10}$ (as 20T4)	$[2]$
20.0.5287094430615384550826573824.1	x^20 - 8x^19 + 38x^18 - 164x^17 + 555x^16 - 1484x^15 + 3300x^14 - 5808x^13 + 8423x^12 - 9552x^11 + 8814x^10 - 5980x^9 + 4373x^8 - 3572x^7 + 3752x^6 - 1168x^5 + 1180x^4 + 536x^3 + 312x^2 - 64x + 4	\( 2^{40}\cdot 37^{10} \)	$D_{10}$ (as 20T4)	$[2]$
20.0.5287094430615384550826573824.2	x^20 - 4x^19 + 10x^18 - 12x^17 + 30x^16 - 132x^15 + 402x^14 - 796x^13 + 645x^12 - 176x^11 - 48x^10 + 56x^9 + 7572x^8 - 8648x^7 - 520x^6 + 1408x^5 + 3012x^4 - 2544x^3 + 544x^2 - 32x + 16	\( 2^{40}\cdot 37^{10} \)	$D_{10}$ (as 20T4)	$[2]$
20.0.5561214638787231316416015625.1	x^20 - 6x^19 + 9x^18 + 14x^17 - 34x^16 - 50x^15 + 132x^14 + 7x^13 + 24x^12 - 323x^11 + 457x^10 - 3573x^9 + 12919x^8 - 21832x^7 + 24538x^6 - 23909x^5 + 18576x^4 - 8077x^3 + 1594x^2 - 1485x + 1019	\( 5^{10}\cdot 7^{10}\cdot 17^{10} \)	$D_{10}$ (as 20T4)	$[4]$
20.0.5561214638787231316416015625.2	x^20 - 6x^19 + 22x^18 - 48x^17 + 99x^16 - 279x^15 + 825x^14 - 1626x^13 + 2616x^12 - 4636x^11 + 8769x^10 - 12770x^9 + 10464x^8 + 6378x^7 - 34663x^6 + 51815x^5 - 32318x^4 - 12998x^3 + 42435x^2 - 31710x + 10031	\( 5^{10}\cdot 7^{10}\cdot 17^{10} \)	$D_{10}$ (as 20T4)	$[4]$ (GRH)
20.0.5969915757478328440239161344.4	x^20 + 4x^18 + 49x^16 + 108x^14 + 300x^12 - 10x^10 + 301x^8 - 116x^6 + 9x^4 + 278x^2 + 100	\( 2^{30}\cdot 11^{18} \)	$D_{10}$ (as 20T4)	$[5]$