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 1681)

Label	Polynomial	Discriminant	Galois group	Class group
20.4.18780357640955901417873.1	x^20 - 2x^19 + 3x^17 - 9x^16 + 20x^15 - 26x^14 + 19x^13 - 5x^12 - 8x^11 + 42x^10 - 89x^9 + 94x^8 - 76x^7 + 75x^6 - 64x^5 + 33x^4 - 14x^3 + 6x^2 - 1	\( 3^{8}\cdot 17^{15} \)	$C_2\times F_5$ (as 20T9)	Trivial
20.0.107192366147491455078125.1	x^20 - 5x^19 + 12x^18 - 20x^17 + 28x^16 - 35x^15 + 34x^14 - 25x^13 + 30x^12 - 70x^11 + 119x^10 - 140x^9 + 208x^8 - 325x^7 + 292x^6 - 85x^5 - 14x^4 - 70x^3 + 40x^2 + 25x + 25	\( 5^{15}\cdot 37^{8} \)	$C_2\times F_5$ (as 20T9)	Trivial
20.0.200000000000000000000000.1	x^20 - 5x^19 + 10x^18 - 10x^17 + 10x^16 - 25x^15 + 40x^14 - 25x^13 + 40x^12 - 200x^11 + 515x^10 - 850x^9 + 1050x^8 - 1075x^7 + 1000x^6 - 875x^5 + 700x^4 - 500x^3 + 300x^2 - 125x + 25	\( 2^{24}\cdot 5^{23} \)	$C_2\times F_5$ (as 20T9)	Trivial
20.4.774840978000000000000000.1	x^20 - 2x^18 - 3x^17 - 9x^16 - 12x^15 - 12x^14 + 18x^13 + 84x^12 + 132x^11 + 174x^10 + 198x^9 + 177x^8 + 120x^7 + 42x^6 + 27x^5 + 48x^4 + 12x^3 - 8x^2 + 3x + 1	\( 2^{16}\cdot 3^{18}\cdot 5^{15} \)	$C_2\times F_5$ (as 20T9)	Trivial
20.4.274968333542346954345703125.2	x^20 - 48x^15 + 449x^10 + 1548x^5 + 1	\( 3^{10}\cdot 5^{31} \)	$C_2\times F_5$ (as 20T9)	Trivial (GRH)
20.0.4503750781250000000000000000.1	x^20 + 10x^18 - 5x^17 + 15x^16 - 46x^15 - 60x^14 - 100x^13 - 30x^12 + 290x^11 + 356x^10 + 470x^9 + 335x^8 - 2190x^7 + 490x^6 - 2261x^5 + 3950x^4 - 1800x^3 + 1630x^2 - 1305x + 311	\( 2^{16}\cdot 5^{23}\cdot 7^{8} \)	$C_2\times F_5$ (as 20T9)	Trivial (GRH)
20.4.4882812500000000000000000000.1	x^20 - 5x^18 + 15x^16 - 30x^14 + 135x^12 - 270x^10 + 50x^8 + 300x^6 - 175x^4 - 100x^2 + 80	\( 2^{20}\cdot 5^{31} \)	$C_2\times F_5$ (as 20T9)	Trivial (GRH)
20.0.23376400555202000000000000000.1	x^20 - 5x^19 + 18x^18 - 48x^17 + 134x^16 - 233x^15 + 416x^14 - 476x^13 + 897x^12 - 786x^11 + 2316x^10 - 854x^9 + 4296x^8 - 870x^7 + 3820x^6 + 110x^5 + 565x^4 - 125x^3 + 50x^2 + 50x + 25	\( 2^{16}\cdot 5^{15}\cdot 43^{8} \)	$C_2\times F_5$ (as 20T9)	Trivial (GRH)
20.4.169675210983039290802001953125.1	x^20 - 8x^19 + 20x^18 + 5x^17 - 139x^16 + 320x^15 - 74x^14 - 1080x^13 + 2051x^12 - 150x^11 - 4520x^10 + 5643x^9 + 946x^8 - 9460x^7 + 7095x^6 + 4345x^5 - 8140x^4 + 1375x^3 + 3025x^2 + 275x + 275	\( 5^{15}\cdot 11^{18} \)	$C_2\times F_5$ (as 20T9)	$[5]$ (GRH)
