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 )

Label	Polynomial	Discriminant	Galois group	Class group
10.0.311663572684817408.3	x^10 - 2x^9 + 78x^8 - 122x^7 + 2702x^6 - 3194x^5 + 51055x^4 - 41284x^3 + 522906x^2 - 220904x + 2319481	\( -\,2^{10}\cdot 11^{8}\cdot 17^{5} \)	$C_{10}$ (as 10T1)	$[5, 220]$ (GRH)
10.0.659594366463529519.3	x^10 - 3x^9 + 94x^8 - 220x^7 + 3810x^6 - 6560x^5 + 82274x^4 - 93093x^3 + 945262x^2 - 527525x + 4638019	\( -\,11^{8}\cdot 79^{5} \)	$C_{10}$ (as 10T1)	$[1775]$ (GRH)
10.0.732082863999706112.1	x^10 + 88x^8 + 2555x^6 + 27397x^4 + 89417x^2 + 89417	\( -\,2^{10}\cdot 89417^{3} \)	$C_2 \wr S_5$ (as 10T39)	$[2, 680]$ (GRH)
10.0.844368344447000483.3	x^10 - 3x^9 + 99x^8 - 232x^7 + 4210x^6 - 7264x^5 + 95124x^4 - 107913x^3 + 1140491x^2 - 638489x + 5822543	\( -\,11^{8}\cdot 83^{5} \)	$C_{10}$ (as 10T1)	$[1965]$ (GRH)
10.0.896474439937004544.3	x^10 - 2x^9 + 98x^8 - 154x^7 + 4174x^6 - 4946x^5 + 95495x^4 - 77044x^3 + 1168338x^2 - 488760x + 6109489	\( -\,2^{10}\cdot 3^{5}\cdot 7^{5}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	$[2, 1010]$ (GRH)
10.0.986083097105956663.1	x^10 - x^9 + 144x^8 - 144x^7 + 7580x^6 - 7580x^5 + 176749x^4 - 176749x^3 + 1747604x^2 - 1747604x + 5831827	\( -\,11^{9}\cdot 53^{5} \)	$C_{10}$ (as 10T1)	$[1208]$ (GRH)
10.0.1068409508282417367.3	x^10 - 3x^9 + 104x^8 - 244x^7 + 4630x^6 - 8004x^5 + 109246x^4 - 124229x^3 + 1364464x^2 - 766089x + 7237273	\( -\,3^{5}\cdot 11^{8}\cdot 29^{5} \)	$C_{10}$ (as 10T1)	$[1830]$ (GRH)
10.0.1215000000000000000.45	x^10 + 10x^8 - 10x^7 + 240x^6 + 158x^5 + 3185x^4 + 3040x^3 + 22730x^2 + 8740x + 68257	\( -\,2^{15}\cdot 3^{5}\cdot 5^{16} \)	$C_{10}$ (as 10T1)	$[1010]$ (GRH)
10.0.1244547474828108800.1	x^10 + 132x^8 + 5690x^6 + 94823x^4 + 536720x^2 + 912425	\( -\,2^{10}\cdot 5^{2}\cdot 36497^{3} \)	$C_2 \wr S_5$ (as 10T39)	$[2, 808]$ (GRH)
10.0.1298596719579529216.1	x^10 + 154x^8 + 8624x^6 + 211288x^4 + 2112880x^2 + 5916064	\( -\,2^{15}\cdot 7^{5}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	$[2, 844]$ (GRH)
10.0.1337668323316656331.1	x^10 - 3x^9 + 109x^8 - 256x^7 + 5070x^6 - 8780x^5 + 124700x^4 - 142113x^3 + 1619869x^2 - 911909x + 8914201	\( -\,7^{5}\cdot 11^{8}\cdot 13^{5} \)	$C_{10}$ (as 10T1)	$[2222]$ (GRH)
10.0.1418758396496190387.1	x^10 - x^9 + 155x^8 - 155x^7 + 8779x^6 - 8779x^5 + 220067x^4 - 220067x^3 + 2332947x^2 - 2332947x + 8249011	\( -\,3^{5}\cdot 11^{9}\cdot 19^{5} \)	$C_{10}$ (as 10T1)	$[2, 802]$ (GRH)
