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 299)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.1884951191814934955008.1	x^10 - 2x^9 + 478x^8 - 762x^7 + 92942x^6 - 111194x^5 + 9184335x^4 - 7359364x^3 + 461126266x^2 - 186336424x + 9409989401	\( -\,2^{10}\cdot 11^{8}\cdot 97^{5} \)	$C_{10}$ (as 10T1)	$[106084]$ (GRH)
10.0.2212037934964419493888.1	x^10 + 682x^8 + 169136x^6 + 18351256x^4 + 812698480x^2 + 10077461152	\( -\,2^{15}\cdot 11^{9}\cdot 31^{5} \)	$C_{10}$ (as 10T1)	$[2, 57606]$ (GRH)
10.0.2643624591337105081387.1	x^10 - x^9 + 705x^8 - 705x^7 + 180929x^6 - 180929x^5 + 20366017x^4 - 20366017x^3 + 943112897x^2 - 943112897x + 12754272961	\( -\,11^{9}\cdot 257^{5} \)	$C_{10}$ (as 10T1)	$[146728]$ (GRH)
10.0.2937451902360726175744.1	x^10 - 2x^9 + 523x^8 - 834x^7 + 111104x^6 - 132956x^5 + 11978835x^4 - 9597214x^3 + 655329103x^2 - 264585970x + 14552228339	\( -\,2^{15}\cdot 11^{8}\cdot 53^{5} \)	$C_{10}$ (as 10T1)	$[148830]$ (GRH)
10.0.3081509678456114571875.1	x^10 - x^9 + 727x^8 - 727x^7 + 192391x^6 - 192391x^5 + 22329583x^4 - 22329583x^3 + 1065940063x^2 - 1065940063x + 14841598399	\( -\,5^{5}\cdot 11^{9}\cdot 53^{5} \)	$C_{10}$ (as 10T1)	$[2, 78492]$ (GRH)
10.0.3188069878865485942031.1	x^10 - 3x^9 + 534x^8 - 1276x^7 + 115570x^6 - 206320x^5 + 12666450x^4 - 15024933x^3 + 702954614x^2 - 415692869x + 15805781531	\( -\,11^{8}\cdot 431^{5} \)	$C_{10}$ (as 10T1)	$[107205]$ (GRH)
10.0.3321204108040761376159.1	x^10 - x^9 + 738x^8 - 738x^7 + 198254x^6 - 198254x^5 + 23357005x^4 - 23357005x^3 + 1131668660x^2 - 1131668660x + 15983044837	\( -\,11^{9}\cdot 269^{5} \)	$C_{10}$ (as 10T1)	$[134200]$ (GRH)
10.0.3338779713382554271875.1	x^10 - 3x^9 + 539x^8 - 1288x^7 + 117730x^6 - 210192x^5 + 13020916x^4 - 15447017x^3 + 729137299x^2 - 431232345x + 16540288711	\( -\,3^{5}\cdot 5^{5}\cdot 11^{8}\cdot 29^{5} \)	$C_{10}$ (as 10T1)	$[22, 7810]$ (GRH)
10.0.3377333342742102701056.1	x^10 - 2x^9 + 538x^8 - 858x^7 + 117518x^6 - 140642x^5 + 13022871x^4 - 10433236x^3 + 731977186x^2 - 295457368x + 16693341281	\( -\,2^{10}\cdot 11^{8}\cdot 109^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 2, 8130]$ (GRH)
10.0.3825419760558518179167.1	x^10 - 3x^9 + 554x^8 - 1324x^7 + 124330x^6 - 222024x^5 + 14123866x^4 - 16760549x^3 + 812086354x^2 - 480472389x + 18909114223	\( -\,3^{5}\cdot 11^{8}\cdot 149^{5} \)	$C_{10}$ (as 10T1)	$[149870]$ (GRH)
10.0.3845324648167853062487.1	x^10 - x^9 + 760x^8 - 760x^7 + 210244x^6 - 210244x^5 + 25505437x^4 - 25505437x^3 + 1272197092x^2 - 1272197092x + 18476541931	\( -\,11^{9}\cdot 277^{5} \)	$C_{10}$ (as 10T1)	$[178258]$ (GRH)
10.0.4044209595901771400192.1	x^10 - 2x^9 + 558x^8 - 890x^7 + 126350x^6 - 151226x^5 + 14506927x^4 - 11621572x^3 + 844401882x^2 - 340728680x + 19932627769	\( -\,2^{10}\cdot 11^{8}\cdot 113^{5} \)	$C_{10}$ (as 10T1)	$[141608]$ (GRH)
10.0.4058114748686028800000.1	x^10 + 770x^8 + 215600x^6 + 26411000x^4 + 1320550000x^2 + 18487700000	\( -\,2^{15}\cdot 5^{5}\cdot 7^{5}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	$[2, 2, 33128]$ (GRH)