20.4.1315377880819141864776611328125.1	x^20 - 144x^15 - 10889x^10 + 259506x^5 + 161051	\( 5^{31}\cdot 7^{10} \)	$C_2\times F_5$ (as 20T9)	Trivial (GRH)
20.4.5000000000000000000000000000000.1	x^20 - 10x^18 + 60x^16 - 240x^14 + 2160x^12 - 8640x^10 + 3200x^8 + 38400x^6 - 44800x^4 - 51200x^2 + 81920	\( 2^{30}\cdot 5^{31} \)	$C_2\times F_5$ (as 20T9)	Trivial (GRH)
20.0.5000000000000000000000000000000.4	x^20 + 10x^18 + 60x^16 + 240x^14 + 2160x^12 + 8640x^10 + 3200x^8 - 38400x^6 - 44800x^4 + 51200x^2 + 81920	\( 2^{30}\cdot 5^{31} \)	$C_2\times F_5$ (as 20T9)	$[2]$ (GRH)
20.20.10054202156858080231167941574353.1	x^20 - x^19 - 33x^18 + 48x^17 + 398x^16 - 758x^15 - 2109x^14 + 5370x^13 + 4019x^12 - 18033x^11 + 3882x^10 + 25627x^9 - 20370x^8 - 8176x^7 + 14111x^6 - 2752x^5 - 1888x^4 + 657x^3 + 22x^2 - 17x + 1	\( 17^{15}\cdot 37^{8} \)	$C_2\times F_5$ (as 20T9)	Trivial (GRH)
20.20.18447363200000000000000000000000.1	x^20 - 40x^18 + 660x^16 - 5800x^14 + 29320x^12 - 86420x^10 + 145120x^8 - 130160x^6 + 55120x^4 - 8800x^2 + 80	\( 2^{28}\cdot 5^{23}\cdot 7^{8} \)	$C_2\times F_5$ (as 20T9)	Trivial (GRH)
20.4.82802905234194108120391845703125.1	x^20 - 2x^19 - 6x^18 - 40x^17 + 42x^16 + 148x^15 + 358x^14 - 294x^13 + 2428x^12 + 12630x^11 + 20819x^10 - 35474x^9 - 210554x^8 - 467528x^7 - 574374x^6 - 350538x^5 - 101396x^4 + 9920x^3 + 46712x^2 + 22468x + 991	\( 3^{10}\cdot 5^{15}\cdot 11^{16} \)	$C_2\times F_5$ (as 20T9)	$[5]$ (GRH)
20.4.120780545291490852832794189453125.1	x^20 - 294x^15 - 64864x^10 + 5348406x^5 + 28629151	\( 5^{31}\cdot 11^{10} \)	$C_2\times F_5$ (as 20T9)	Trivial (GRH)
20.0.288325195312500000000000000000000.2	x^20 + 15x^18 + 135x^16 + 810x^14 + 10935x^12 + 65610x^10 + 36450x^8 - 656100x^6 - 1148175x^4 + 1968300x^2 + 4723920	\( 2^{20}\cdot 3^{10}\cdot 5^{31} \)	$C_2\times F_5$ (as 20T9)	$[2, 2]$ (GRH)
20.0.641953627807088196277618408203125.2	x^20 - 144x^15 + 9986x^10 - 6429744x^5 + 844596301	\( 5^{31}\cdot 13^{10} \)	$C_2\times F_5$ (as 20T9)	$[2]$ (GRH)
20.4.1470391355634309152000000000000000.2	x^20 - 5x^18 - 129x^16 - 620x^14 - 1509x^12 - 2355x^10 - 864x^8 - 410x^6 + 1401x^4 + 2290x^2 + 1805	\( 2^{20}\cdot 5^{15}\cdot 11^{16} \)	$C_2\times F_5$ (as 20T9)	$[5]$ (GRH)
20.4.3177714547665748337794219970703125.1	x^20 - 2x^19 - 10x^18 - 20x^17 - 14x^16 + 380x^15 + 116x^14 + 2555x^13 - 5209x^12 + 7230x^11 - 29195x^10 + 50437x^9 - 54804x^8 + 151255x^7 - 200155x^6 + 184205x^5 - 249815x^4 + 320775x^3 + 21600x^2 - 35775x - 119475	\( 5^{15}\cdot 19^{18} \)	$C_2\times F_5$ (as 20T9)	Trivial (GRH)