10.0.1658668159016309375.3	x^10 - 3x^9 + 114x^8 - 268x^7 + 5530x^6 - 9592x^5 + 141546x^4 - 161637x^3 + 1909514x^2 - 1077605x + 10888151	\( -\,5^{5}\cdot 11^{8}\cdot 19^{5} \)	$C_{10}$ (as 10T1)	$[1640]$ (GRH)
10.0.1833540124521600000.1	x^10 + 165x^8 + 9900x^6 + 259875x^4 + 2784375x^2 + 8353125	\( -\,2^{10}\cdot 3^{5}\cdot 5^{5}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	$[2, 2, 362]$ (GRH)
10.0.1991513897770090991.3	x^10 - x^9 + 166x^8 - 166x^7 + 10066x^6 - 10066x^5 + 269941x^4 - 269941x^3 + 3054316x^2 - 3054316x + 11407441	\( -\,11^{9}\cdot 61^{5} \)	$C_{10}$ (as 10T1)	$[1650]$ (GRH)
10.0.2485006933392588583.3	x^10 - 3x^9 + 124x^8 - 292x^7 + 6510x^6 - 11324x^5 + 179654x^4 - 205893x^3 + 2603356x^2 - 1475609x + 15881293	\( -\,11^{8}\cdot 103^{5} \)	$C_{10}$ (as 10T1)	$[3, 3, 3, 75]$ (GRH)
10.0.2608003547238662144.1	x^10 - 2x^9 + 123x^8 - 194x^7 + 6464x^6 - 7676x^5 + 180115x^4 - 145054x^3 + 2652783x^2 - 1100690x + 16510339	\( -\,2^{15}\cdot 11^{8}\cdot 13^{5} \)	$C_{10}$ (as 10T1)	$[1986]$ (GRH)
10.0.2735904600107696875.1	x^10 - x^9 + 177x^8 - 177x^7 + 11441x^6 - 11441x^5 + 326833x^4 - 326833x^3 + 3931313x^2 - 3931313x + 15465649	\( -\,5^{5}\cdot 11^{9}\cdot 13^{5} \)	$C_{10}$ (as 10T1)	$[2, 1382]$ (GRH)
10.0.3006494195374653467.3	x^10 - 3x^9 + 129x^8 - 304x^7 + 7030x^6 - 12244x^5 + 201036x^4 - 230769x^3 + 3013769x^2 - 1711589x + 18985373	\( -\,11^{8}\cdot 107^{5} \)	$C_{10}$ (as 10T1)	$[3615]$ (GRH)
10.0.3612071805471604431.1	x^10 - 3x^9 + 134x^8 - 316x^7 + 7570x^6 - 13200x^5 + 224050x^4 - 257573x^3 + 3470854x^2 - 1974789x + 22556491	\( -\,3^{5}\cdot 11^{8}\cdot 37^{5} \)	$C_{10}$ (as 10T1)	$[3448]$ (GRH)
10.0.3687904108026165159.1	x^10 - x^9 + 188x^8 - 188x^7 + 12904x^6 - 12904x^5 + 391205x^4 - 391205x^3 + 4984860x^2 - 4984860x + 20603287	\( -\,3^{5}\cdot 11^{9}\cdot 23^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 2, 2, 132]$ (GRH)
10.0.4311522760038071875.1	x^10 - 3x^9 + 139x^8 - 328x^7 + 8130x^6 - 14192x^5 + 248756x^4 - 286377x^3 + 3978019x^2 - 2267225x + 26645431	\( -\,5^{5}\cdot 11^{8}\cdot 23^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 2, 202]$ (GRH)
10.0.4368461761474609375.3	x^10 - 5x^9 + 30x^8 - 80x^7 + 520x^6 - 1494x^5 + 8050x^4 - 18165x^3 + 65760x^2 - 73895x + 192493	\( -\,5^{16}\cdot 31^{5} \)	$C_{10}$ (as 10T1)	$[1965]$ (GRH)
10.0.4502268874408211456.3	x^10 - 2x^9 + 138x^8 - 218x^7 + 8078x^6 - 9602x^5 + 249271x^4 - 200596x^3 + 4044546x^2 - 1672088x + 27589441	\( -\,2^{10}\cdot 11^{8}\cdot 29^{5} \)	$C_{10}$ (as 10T1)	$[11, 330]$ (GRH)
10.0.4767194945484112896.1	x^10 + 60x^8 + 1152x^6 + 8721x^4 + 22842x^2 + 10449	\( -\,2^{10}\cdot 3^{5}\cdot 19^{4}\cdot 43^{5} \)	$D_{10}$ (as 10T3)	$[2, 534]$ (GRH)
