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 90)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.14124392182549037734912.1	x^20 + x^18 + 5x^16 + 2x^14 + x^12 - 7x^10 - 14x^8 - 3x^6 + x^4 + 7x^2 + 7	\( 2^{10}\cdot 7^{11}\cdot 17^{8} \)	20T525	Trivial
20.0.46408717171232552557568.1	x^20 - 5x^19 + 15x^18 - 31x^17 + 51x^16 - 69x^15 + 80x^14 - 95x^13 + 117x^12 - 113x^11 + 90x^10 - 55x^9 + 13x^8 + 13x^7 - 11x^6 + 15x^5 - 12x^4 - 2x^3 + 9x^2 - 5x + 1	\( 2^{10}\cdot 7^{10}\cdot 17^{8}\cdot 23 \)	20T525	Trivial
20.2.202312357996686362657792.1	x^20 + 3x^18 + 6x^16 + x^14 - 13x^12 - 33x^10 - 41x^8 - 29x^6 - 30x^4 - 17x^2 - 17	\( -\,2^{10}\cdot 7^{8}\cdot 17^{11} \)	20T525	Trivial (GRH)
20.2.583135620108095986484224.2	x^20 - 7x^19 + 25x^18 - 61x^17 + 112x^16 - 168x^15 + 217x^14 - 255x^13 + 268x^12 - 190x^11 + 5x^10 + 294x^9 - 606x^8 + 808x^7 - 822x^6 + 669x^5 - 431x^4 + 212x^3 - 70x^2 + 13x - 1	\( -\,2^{10}\cdot 7^{10}\cdot 17^{10} \)	20T525	Trivial (GRH)
20.0.6473995455893963605049344.1	x^20 - 7x^19 + 22x^18 - 41x^17 + 46x^16 - 13x^15 - 38x^14 + 45x^13 + x^12 - 75x^11 + 118x^10 - 132x^9 + 133x^8 - 181x^7 + 243x^6 - 119x^5 + 114x^4 - 58x^3 + 89x^2 + 2x + 19	\( 2^{15}\cdot 7^{8}\cdot 17^{11} \)	20T525	Trivial (GRH)
20.0.6740099894143626268524497.1	x^20 - 3x^19 + 9x^18 - 4x^17 - 2x^16 + 35x^15 - 13x^14 + 7x^13 + 102x^12 - 88x^11 + 154x^10 - 25x^9 + 54x^8 + 51x^7 + 24x^6 + 20x^5 + 25x^4 + 5x^3 + 6x^2 + 2x + 1	\( 7^{8}\cdot 11^{2}\cdot 17^{10}\cdot 4793 \)	20T525	Trivial (GRH)
20.4.10627349158296524814906368.1	x^20 - 7x^19 + 18x^18 - 10x^17 - 65x^16 + 214x^15 - 307x^14 + 122x^13 + 409x^12 - 997x^11 + 1171x^10 - 725x^9 - 146x^8 + 1095x^7 - 1776x^6 + 1845x^5 - 1253x^4 + 467x^3 - 15x^2 - 53x + 13	\( 2^{10}\cdot 7^{8}\cdot 17^{10}\cdot 19\cdot 47 \)	20T525	Trivial (GRH)
20.4.18660339843459071567495168.2	x^20 - 2x^19 - 5x^18 + 21x^17 - 13x^16 - 33x^15 + 63x^14 - 34x^13 - 13x^12 + 15x^11 - 86x^10 + 81x^9 - 132x^8 - 163x^7 - 159x^6 - 181x^5 - 56x^4 - 29x^3 - 7x^2 - 1	\( 2^{15}\cdot 7^{10}\cdot 17^{10} \)	20T525	Trivial (GRH)
20.0.10473339213126553396125334765568.1	x^20 - 4x^18 - 6x^16 + 4x^14 + 265x^12 + 72x^10 + 1092x^8 - 64x^6 + 14528x^4 + 16896x^2 + 51200	\( 2^{27}\cdot 727^{8} \)	20T525	$[11]$ (GRH)
20.14.163023866649059818618082021484375.1	x^20 - 4x^19 - 22x^18 + 90x^17 + 200x^16 - 806x^15 - 1092x^14 + 3858x^13 + 4384x^12 - 11359x^11 - 13643x^10 + 24276x^9 + 27710x^8 - 41649x^7 - 25253x^6 + 42381x^5 + 6277x^4 - 20061x^3 + 2245x^2 + 3297x - 829	\( -\,3^{8}\cdot 5^{10}\cdot 239^{9} \)	20T525	Trivial (GRH)