20.0.9387703148876316845417022705078125.2	x^20 - 5x^19 + 25x^18 - 35x^17 + 270x^16 - 919x^15 + 4850x^14 + 24400x^13 + 158005x^12 + 323200x^11 + 240476x^10 - 2451535x^9 - 9806600x^8 - 22103305x^7 - 18499285x^6 + 36486691x^5 + 184536915x^4 + 378693200x^3 + 498508960x^2 + 402067640x + 168988496	\( 5^{31}\cdot 17^{10} \)	$C_2\times F_5$ (as 20T9)	$[2]$ (GRH)
20.0.10019151533337487082567413330078125.2	x^20 - 8x^19 + 42x^18 - 204x^17 + 928x^16 - 3530x^15 + 12796x^14 - 40207x^13 + 115483x^12 - 299394x^11 + 694684x^10 - 1456697x^9 + 2707188x^8 - 4255273x^7 + 5598538x^6 - 6354447x^5 + 6400086x^4 - 5497910x^3 + 3643915x^2 - 1608255x + 377245	\( 3^{10}\cdot 5^{15}\cdot 11^{18} \)	$C_2\times F_5$ (as 20T9)	$[2, 2, 10]$ (GRH)
20.4.28550002061766572296619415283203125.1	x^20 - 5x^19 - 10x^18 + 225x^17 - 835x^16 + 623x^15 + 9665x^14 - 65095x^13 + 212270x^12 - 167595x^11 - 1654471x^10 + 6783670x^9 - 12617985x^8 - 6471845x^7 + 95240190x^6 - 35696808x^5 - 334401910x^4 + 81011030x^3 + 520007480x^2 - 283432920x + 293849141	\( 5^{31}\cdot 19^{10} \)	$C_2\times F_5$ (as 20T9)	Trivial (GRH)
20.0.77671748484489507973194122314453125.2	x^20 - 5x^19 + 30x^18 - 50x^17 + 430x^16 - 1319x^15 + 7885x^14 + 40785x^13 + 317315x^12 + 799150x^11 + 1072566x^10 - 5300355x^9 - 28263385x^8 - 79891605x^7 - 100137290x^6 + 71914741x^5 + 734798300x^4 + 1874737995x^3 + 2942848715x^2 + 2827663210x + 1410941641	\( 3^{10}\cdot 5^{31}\cdot 7^{10} \)	$C_2\times F_5$ (as 20T9)	n/a
20.0.177917354031751407392000000000000000.2	x^20 + 66x^16 + 440x^14 - 1749x^12 + 10340x^10 - 11374x^8 - 21780x^6 + 246961x^4 - 350900x^2 + 242000	\( 2^{20}\cdot 5^{15}\cdot 11^{18} \)	$C_2\times F_5$ (as 20T9)	$[2, 2, 10]$ (GRH)
20.4.192907225404162891209125518798828125.1	x^20 - 5x^19 - 15x^18 + 280x^17 - 945x^16 + 198x^15 + 14180x^14 - 97645x^13 + 351970x^12 - 255555x^11 - 3611196x^10 + 14891330x^9 - 27752675x^8 - 29312330x^7 + 303998195x^6 - 85381863x^5 - 1286617875x^4 + 298330310x^3 + 2109281000x^2 - 1225863600x + 2214298096	\( 5^{31}\cdot 23^{10} \)	$C_2\times F_5$ (as 20T9)	n/a
20.4.295245000000000000000000000000000000.1	x^20 - 30x^18 + 540x^16 - 6480x^14 + 174960x^12 - 2099520x^10 + 2332800x^8 + 83980800x^6 - 293932800x^4 - 1007769600x^2 + 4837294080	\( 2^{30}\cdot 3^{10}\cdot 5^{31} \)	$C_2\times F_5$ (as 20T9)	n/a
20.0.295245000000000000000000000000000000.2	x^20 + 30x^18 + 540x^16 + 6480x^14 + 174960x^12 + 2099520x^10 + 2332800x^8 - 83980800x^6 - 293932800x^4 + 1007769600x^2 + 4837294080	\( 2^{30}\cdot 3^{10}\cdot 5^{31} \)	$C_2\times F_5$ (as 20T9)	n/a
