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
20.0.695623523818852398025.1	x^20 - 5x^19 + 12x^18 - 18x^17 + 20x^16 - 23x^15 + 33x^14 - 44x^13 + 47x^12 - 51x^11 + 78x^10 - 122x^9 + 143x^8 - 115x^7 + 61x^6 - 22x^5 + 10x^4 - 9x^3 + 6x^2 - 2x + 1	\( 5^{2}\cdot 23^{2}\cdot 47^{10} \)	20T412	Trivial
20.0.172004164305285576392704.3	x^20 - 2x^18 + 4x^16 - 13x^14 + 16x^12 - 11x^10 + 16x^8 - 13x^6 + 4x^4 - 2x^2 + 1	\( 2^{20}\cdot 47^{8}\cdot 83^{2} \)	20T412	Trivial (GRH)
20.4.252040366516203798224329.1	x^20 - 7x^19 + 27x^18 - 83x^17 + 203x^16 - 404x^15 + 677x^14 - 958x^13 + 1122x^12 - 1101x^11 + 925x^10 - 680x^9 + 536x^8 - 546x^7 + 546x^6 - 422x^5 + 249x^4 - 118x^3 + 39x^2 - 4x - 1	\( 11^{2}\cdot 47^{10}\cdot 199^{2} \)	20T412	Trivial (GRH)
20.4.1536632364115844947237225.1	x^20 - 5x^19 + 2x^18 + 26x^17 - 33x^16 - 38x^15 + 31x^14 + 148x^13 - 147x^12 - 75x^11 + 20x^10 + 198x^9 - 163x^8 + 24x^7 + 15x^6 + 57x^5 - 102x^4 + 11x^3 + 37x^2 + 5x - 11	\( 5^{2}\cdot 23^{2}\cdot 47^{12} \)	20T412	Trivial (GRH)
20.4.2172224423052426981920049.1	x^20 - 9x^19 + 40x^18 - 110x^17 + 206x^16 - 274x^15 + 243x^14 - 65x^13 - 199x^12 + 380x^11 - 458x^10 + 656x^9 - 976x^8 + 1041x^7 - 691x^6 + 244x^5 + 2x^4 - 51x^3 + 27x^2 - 7x + 1	\( 3^{2}\cdot 19^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.4.30332917774535413894346169.1	x^20 - 10x^19 + 55x^18 - 210x^17 + 602x^16 - 1348x^15 + 2390x^14 - 3340x^13 + 3576x^12 - 2684x^11 + 933x^10 + 785x^9 - 1638x^8 + 1496x^7 - 842x^6 + 239x^5 + 51x^4 - 88x^3 + 42x^2 - 10x + 1	\( 3^{2}\cdot 71^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.4.56616231569252868345943881.1	x^20 + 5x^18 - 19x^16 - 67x^14 - 7x^12 + 77x^10 - 7x^8 - 67x^6 - 19x^4 + 5x^2 + 1	\( 3^{2}\cdot 97^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.4.175950178267246585535523969.2	x^20 + 6x^18 - 11x^16 - 102x^14 - 304x^12 - 524x^10 - 525x^8 - 226x^6 + 123x^4 + 34x^2 + 1	\( 3^{6}\cdot 19^{2}\cdot 401^{8} \)	20T412	$[2]$ (GRH)
20.8.175950178267246585535523969.2	x^20 + 2x^18 - 23x^16 + 19x^14 + 20x^12 - 19x^10 + 20x^8 + 19x^6 - 23x^4 + 2x^2 + 1	\( 3^{6}\cdot 19^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.4.175950178267246585535523969.3	x^20 - 8x^19 + 32x^18 - 87x^17 + 175x^16 - 255x^15 + 236x^14 + 15x^13 - 637x^12 + 1645x^11 - 2894x^10 + 4143x^9 - 5024x^8 + 5237x^7 - 4780x^6 + 3751x^5 - 2520x^4 + 1479x^3 - 678x^2 + 249x - 79	\( 3^{6}\cdot 19^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.8.175950178267246585535523969.3	x^20 - x^19 - 8x^18 + 10x^17 + 18x^16 - 39x^15 + 25x^14 + 86x^13 - 193x^12 + 9x^11 + 283x^10 - 371x^9 + 87x^8 + 220x^7 - 273x^6 + 204x^5 - 111x^4 + 51x^3 + 22x^2 - 24x + 3	\( 3^{6}\cdot 