10.0.4794980842527532007.1	x^10 + 42x^8 + 709x^6 + 5628x^4 + 17956x^2 + 5447	\( -\,13^{5}\cdot 419^{5} \)	$D_5$ (as 10T2)	$[11, 132]$ (GRH)
10.0.4888194375992041763.3	x^10 - x^9 + 199x^8 - 199x^7 + 14455x^6 - 14455x^5 + 463519x^4 - 463519x^3 + 6237199x^2 - 6237199x + 27022447	\( -\,11^{9}\cdot 73^{5} \)	$C_{10}$ (as 10T1)	$[6050]$ (GRH)
10.0.4910540008544921875.3	x^10 + 110x^8 - 30x^7 + 2825x^6 - 2491x^5 + 15100x^4 + 8495x^3 + 29515x^2 + 65125x + 180299	\( -\,5^{17}\cdot 23^{5} \)	$C_{10}$ (as 10T1)	$[1822]$ (GRH)
10.0.5115361002064185719.3	x^10 - 3x^9 + 144x^8 - 340x^7 + 8710x^6 - 15220x^5 + 275214x^4 - 317253x^3 + 4538792x^2 - 2590985x + 31306529	\( -\,7^{5}\cdot 11^{8}\cdot 17^{5} \)	$C_{10}$ (as 10T1)	$[3550]$ (GRH)
10.0.5333934907699200000.1	x^10 - 2x^9 + 143x^8 - 226x^7 + 8656x^6 - 10292x^5 + 275747x^4 - 221854x^3 + 4611783x^2 - 1904586x + 32377951	\( -\,2^{15}\cdot 3^{5}\cdot 5^{5}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	$[2, 3310]$ (GRH)
10.0.5502308171359302527.1	x^10 - x^9 + 64x^8 - 69x^7 + 1239x^6 + 363x^5 + 11501x^4 + 11077x^3 + 71822x^2 + 31101x + 16893	\( -\,7^{5}\cdot 41^{9} \)	$C_{10}$ (as 10T1)	$[11, 154]$
10.0.5978636205811106816.3	x^10 + 209x^8 + 15884x^6 + 528143x^4 + 7167655x^2 + 27237089	\( -\,2^{10}\cdot 11^{9}\cdot 19^{5} \)	$C_{10}$ (as 10T1)	$[2, 2050]$ (GRH)
10.0.6034857761594872683.1	x^10 - 3x^9 + 149x^8 - 352x^7 + 9310x^6 - 16284x^5 + 303484x^4 - 350273x^3 + 5156821x^2 - 2948229x + 36597793	\( -\,3^{5}\cdot 11^{8}\cdot 41^{5} \)	$C_{10}$ (as 10T1)	$[3410]$ (GRH)
10.0.6334836241526812799.1	x^10 - 2x^9 - 7x^8 + 93x^7 + 798x^6 - 1355x^5 + 11444x^4 + 11524x^3 + 90928x^2 + 39504x + 212800	\( -\,13^{5}\cdot 443^{5} \)	$D_{10}$ (as 10T3)	$[1188]$ (GRH)
10.0.6791250644112605184.1	x^10 - 2x^9 + 7x^8 + 18x^7 + 200x^6 - 768x^5 + 5083x^4 - 11958x^3 + 39139x^2 - 46270x + 99175	\( -\,2^{15}\cdot 3^{5}\cdot 31^{8} \)	$C_{10}$ (as 10T1)	$[1310]$ (GRH)
10.0.7082067896149153567.1	x^10 - 3x^9 + 154x^8 - 364x^7 + 9930x^6 - 17384x^5 + 333626x^4 - 385509x^3 + 5835874x^2 - 3341189x + 42581023	\( -\,11^{8}\cdot 127^{5} \)	$C_{10}$ (as 10T1)	$[3025]$ (GRH)
10.0.7873687216519509375.1	x^10 - 2x^9 + 95x^8 - 198x^7 + 3203x^6 - 6660x^5 + 45416x^4 - 87734x^3 + 267949x^2 - 200010x + 579441	\( -\,3^{5}\cdot 5^{5}\cdot 401^{5} \)	$D_{10}$ (as 10T3)	$[2, 2, 2, 198]$ (GRH)
10.0.8269856231139440531.2	x^10 - 3x^9 + 159x^8 - 376x^7 + 10570x^6 - 18520x^5 + 365700x^4 - 423033x^3 + 6579839x^2 - 3772169x + 49321931	\( -\,11^{8}\cdot 131^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 550]$ (GRH)