20.18.163023866649059818618082021484375.1	x^20 - 8x^19 + 3x^18 + 121x^17 - 246x^16 - 638x^15 + 2315x^14 + 1292x^13 - 10548x^12 - 804x^11 + 27547x^10 + 2633x^9 - 40347x^8 - 11191x^7 + 28572x^6 + 12631x^5 - 7548x^4 - 4002x^3 + 635x^2 + 320x - 29	\( -\,3^{8}\cdot 5^{10}\cdot 239^{9} \)	20T525	Trivial (GRH)
20.0.670293709640099417352021424996352.1	x^20 - 12x^18 + 63x^16 - 112x^14 - 421x^12 + 2540x^10 - 2335x^8 - 8880x^6 + 20004x^4 - 10912x^2 + 3200	\( 2^{33}\cdot 727^{8} \)	20T525	$[11]$ (GRH)
20.14.815119333245299093090410107421875.1	x^20 - 7x^19 + 83x^17 - 166x^16 - 187x^15 + 1345x^14 - 298x^13 - 2757x^12 + 4195x^11 + 5736x^10 - 5813x^9 - 8745x^8 - 47x^7 + 6396x^6 + 3547x^5 - 1956x^4 - 1500x^3 + 187x^2 + 66x - 1	\( -\,3^{8}\cdot 5^{11}\cdot 239^{9} \)	20T525	$[2]$ (GRH)
20.10.815119333245299093090410107421875.2	x^20 - 6x^19 + 3x^18 + 45x^17 - 93x^16 + 148x^15 - 539x^14 - 489x^13 + 3422x^12 - 894x^11 + 2973x^10 - 11008x^9 + 12614x^8 - 54399x^7 + 47350x^6 + 33765x^5 - 16959x^4 - 2255x^3 - 5890x^2 + 1605x + 605	\( -\,3^{8}\cdot 5^{11}\cdot 239^{9} \)	20T525	$[2]$ (GRH)
20.14.1467214799841538367562738193359375.1	x^20 - 4x^19 - 28x^18 + 139x^17 + 189x^16 - 1695x^15 + 885x^14 + 8148x^13 - 12751x^12 - 11190x^11 + 34205x^10 + 1662x^9 - 45780x^8 + 8426x^7 + 42749x^6 - 19900x^5 - 12502x^4 + 7338x^3 + 124x^2 - 44x - 1	\( -\,3^{10}\cdot 5^{10}\cdot 239^{9} \)	20T525	Trivial (GRH)
20.2.1467214799841538367562738193359375.1	x^20 - 4x^19 + 12x^18 - 10x^17 + 61x^16 - 9x^15 + 719x^14 - 285x^13 - 240x^12 - 4485x^11 + 1240x^10 + 9340x^9 - 1878x^8 - 10865x^7 - 68633x^6 - 80518x^5 - 84687x^4 - 48647x^3 - 18875x^2 - 187x - 3449	\( -\,3^{10}\cdot 5^{10}\cdot 239^{9} \)	20T525	Trivial (GRH)
20.6.1467214799841538367562738193359375.1	x^20 - 4x^19 - 22x^18 + 81x^17 + 169x^16 - 626x^15 - 341x^14 + 2196x^13 - 1972x^12 - 2961x^11 + 7741x^10 - 7092x^9 - 196x^8 + 20087x^7 - 35775x^6 + 17141x^5 + 32384x^4 - 60453x^3 + 34750x^2 - 1938x - 3249	\( -\,3^{10}\cdot 5^{10}\cdot 239^{9} \)	20T525	Trivial (GRH)
20.6.1467214799841538367562738193359375.2	x^20 - 10x^19 + 69x^18 - 336x^17 + 1174x^16 - 3068x^15 + 5396x^14 - 4278x^13 - 8489x^12 + 40768x^11 - 80876x^10 + 92029x^9 - 24941x^8 - 119760x^7 + 258225x^6 - 293603x^5 + 218300x^4 - 109620x^3 + 35827x^2 - 6808x + 529	\( -\,3^{10}\cdot 5^{10}\cdot 239^{9} \)	20T525	Trivial (GRH)
20.10.1467214799841538367562738193359375.3	x^20 - 5x^19 - 14x^18 + 73x^17 - 15x^16 - 253x^15 + 246x^14 - 596x^13 + 1397x^12 + 579x^11 - 2239x^10 + 3043x^9 - 4889x^8 + 3648x^7 + 165x^6 - 5816x^5 + 6387x^4 - 2450x^3 + 279x^2 + 285x - 55	\( -\,3^{10}\cdot 5^{10}\cdot 239^{9} \)	20T525	Trivial (GRH)