20.4.396107830343483954099825714111328125.1	x^20 - 3x^19 - 25x^18 + 85x^17 + 390x^16 - 619x^15 - 3918x^14 + 385x^13 + 34925x^12 + 29720x^11 - 270083x^10 - 443136x^9 + 1143615x^8 + 3870405x^7 + 873000x^6 - 14910222x^5 - 18671249x^4 + 17902740x^3 + 5924040x^2 - 41740760x + 18411920	\( 5^{15}\cdot 7^{10}\cdot 11^{16} \)	$C_2\times F_5$ (as 20T9)	$[5]$ (GRH)
20.4.519780793144362253735210235595703125.1	x^20 - x^19 + 9x^18 - 41x^17 + 154x^16 - 773x^15 + 2026x^14 - 4929x^13 + 12491x^12 - 11134x^11 - 15441x^10 + 91658x^9 - 228717x^8 - 233197x^7 + 1624938x^6 - 1158742x^5 - 2192037x^4 + 3529578x^3 - 2820992x^2 + 2354928x - 261584	\( 3^{10}\cdot 5^{15}\cdot 19^{16} \)	$C_2\times F_5$ (as 20T9)	$[4, 4]$ (GRH)
20.0.1379273676757812500000000000000000000.2	x^20 + 35x^18 + 735x^16 + 10290x^14 + 324135x^12 + 4537890x^10 + 5882450x^8 - 247062900x^6 - 1008840175x^4 + 4035360700x^2 + 22598019920	\( 2^{20}\cdot 5^{31}\cdot 7^{10} \)	$C_2\times F_5$ (as 20T9)	n/a
20.4.1505680748169532571648000000000000000.1	x^20 - 10x^18 - 516x^16 - 4960x^14 - 24144x^12 - 75360x^10 - 55296x^8 - 52480x^6 + 358656x^4 + 1172480x^2 + 1848320	\( 2^{30}\cdot 5^{15}\cdot 11^{16} \)	$C_2\times F_5$ (as 20T9)	$[5, 5]$ (GRH)
20.0.1505680748169532571648000000000000000.2	x^20 + 10x^18 - 516x^16 + 4960x^14 - 24144x^12 + 75360x^10 - 55296x^8 + 52480x^6 + 358656x^4 - 1172480x^2 + 1848320	\( 2^{30}\cdot 5^{15}\cdot 11^{16} \)	$C_2\times F_5$ (as 20T9)	$[10]$ (GRH)
20.0.1959070718382489867508411407470703125.2	x^20 - 5x^19 + 40x^18 - 80x^17 + 840x^16 - 2329x^15 + 17495x^14 + 92155x^13 + 934495x^12 + 3023350x^11 + 6716306x^10 - 16162825x^9 - 138381605x^8 - 538651975x^7 - 1008503770x^6 - 270425399x^5 + 5808953160x^4 + 21092371985x^3 + 43037450335x^2 + 53878854080x + 35445196901	\( 5^{31}\cdot 29^{10} \)	$C_2\times F_5$ (as 20T9)	n/a
20.4.3816691632293169386684894561767578125.1	x^20 - 5x^19 - 25x^18 + 390x^17 - 1075x^16 - 1282x^15 + 24500x^14 - 185365x^13 + 839990x^12 - 575235x^11 - 12799606x^10 + 53786260x^9 - 99979485x^8 - 217085270x^7 + 1894042635x^6 - 255897903x^5 - 10721050195x^4 + 2198708690x^3 + 18277709420x^2 - 12345750840x + 49350856976	\( 5^{31}\cdot 31^{10} \)	$C_2\times F_5$ (as 20T9)	n/a