19^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.4.175950178267246585535523969.4	x^20 - 9x^19 + 44x^18 - 151x^17 + 403x^16 - 921x^15 + 1868x^14 - 3313x^13 + 5157x^12 - 7152x^11 + 8814x^10 - 9561x^9 + 9115x^8 - 7603x^7 + 5432x^6 - 3224x^5 + 1532x^4 - 546x^3 + 132x^2 - 18x + 1	\( 3^{6}\cdot 19^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.4.1063127015022637194496057321.1	x^20 - 5x^19 + 5x^18 + 30x^17 - 127x^16 + 225x^15 - 235x^14 + 307x^13 - 713x^12 + 1223x^11 - 1249x^10 + 871x^9 - 704x^8 + 699x^7 - 363x^6 - 140x^5 + 325x^4 - 207x^3 + 69x^2 - 12x + 1	\( 13^{2}\cdot 97^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.0.1818010102612675439108642401.1	x^20 - 9x^19 + 33x^18 - 52x^17 - 13x^16 + 179x^15 - 164x^14 - 528x^13 + 1963x^12 - 3215x^11 + 2883x^10 - 690x^9 - 1618x^8 + 1884x^7 - 126x^6 - 1516x^5 + 1571x^4 - 698x^3 + 97x^2 + 18x + 9	\( 17^{2}\cdot 97^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.12.2456966339737368525442039689.1	x^20 - 3x^19 - 15x^18 + 64x^17 + 10x^16 - 364x^15 + 356x^14 + 867x^13 - 1629x^12 - 617x^11 + 3190x^10 - 1254x^9 - 2721x^8 + 2588x^7 + 575x^6 - 1534x^5 + 208x^4 + 407x^3 - 55x^2 - 66x - 9	\( 3^{6}\cdot 71^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.0.2456966339737368525442039689.2	x^20 - 6x^19 + 20x^18 - 50x^17 + 111x^16 - 204x^15 + 286x^14 - 262x^13 + 168x^12 - 108x^11 + 138x^10 - 202x^9 + 200x^8 - 141x^7 + 116x^6 - 107x^5 + 68x^4 - 30x^3 + 16x^2 - 6x + 1	\( 3^{6}\cdot 71^{2}\cdot 401^{8} \)	20T412	$[4]$ (GRH)
20.0.4585914757109482336021454361.1	x^20 - 8x^19 + 35x^18 - 102x^17 + 221x^16 - 375x^15 + 509x^14 - 490x^13 + 224x^12 - 181x^11 + 1382x^10 - 3346x^9 + 3365x^8 - 1116x^7 + 808x^6 - 3709x^5 + 5049x^4 - 2899x^3 + 805x^2 - 325x + 169	\( 3^{6}\cdot 97^{2}\cdot 401^{8} \)	20T412	$[2]$ (GRH)
20.12.4585914757109482336021454361.1	x^20 - 6x^19 + 4x^18 + 32x^17 - 46x^16 - 19x^15 - 62x^14 - 40x^13 + 1137x^12 - 525x^11 - 3389x^10 + 2071x^9 + 4487x^8 - 2894x^7 - 2837x^6 + 1880x^5 + 764x^4 - 522x^3 - 65x^2 + 19x + 1	\( 3^{6}\cdot 97^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.0.28238918168264014000549120201.1	x^20 - 2x^19 - 7x^17 + 17x^16 - 20x^15 + 20x^14 + 35x^13 + 23x^12 - 76x^11 - 127x^10 + 198x^9 - 131x^8 - 349x^7 + 620x^6 + 92x^5 - 563x^4 + 228x^3 + 223x^2 - 90x + 9	\( 67^{2}\cdot 97^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.0.202606202716249204085320843264.1	x^20 - 10x^18 + 48x^16 - 135x^14 + 254x^12 - 337x^10 + 317x^8 - 180x^6 + 9x^4 + 59x^2 + 1	\( 2^{20}\cdot 17^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.0.202606202716249204085320843264.2	x^20 + 3x^18 + 13x^16 + 23x^14 + 17x^12 + 72x^10 + 92x^8 + 71x^6 + 292x^4 + 279x^2 + 1	\( 2^{20}\cdot 17^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.0.202606202716249204085320843264.3	x^20 + 4x^18 - 3x^16 + 3x^14 + 4x^12 - x^10 + 4x^8 + 3x^6 - 3x^4 + 4x^2 + 1	\( 2^{20}\cdot 17^{2}\cdot 401^{8} \)	20T412	$[4]$ (GRH)