20.10.1467214799841538367562738193359375.4	x^20 - 6x^19 + 12x^18 - 6x^17 - 29x^16 + 148x^15 - 356x^14 + 263x^13 + 592x^12 - 2150x^11 + 2486x^10 + 3283x^9 - 10683x^8 + 375x^7 + 16903x^6 - 7773x^5 - 9342x^4 + 7323x^3 - 801x^2 - 320x + 55	\( -\,3^{10}\cdot 5^{10}\cdot 239^{9} \)	20T525	Trivial (GRH)
20.10.4075596666226495465452050537109375.1	x^20 - 5x^19 - 9x^18 + 127x^17 - 397x^16 + 330x^15 + 1670x^14 - 6707x^13 + 9906x^12 + 2065x^11 - 36253x^10 + 66812x^9 - 41659x^8 - 52485x^7 + 139583x^6 - 123767x^5 + 10046x^4 + 101145x^3 - 118335x^2 + 57792x - 9871	\( -\,3^{8}\cdot 5^{12}\cdot 239^{9} \)	20T525	$[2]$ (GRH)
20.14.4075596666226495465452050537109375.1	x^20 - 15x^18 - 19x^17 + 58x^16 + 109x^15 - 344x^14 + 1548x^13 + 5860x^12 - 13918x^11 - 33252x^10 + 34151x^9 + 66757x^8 - 23680x^7 - 32803x^6 - 9863x^5 - 30395x^4 + 13443x^3 + 26654x^2 - 3750x - 4491	\( -\,3^{8}\cdot 5^{12}\cdot 239^{9} \)	20T525	Trivial (GRH)
20.10.4075596666226495465452050537109375.2	x^20 - 9x^19 + 25x^18 - 9x^17 - 97x^16 + 221x^15 + 302x^14 - 1754x^13 + 1216x^12 + 3185x^11 - 7955x^10 - 114x^9 + 18905x^8 + 216x^7 - 18394x^6 - 5613x^5 + 2181x^4 - 891x^3 - 738x^2 + 216x + 81	\( -\,3^{8}\cdot 5^{12}\cdot 239^{9} \)	20T525	Trivial (GRH)
20.14.4075596666226495465452050537109375.2	x^20 - 10x^19 + 33x^18 - 12x^17 - 287x^16 + 1276x^15 - 2187x^14 - 1513x^13 + 14905x^12 - 33361x^11 + 24582x^10 + 55042x^9 - 148264x^8 + 121493x^7 + 82548x^6 - 313055x^5 + 101822x^4 + 286818x^3 - 64330x^2 - 125501x - 25541	\( -\,3^{8}\cdot 5^{12}\cdot 239^{9} \)	20T525	Trivial (GRH)
20.10.5092151360596147886766002500000000.1	x^20 - 4x^19 - 28x^18 + 107x^17 + 275x^16 - 887x^15 - 1757x^14 + 2953x^13 + 10339x^12 - 9144x^11 - 22883x^10 - 14527x^9 + 96743x^8 - 14161x^7 - 136209x^6 + 79301x^5 + 54262x^4 - 41964x^3 - 12243x^2 + 8566x + 2284	\( -\,2^{8}\cdot 5^{10}\cdot 1093^{8} \)	20T525	Trivial (GRH)
20.6.5092151360596147886766002500000000.1	x^20 + 10x^18 + 21x^16 - 60x^14 - 244x^12 - 104x^10 + 371x^8 + 298x^6 - 109x^4 - 104x^2 - 16	\( -\,2^{8}\cdot 5^{10}\cdot 1093^{8} \)	20T525	$[4]$ (GRH)
20.10.5480543527895745245520809137537024.1	x^20 + 2x^18 - 79x^16 - 16x^14 + 1225x^12 + 506x^10 - 5465x^8 - 2080x^6 + 6447x^4 + 18x^2 - 1	\( -\,2^{38}\cdot 613^{8} \)	20T525	Trivial (GRH)
20.14.6846284423532426067978240000000000.1	x^20 - 11x^18 + 2x^16 + 339x^14 - 1319x^12 + 1396x^10 + 1124x^8 - 3165x^6 + 1993x^4 - 368x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 401^{8} \)	20T525	Trivial (GRH)