10.0.4226352285126106054656.1	x^10 - 2x^9 + 563x^8 - 898x^7 + 128608x^6 - 153932x^5 + 14894771x^4 - 11932126x^3 + 874423551x^2 - 352816098x + 20816149771	\( -\,2^{15}\cdot 3^{5}\cdot 11^{8}\cdot 19^{5} \)	$C_{10}$ (as 10T1)	$[2, 66524]$ (GRH)
10.0.4356381114598275625984.1	x^10 + 781x^8 + 221804x^6 + 27559147x^4 + 1397642455x^2 + 19846522861	\( -\,2^{10}\cdot 11^{9}\cdot 71^{5} \)	$C_{10}$ (as 10T1)	$[10, 17050]$ (GRH)
10.0.4433619989050594959375.1	x^10 - x^9 + 782x^8 - 782x^7 + 222586x^6 - 222586x^5 + 27781733x^4 - 27781733x^3 + 1425424188x^2 - 1425424188x + 21271947049	\( -\,3^{5}\cdot 5^{5}\cdot 11^{9}\cdot 19^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 45550]$ (GRH)
10.0.4560856796944425470383.1	x^10 - 3x^9 + 574x^8 - 1372x^7 + 133410x^6 - 238304x^5 + 15688994x^4 - 18624933x^3 + 933456526x^2 - 552543269x + 22481787043	\( -\,11^{8}\cdot 463^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 13454]$ (GRH)
10.0.4761303702659742527267.1	x^10 - 3x^9 + 579x^8 - 1384x^7 + 135730x^6 - 242464x^5 + 16097556x^4 - 19111689x^3 + 965814059x^2 - 571761689x + 23454226223	\( -\,11^{8}\cdot 467^{5} \)	$C_{10}$ (as 10T1)	$[129647]$ (GRH)
10.0.4968737082129311238231.1	x^10 - 3x^9 + 584x^8 - 1396x^7 + 138070x^6 - 246660x^5 + 16513150x^4 - 19606853x^3 + 999005584x^2 - 591477129x + 24460026361	\( -\,3^{5}\cdot 11^{8}\cdot 157^{5} \)	$C_{10}$ (as 10T1)	$[127856]$ (GRH)
10.0.5021708213726393761792.1	x^10 - 2x^9 + 583x^8 - 930x^7 + 137840x^6 - 164996x^5 + 16515267x^4 - 13229662x^3 + 1002584407x^2 - 404409370x + 24668971559	\( -\,2^{15}\cdot 11^{8}\cdot 59^{5} \)	$C_{10}$ (as 10T1)	$[5, 26430]$ (GRH)
10.0.5091810920749800593863.1	x^10 - x^9 + 804x^8 - 804x^7 + 235280x^6 - 235280x^5 + 30189589x^4 - 30189589x^3 + 1592092844x^2 - 1592092844x + 24395880367	\( -\,11^{9}\cdot 293^{5} \)	$C_{10}$ (as 10T1)	$[100650]$ (GRH)
10.0.5405290610206916651519.1	x^10 - 3x^9 + 594x^8 - 1420x^7 + 142810x^6 - 255160x^5 + 17365674x^4 - 20622693x^3 + 1067947562x^2 - 632433125x + 26575128119	\( -\,11^{8}\cdot 479^{5} \)	$C_{10}$ (as 10T1)	$[11, 11, 1375]$ (GRH)
10.0.5634782213054159802483.1	x^10 - 3x^9 + 599x^8 - 1432x^7 + 145210x^6 - 259464x^5 + 17802724x^4 - 21143513x^3 + 1103726791x^2 - 653690889x + 27686175043	\( -\,3^{5}\cdot 7^{5}\cdot 11^{8}\cdot 23^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 2, 10, 710]$ (GRH)
10.0.5825948542184271384191.1	x^10 - x^9 + 826x^8 - 826x^7 + 248326x^6 - 248326x^5 + 32732701x^4 - 32732701x^3 + 1772967076x^2 - 1772967076x + 27876482701	\( -\,7^{5}\cdot 11^{9}\cdot 43^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 2, 2, 5436]$ (GRH)
10.0.5872003250814906099367.1	x^10 - 3x^9 + 604x^8 - 1444x^7 + 147630x^6 - 263804x^5 + 18247046x^4 - 21673029x^3 + 1140397564x^2 - 675480089x + 28834073773	\( -\,11^{8}\cdot 487^{5} \)	$C_{10}$ (as 10T1)	$[19, 5453]$ (GRH)
10.0.5932538854739121963008.1	x^10 - 2x^9 + 603x^8 - 962x^7 + 147392x^6 - 176444x^5 + 18249235x^4 - 14618014x^3 + 1144342191x^2 - 461464274x + 29072249251	\( -\,2^{15}\cdot 11^{8}\cdot 61^{5} \)	$C_{10}$ (as 10T1)	$[110050]$ (GRH)