20.8.349295859451253311119725799249.3	x^20 - 25x^16 + 12x^14 - 120x^13 + 292x^12 + 198x^11 + 511x^10 + 912x^9 - 3371x^8 - 8190x^7 - 7766x^6 - 2166x^5 + 2193x^4 + 1431x^3 + 106x^2 - 30x + 1	\( 3^{2}\cdot 19^{2}\cdot 401^{10} \)	20T412	Trivial (GRH)
20.8.370860488708982107131954069504.1	x^20 - 16x^18 + 90x^16 - 232x^14 + 375x^12 - 435x^10 + 375x^8 - 232x^6 + 90x^4 - 16x^2 + 1	\( 2^{20}\cdot 23^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.8.370860488708982107131954069504.2	x^20 + 4x^18 - 17x^16 - 59x^14 + 60x^12 - 9x^10 + 252x^8 + 209x^6 + 157x^4 - 28x^2 + 1	\( 2^{20}\cdot 23^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.4.991469737933152814126207682281.1	x^20 - 21x^18 + 172x^16 - 753x^14 + 2321x^12 - 5692x^10 + 11298x^8 - 22427x^6 + 37401x^4 - 40334x^2 + 25281	\( 97^{2}\cdot 397^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.12.1066311537478944773058038071296.1	x^20 - 14x^18 + 79x^16 - 266x^14 + 693x^12 - 1359x^10 + 1782x^8 - 1656x^6 + 847x^4 - 183x^2 + 9	\( 2^{20}\cdot 3^{2}\cdot 13^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.0.2277742396626621674993797300224.1	x^20 + 13x^18 + 58x^16 + 89x^14 - 82x^12 - 396x^10 - 129x^8 + 653x^6 + 599x^4 + 57x^2 + 1	\( 2^{20}\cdot 3^{2}\cdot 19^{2}\cdot 401^{8} \)	20T412	$[18]$ (GRH)
20.12.2277742396626621674993797300224.1	x^20 - 13x^18 + 58x^16 - 89x^14 - 82x^12 + 396x^10 - 129x^8 - 653x^6 + 599x^4 - 57x^2 + 1	\( 2^{20}\cdot 3^{2}\cdot 19^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.4.2277742396626621674993797300224.1	x^20 + 3x^18 - 5x^14 - 5x^12 - 7x^10 - 5x^8 - 5x^6 + 3x^2 + 1	\( 2^{20}\cdot 3^{2}\cdot 19^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.8.2277742396626621674993797300224.1	x^20 + 4x^18 - 19x^16 - 148x^14 - 343x^12 - 171x^10 + 835x^8 + 932x^6 - 1106x^4 + 183x^2 + 1	\( 2^{20}\cdot 3^{2}\cdot 19^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.0.2277742396626621674993797300224.2	x^20 + 14x^18 + 101x^16 + 447x^14 + 1186x^12 + 1955x^10 + 2160x^8 + 1497x^6 + 513x^4 + 48x^2 + 1	\( 2^{20}\cdot 3^{2}\cdot 19^{2}\cdot 401^{8} \)	20T412	$[2]$ (GRH)
20.4.2277742396626621674993797300224.2	x^20 - x^18 + 11x^16 + 72x^14 - 109x^12 - 415x^10 - 210x^8 + 93x^6 + 67x^4 + 9x^2 + 1	\( 2^{20}\cdot 3^{2}\cdot 19^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.0.2277742396626621674993797300224.3	x^20 + 17x^18 + 110x^16 + 378x^14 + 786x^12 + 1030x^10 + 866x^8 + 469x^6 + 154x^4 + 25x^2 + 1	\( 2^{20}\cdot 3^{2}\cdot 19^{2}\cdot 401^{8} \)	20T412	$[2, 6]$ (GRH)