20.0.6422646617589481211251988555908203125.1	x^20 - 9x^19 + 34x^18 - 44x^17 - 265x^16 + 1286x^15 - 773x^14 - 3682x^13 + 13368x^12 + 20263x^11 - 34508x^10 - 44433x^9 + 246404x^8 + 66122x^7 - 138042x^6 - 33663x^5 + 299206x^4 + 241895x^3 + 108785x^2 + 43805x + 8705	\( 5^{15}\cdot 29^{18} \)	$C_2\times F_5$ (as 20T9)	$[2, 2]$ (GRH)
20.0.7131970418917243368923664093017578125.2	x^20 - 5x^19 + 45x^18 - 95x^17 + 1090x^16 - 2939x^15 + 24430x^14 + 128940x^13 + 1449605x^12 + 5100880x^11 + 13220076x^10 - 24508695x^9 - 259823140x^8 - 1145438325x^7 - 2438250905x^6 - 1385834729x^5 + 13088961695x^4 + 55400347980x^3 + 125265538040x^2 + 174097207960x + 128412299536	\( 3^{10}\cdot 5^{31}\cdot 11^{10} \)	$C_2\times F_5$ (as 20T9)	n/a
20.4.9230125234163877365792000000000000000.1	x^20 - x^18 - 109x^16 + 149x^14 - 2014x^12 - 36365x^10 + 127585x^8 - 1005950x^6 + 733025x^4 + 67500x^2 + 50000	\( 2^{20}\cdot 5^{15}\cdot 19^{16} \)	$C_2\times F_5$ (as 20T9)	Trivial (GRH)
20.4.21333423461884919389012763702392578125.1	x^20 - 7x^19 + 2x^18 + 85x^17 - 89x^16 - 485x^15 - 502x^14 + 7124x^13 - 3389x^12 - 37645x^11 + 1825x^10 + 232525x^9 + 94360x^8 - 986175x^7 - 1307700x^6 + 1275150x^5 + 3604650x^4 + 1354000x^3 - 3259625x^2 - 3537500x - 968125	\( 5^{15}\cdot 31^{18} \)	$C_2\times F_5$ (as 20T9)	$[5]$ (GRH)
20.0.22391715889879730530083179473876953125.1	x^20 - 5x^19 + 50x^18 - 110x^17 + 1370x^16 - 3619x^15 + 33025x^14 + 174325x^13 + 2145955x^12 + 8083750x^11 + 23745326x^10 - 34682135x^9 - 452982025x^8 - 2228991105x^7 - 5269012810x^6 - 4302198659x^5 + 26632021340x^4 + 130244452175x^3 + 322173998635x^2 + 490733138390x + 401120497321	\( 5^{31}\cdot 37^{10} \)	$C_2\times F_5$ (as 20T9)	n/a
20.4.37906719768380750901997089385986328125.1	x^20 - 5x^19 - 35x^18 + 500x^17 - 1085x^16 - 3602x^15 + 35340x^14 - 305645x^13 + 1752770x^12 - 1234795x^11 - 35238496x^10 + 150274870x^9 - 275565135x^8 - 919172770x^7 + 7876207515x^6 - 176450583x^5 - 55565363835x^4 + 9898849230x^3 + 91075080080x^2 - 73949086720x + 521177724016	\( 3^{10}\cdot 5^{31}\cdot 13^{10} \)	$C_2\times F_5$ (as 20T9)	n/a
20.0.47929047471561558446078911407470703125.2	x^20 - 6x^19 + 10x^18 + 30x^17 - 231x^16 - 846x^15 + 14657x^14 - 96020x^13 + 424696x^12 - 1471866x^11 + 4600432x^10 - 13640902x^9 + 41055054x^8 - 108630102x^7 + 263443921x^6 - 515816388x^5 + 871193851x^4 - 1118784220x^3 + 1251134700x^2 - 767760000x + 778286125	\( 5^{15}\cdot 7^{10}\cdot 11^{18} \)	$C_2\times F_5$ (as 20T9)	$[2, 2, 20]$ (GRH)