20.18.6846284423532426067978240000000000.1	x^20 - 17x^18 + 75x^16 + 149x^14 - 2101x^12 + 6967x^10 - 11647x^8 + 10815x^6 - 5413x^4 + 1251x^2 - 81	\( -\,2^{20}\cdot 5^{10}\cdot 401^{8} \)	20T525	Trivial (GRH)
20.2.6846284423532426067978240000000000.1	x^20 + 25x^18 + 229x^16 + 983x^14 + 2031x^12 + 1712x^10 + 45x^8 - 535x^6 - 220x^4 - 29x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 401^{8} \)	20T525	Trivial (GRH)
20.6.6846284423532426067978240000000000.1	x^20 + 13x^18 + 40x^16 - 103x^14 - 630x^12 - 199x^10 + 2277x^8 + 2243x^6 - 961x^4 - 1229x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 401^{8} \)	20T525	Trivial (GRH)
20.10.6846284423532426067978240000000000.2	x^20 - 9x^18 - 23x^16 + 351x^14 - 407x^12 - 1255x^10 - 528x^8 + 177x^6 + 138x^4 + 17x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 401^{8} \)	20T525	Trivial (GRH)
20.14.6846284423532426067978240000000000.2	x^20 - 9x^18 - 53x^16 + 644x^14 - 1580x^12 + 503x^10 + 1514x^8 - 1036x^6 - 16x^4 + 42x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 401^{8} \)	20T525	Trivial (GRH)
20.6.6846284423532426067978240000000000.2	x^20 + 5x^18 - 64x^16 - 485x^14 - 987x^12 + 239x^10 + 3387x^8 + 4422x^6 + 2059x^4 + 153x^2 - 81	\( -\,2^{20}\cdot 5^{10}\cdot 401^{8} \)	20T525	Trivial (GRH)
20.10.6846284423532426067978240000000000.3	x^20 - x^18 - 70x^16 - 6x^14 + 979x^12 + 629x^10 - 1729x^8 - 21x^6 + 685x^4 - 187x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 401^{8} \)	20T525	Trivial (GRH)
20.14.6846284423532426067978240000000000.3	x^20 - 15x^18 + 10x^16 + 477x^14 - 712x^12 - 3009x^10 + 5686x^8 - 1107x^6 - 2213x^4 + 1044x^2 - 81	\( -\,2^{20}\cdot 5^{10}\cdot 401^{8} \)	20T525	Trivial (GRH)
20.6.6846284423532426067978240000000000.3	x^20 + 11x^18 + 33x^16 - 16x^14 - 206x^12 - 200x^10 + 176x^8 + 257x^6 + 33x^4 - 7x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 401^{8} \)	20T525	Trivial (GRH)
20.10.6846284423532426067978240000000000.4	x^20 - x^18 - 27x^16 - 10x^14 + 187x^12 + 193x^10 - 274x^8 - 364x^6 - 30x^4 + 47x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 401^{8} \)	20T525	Trivial (GRH)
20.6.6846284423532426067978240000000000.4	x^20 + 16x^18 + 31x^16 - 237x^14 - 702x^12 + 181x^10 + 1525x^8 + 567x^6 - 760x^4 - 522x^2 - 81	\( -\,2^{20}\cdot 5^{10}\cdot 401^{8} \)	20T525	Trivial (GRH)
20.10.6846284423532426067978240000000000.5	x^20 - 9x^18 - 24x^16 + 329x^14 - 70x^12 - 2983x^10 + 3293x^8 - 106x^6 - 329x^4 - 40x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 401^{8} \)	20T525	Trivial (GRH)