10.0.9973234325914157056.1	x^10 - 2x^9 + 163x^8 - 258x^7 + 11168x^6 - 13292x^5 + 400371x^4 - 321886x^3 + 7495711x^2 - 3084418x + 58603931	\( -\,2^{15}\cdot 11^{8}\cdot 17^{5} \)	$C_{10}$ (as 10T1)	$[7964]$ (GRH)
10.0.10462339170938084375.1	x^10 - x^9 + 232x^8 - 232x^7 + 19636x^6 - 19636x^5 + 732733x^4 - 732733x^3 + 11429188x^2 - 11429188x + 56354299	\( -\,5^{5}\cdot 11^{9}\cdot 17^{5} \)	$C_{10}$ (as 10T1)	$[2, 4354]$ (GRH)
10.0.11122834686060421819.1	x^10 - 3x^9 + 169x^8 - 400x^7 + 11910x^6 - 20900x^5 + 435884x^4 - 505233x^3 + 8278657x^2 - 4757765x + 65359909	\( -\,11^{8}\cdot 139^{5} \)	$C_{10}$ (as 10T1)	$[5, 5, 165]$ (GRH)
10.0.11927796406807986176.1	x^10 + 60x^8 + 1252x^6 + 10560x^4 + 30976x^2 + 26144	\( -\,2^{15}\cdot 19^{5}\cdot 43^{5} \)	$D_{10}$ (as 10T3)	$[2, 992]$ (GRH)
10.0.12395717562025209375.1	x^10 - 2x^9 + 75x^8 - 169x^7 + 785x^6 - 2430x^5 + 10231x^4 - 19733x^3 + 52899x^2 - 61257x + 84969	\( -\,3^{4}\cdot 5^{5}\cdot 547^{5} \)	$D_{10}$ (as 10T3)	$[31, 62]$ (GRH)
10.0.13166920084176282259.1	x^10 - x^9 + 243x^8 - 243x^7 + 21539x^6 - 21539x^5 + 841435x^4 - 841435x^3 + 13725515x^2 - 13725515x + 70415467	\( -\,11^{9}\cdot 89^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 2, 328]$ (GRH)
10.0.15221240859271287808.1	x^10 - 2x^9 + 178x^8 - 282x^7 + 13262x^6 - 15794x^5 + 515175x^4 - 414004x^3 + 10416946x^2 - 4276984x + 87678161	\( -\,2^{10}\cdot 11^{8}\cdot 37^{5} \)	$C_{10}$ (as 10T1)	$[19, 418]$ (GRH)
10.0.15540797558102029312.1	x^10 + 253x^8 + 23276x^6 + 936859x^4 + 15391255x^2 + 70799773	\( -\,2^{10}\cdot 11^{9}\cdot 23^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 2, 2, 202]$ (GRH)
10.0.16827756447434244631.2	x^10 - 3x^9 + 184x^8 - 436x^7 + 14070x^6 - 24740x^5 + 557150x^4 - 647493x^3 + 11417824x^2 - 6583049x + 96980521	\( -\,11^{8}\cdot 151^{5} \)	$C_{10}$ (as 10T1)	$[5285]$ (GRH)
10.0.17392396235086856192.1	x^10 - 2x^9 + 183x^8 - 290x^7 + 14000x^6 - 16676x^5 + 557827x^4 - 448222x^3 + 11558007x^2 - 4742330x + 99588919	\( -\,2^{15}\cdot 11^{8}\cdot 19^{5} \)	$C_{10}$ (as 10T1)	$[7626]$ (GRH)
10.0.17877721346595844207.1	x^10 + 46x^8 + 845x^6 + 7268x^4 + 24964x^2 + 7087	\( -\,19^{5}\cdot 373^{5} \)	$D_5$ (as 10T2)	$[19, 114]$ (GRH)
10.0.19177852413562596875.1	x^10 - 3x^9 + 189x^8 - 448x^7 + 14830x^6 - 26092x^5 + 602076x^4 - 700257x^3 + 12639629x^2 - 7294565x + 109881641	\( -\,5^{5}\cdot 11^{8}\cdot 31^{5} \)	$C_{10}$ (as 10T1)	$[8324]$ (GRH)

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