20.16.6460964582120943476990715887616.1	x^20 - 32x^18 + 344x^16 - 1374x^14 + 1232x^12 + 3694x^10 - 7011x^8 + 2760x^6 + 166x^4 - 84x^2 + 1	\( 2^{30}\cdot 3^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.8.6460964582120943476990715887616.1	x^20 - 4x^19 - 16x^18 + 90x^17 + 12x^16 - 610x^15 + 464x^14 + 1722x^13 - 2067x^12 - 2010x^11 + 3584x^10 + 644x^9 - 955x^8 + 966x^7 - 2928x^6 + 1628x^5 + 5701x^4 - 582x^3 - 1916x^2 - 6x + 39	\( 2^{30}\cdot 3^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.4.30363970676061540912001893145081.1	x^20 - 5x^19 - 11x^18 + 60x^17 + 99x^16 - 370x^15 - 542x^14 + 1544x^13 + 1221x^12 - 3852x^11 + 692x^10 + 5324x^9 - 7678x^8 - 1042x^7 + 22475x^6 + 10809x^5 + 5905x^4 + 25149x^3 + 14148x^2 - 2295x + 81	\( 13^{6}\cdot 97^{2}\cdot 401^{8} \)	20T412	$[2]$ (GRH)
20.16.31806369588351246159677928505344.1	x^20 - 15x^18 + 22x^16 + 20x^14 + 878x^12 - 3526x^10 + 5228x^8 - 3721x^6 + 1306x^4 - 201x^2 + 9	\( 2^{20}\cdot 3^{2}\cdot 71^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.4.151842021780313265349792921973921.1	x^20 - 8x^19 + 14x^18 + 20x^17 + 73x^16 - 739x^15 + 722x^14 + 2905x^13 - 4942x^12 - 5846x^11 + 13377x^10 + 9397x^9 - 27547x^8 - 2709x^7 + 30236x^6 - 6048x^5 - 22095x^4 + 13743x^3 + 2268x^2 - 3888x + 729	\( 17^{6}\cdot 97^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.8.151842021780313265349792921973921.1	x^20 - 8x^19 + 13x^18 + 41x^17 - 158x^16 - 60x^15 + 573x^14 + 884x^13 - 4568x^12 + 4310x^11 + 5135x^10 - 15080x^9 + 9292x^8 + 5801x^7 - 6242x^6 - 7374x^5 + 8433x^4 + 4832x^3 - 5330x^2 - 115x + 529	\( 17^{6}\cdot 97^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.0.211300041885398707129826254258176.1	x^20 + 24x^18 + 234x^16 + 1222x^14 + 3778x^12 + 7176x^10 + 8348x^8 + 5683x^6 + 2014x^4 + 272x^2 + 1	\( 2^{20}\cdot 3^{4}\cdot 61^{2}\cdot 401^{8} \)	20T412	$[120]$ (GRH)
20.0.463378613159711142474292153810944.1	x^20 + 22x^18 + 202x^16 + 1005x^14 + 2937x^12 + 5095x^10 + 5027x^8 + 2523x^6 + 519x^4 + 41x^2 + 1	\( 2^{20}\cdot 3^{2}\cdot 271^{2}\cdot 401^{8} \)	20T412	$[3, 120]$ (GRH)
20.20.463378613159711142474292153810944.1	x^20 - 22x^18 + 202x^16 - 1005x^14 + 2937x^12 - 5095x^10 + 5027x^8 - 2523x^6 + 519x^4 - 41x^2 + 1	\( 2^{20}\cdot 3^{2}\cdot 271^{2}\cdot 401^{8} \)	20T412	Trivial (GRH)
20.20.9360572824754047547641494848050281.1	x^20 - 4x^19 - 42x^18 + 171x^17 + 655x^16 - 2851x^15 - 4591x^14 + 23573x^13 + 12402x^12 - 102044x^11 + 11188x^10 + 220411x^9 - 117850x^8 - 193976x^7 + 173604x^6 + 26193x^5 - 68055x^4 + 22346x^3 - 1734x^2 - 127x + 1	\( 3^{6}\cdot 139^{2}\cdot 401^{8}\cdot 997^{2} \)	20T412	Trivial (GRH)