20.6.6846284423532426067978240000000000.5	x^20 + 21x^18 + 130x^16 + 128x^14 - 1130x^12 - 3098x^10 - 525x^8 + 5552x^6 + 5504x^4 + 1377x^2 - 81	\( -\,2^{20}\cdot 5^{10}\cdot 401^{8} \)	20T525	Trivial (GRH)
20.10.6846284423532426067978240000000000.6	x^20 - 3x^18 - 43x^16 + 118x^14 + 344x^12 - 1272x^10 + 739x^8 + 690x^6 - 460x^4 - 104x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 401^{8} \)	20T525	Trivial (GRH)
20.8.14282281564801524093709347890645941.1	x^20 - 10x^19 + 58x^18 - 237x^17 + 732x^16 - 1776x^15 + 3414x^14 - 5160x^13 + 5909x^12 - 4540x^11 + 1069x^10 + 2866x^9 - 5050x^8 + 4576x^7 - 2545x^6 + 727x^5 + 74x^4 - 162x^3 + 67x^2 - 13x + 1	\( 7^{2}\cdot 13^{10}\cdot 61\cdot 277^{8} \)	20T525	Trivial (GRH)
20.16.14390904535739547813668680751953125.1	x^20 - 10x^19 + 34x^18 - 21x^17 - 148x^16 + 368x^15 - 129x^14 - 743x^13 + 1251x^12 - 109x^11 - 1842x^10 + 1614x^9 + 872x^8 - 1677x^7 + 112x^6 + 685x^5 - 200x^4 - 109x^3 + 45x^2 + 6x - 1	\( 3^{2}\cdot 5^{10}\cdot 401^{8}\cdot 244901 \)	20T525	Trivial (GRH)
20.8.23533415996900471975491413486328125.1	x^20 - 10x^19 + 50x^18 - 165x^17 + 384x^16 - 624x^15 + 615x^14 - 15x^13 - 1174x^12 + 2273x^11 - 2252x^10 + 705x^9 + 1389x^8 - 2457x^7 + 1816x^6 - 348x^5 - 584x^4 + 611x^3 - 227x^2 + 12x + 19	\( 3^{8}\cdot 5^{10}\cdot 239^{8}\cdot 34501 \)	20T525	Trivial (GRH)
20.4.30331521634966280188194686254636032.1	x^20 + 11x^18 + 31x^16 - 60x^14 - 459x^12 - 773x^10 - 278x^8 + 405x^6 + 378x^4 + 96x^2 + 7	\( 2^{10}\cdot 3^{10}\cdot 7\cdot 19^{10}\cdot 43^{8} \)	20T525	Trivial (GRH)
20.8.59705773703379638670871205517459456.1	x^20 - 10x^19 + 53x^18 - 192x^17 + 506x^16 - 988x^15 + 1372x^14 - 1086x^13 - 350x^12 + 2646x^11 - 4428x^10 + 4138x^9 - 1636x^8 - 1392x^7 + 2813x^6 - 2176x^5 + 744x^4 + 134x^3 - 227x^2 + 78x - 9	\( 2^{30}\cdot 3^{2}\cdot 401^{8}\cdot 9241 \)	20T525	Trivial (GRH)
20.4.1486244560113347729221539626477165568.1	x^20 + 29x^18 + 233x^16 - 329x^14 - 11818x^12 - 41203x^10 + 19869x^8 + 236114x^6 + 132013x^4 + 15827x^2 + 343	\( 2^{10}\cdot 3^{10}\cdot 7^{3}\cdot 19^{10}\cdot 43^{8} \)	20T525	Trivial (GRH)
20.8.1486244560113347729221539626477165568.1	x^20 - 29x^18 + 154x^16 + 628x^14 - 2456x^12 - 8032x^10 - 219x^8 + 14425x^6 + 13230x^4 + 4018x^2 + 343	\( 2^{10}\cdot 3^{10}\cdot 7^{3}\cdot 19^{10}\cdot 43^{8} \)	20T525	Trivial (GRH)
20.10.2745360053836502853259274240000000000.1	x^20 + 7x^18 - 155x^16 - 244x^14 + 7328x^12 - 20068x^10 - 6319x^8 + 56864x^6 - 12743x^4 - 7619x^2 - 401	\( -\,2^{20}\cdot 5^{10}\cdot 401^{9} \)	20T525	Trivial (GRH)