20.0.62504128134587784297764301300048828125.2	x^20 - 5x^19 + 55x^18 - 125x^17 + 1680x^16 - 4369x^15 + 43460x^14 + 229210x^13 + 3060265x^12 + 12199900x^11 + 39844916x^10 - 46253755x^9 - 744886310x^8 - 4046349655x^7 - 10452282415x^6 - 10776463559x^5 + 49933574625x^4 + 280542235970x^3 + 751545978640x^2 + 1241779064960x + 1114173964016	\( 5^{31}\cdot 41^{10} \)	$C_2\times F_5$ (as 20T9)	n/a
20.0.86825139158850321116448000000000000000.4	x^20 + 15x^18 - 1161x^16 + 16740x^14 - 122229x^12 + 572265x^10 - 629856x^8 + 896670x^6 + 9191961x^4 - 45074070x^2 + 106583445	\( 2^{20}\cdot 3^{10}\cdot 5^{15}\cdot 11^{16} \)	$C_2\times F_5$ (as 20T9)	$[5, 10, 10]$ (GRH)
20.4.100636306746323821134865283966064453125.1	x^20 - 5x^19 - 40x^18 + 555x^17 - 1045x^16 - 5077x^15 + 40505x^14 - 378895x^13 + 2435570x^12 - 1764255x^11 - 54740221x^10 + 234681130x^9 - 425930625x^8 - 1679254355x^7 + 14514361470x^6 + 372998712x^5 - 112341446200x^4 + 18580850960x^3 + 175486910000x^2 - 158789506050x + 1412257296521	\( 5^{31}\cdot 43^{10} \)	$C_2\times F_5$ (as 20T9)	n/a
20.0.126647581059570312500000000000000000000.2	x^20 + 55x^18 + 1815x^16 + 39930x^14 + 1976535x^12 + 43483770x^10 + 88578050x^8 - 5846151300x^6 - 37512804175x^4 + 235794769100x^2 + 2074993968080	\( 2^{20}\cdot 5^{31}\cdot 11^{10} \)	$C_2\times F_5$ (as 20T9)	n/a
20.4.182187370528513441169408000000000000000.1	x^20 + 264x^16 - 3520x^14 - 27984x^12 - 330880x^10 - 727936x^8 + 2787840x^6 + 63222016x^4 + 179660800x^2 + 247808000	\( 2^{30}\cdot 5^{15}\cdot 11^{18} \)	$C_2\times F_5$ (as 20T9)	$[10]$ (GRH)
20.0.182187370528513441169408000000000000000.2	x^20 + 264x^16 + 3520x^14 - 27984x^12 + 330880x^10 - 727936x^8 - 2787840x^6 + 63222016x^4 - 179660800x^2 + 247808000	\( 2^{30}\cdot 5^{15}\cdot 11^{18} \)	$C_2\times F_5$ (as 20T9)	$[2, 2, 20]$ (GRH)
20.0.187640866325114773598410895050048828125.1	x^20 - 3x^19 + 26x^18 + 97x^17 - 294x^16 - 440x^15 + 1705x^14 - 8469x^13 - 25967x^12 - 57053x^11 - 45091x^10 + 433083x^9 + 1796869x^8 + 4440981x^7 + 17183403x^6 + 35686946x^5 + 51034338x^4 + 54483025x^3 + 40765960x^2 + 24180423x + 8509591	\( 3^{10}\cdot 5^{15}\cdot 19^{18} \)	$C_2\times F_5$ (as 20T9)	$[2, 2, 2, 2, 2]$ (GRH)
20.0.193315443721344440894830801055908203125.2	x^20 - 3x^19 + 100x^18 - 190x^17 + 3990x^16 - 5019x^15 + 84557x^14 - 80690x^13 + 1053075x^12 - 972755x^11 + 8039592x^10 - 8576736x^9 + 39544565x^8 - 45897320x^7 + 141614400x^6 - 123999347x^5 + 380740776x^4 - 184199435x^3 + 502243165x^2 - 464217385x + 121715395	\( 5^{15}\cdot 11^{16}\cdot 13^{10} \)	$C_2\times F_5$ (as 20T9)	$[10]$ (GRH)