10.0.6117147349441995538331.1	x^10 - 3x^9 + 609x^8 - 1456x^7 + 150070x^6 - 268180x^5 + 18698700x^4 - 22211313x^3 + 1177974569x^2 - 697809509x + 30019733501	\( -\,11^{8}\cdot 491^{5} \)	$C_{10}$ (as 10T1)	$[119295]$ (GRH)
10.0.6223480930531534346875.1	x^10 - x^9 + 837x^8 - 837x^7 + 254981x^6 - 254981x^5 + 34056133x^4 - 34056133x^3 + 1868975813x^2 - 1868975813x + 29759754949	\( -\,5^{5}\cdot 11^{9}\cdot 61^{5} \)	$C_{10}$ (as 10T1)	$[2, 65924]$ (GRH)
10.0.6631995294177230343619.1	x^10 - 3x^9 + 619x^8 - 1480x^7 + 155010x^6 - 277040x^5 + 19624244x^4 - 23314473x^3 + 1255906627x^2 - 744124505x + 32508046999	\( -\,11^{8}\cdot 499^{5} \)	$C_{10}$ (as 10T1)	$[134013]$ (GRH)
10.0.6642423532958389282359.1	x^10 - x^9 + 848x^8 - 848x^7 + 261724x^6 - 261724x^5 + 35414765x^4 - 35414765x^3 + 1968832020x^2 - 1968832020x + 31743457747	\( -\,3^{5}\cdot 11^{9}\cdot 103^{5} \)	$C_{10}$ (as 10T1)	$[2, 67100]$ (GRH)
10.0.6902102532282980110583.1	x^10 - 3x^9 + 624x^8 - 1492x^7 + 157510x^6 - 281524x^5 + 20098254x^4 - 23879493x^3 + 1296291656x^2 - 768128009x + 33812593793	\( -\,11^{8}\cdot 503^{5} \)	$C_{10}$ (as 10T1)	$[5, 45255]$ (GRH)
10.0.6971193481768943910912.1	x^10 + 858x^8 + 267696x^6 + 36540504x^4 + 2035828080x^2 + 31758918048	\( -\,2^{15}\cdot 3^{5}\cdot 11^{9}\cdot 13^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 40804]$ (GRH)
10.0.7083629765056720310963.1	x^10 - x^9 + 859x^8 - 859x^7 + 268555x^6 - 268555x^5 + 36809059x^4 - 36809059x^3 + 2072637139x^2 - 2072637139x + 33831555187	\( -\,11^{9}\cdot 313^{5} \)	$C_{10}$ (as 10T1)	$[118096]$ (GRH)
10.0.7429670943845196502016.1	x^10 + 869x^8 + 274604x^6 + 37964003x^4 + 2142254455x^2 + 33847620389	\( -\,2^{10}\cdot 11^{9}\cdot 79^{5} \)	$C_{10}$ (as 10T1)	$[2, 64016]$ (GRH)
10.0.7468716625208931446431.1	x^10 - 3x^9 + 634x^8 - 1516x^7 + 162570x^6 - 290600x^5 + 21069050x^4 - 25036773x^3 + 1379975554x^2 - 817872389x + 36547313791	\( -\,7^{5}\cdot 11^{8}\cdot 73^{5} \)	$C_{10}$ (as 10T1)	$[161714]$ (GRH)
10.0.7547975425189709416687.1	x^10 - x^9 + 870x^8 - 870x^7 + 275474x^6 - 275474x^5 + 38239477x^4 - 38239477x^3 + 2180493932x^2 - 2180493932x + 36028114321	\( -\,11^{9}\cdot 317^{5} \)	$C_{10}$ (as 10T1)	$[180628]$ (GRH)
10.0.7765646666851839321875.1	x^10 - 3x^9 + 639x^8 - 1528x^7 + 165130x^6 - 295192x^5 + 21565956x^4 - 25629177x^3 + 1423305119x^2 - 843631625x + 37979471531	\( -\,5^{5}\cdot 11^{8}\cdot 103^{5} \)	$C_{10}$ (as 10T1)	$[130506]$ (GRH)
10.0.7841334658442081043456.1	x^10 - 2x^9 + 638x^8 - 1018x^7 + 164878x^6 - 197402x^5 + 21568271x^4 - 17275396x^3 + 1427948346x^2 - 575579688x + 38276049241	\( -\,2^{10}\cdot 3^{5}\cdot 11^{8}\cdot 43^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 2, 2, 6330]$ (GRH)
10.0.8036358984236448717291.1	x^10 - x^9 + 881x^8 - 881x^7 + 282481x^6 - 282481x^5 + 39706481x^4 - 39706481x^3 + 2292506481x^2 - 2292506481x + 38337306481	\( -\,3^{5}\cdot 11^{9}\cdot 107^{5} \)	$C_{10}$ (as 10T1)	$[22, 6248]$ (GRH)
10.0.8071946420583835387719.1	x^10 - 3x^9 + 644x^8 - 1540x^7 + 167710x^6 - 299820x^5 + 22070614x^4 - 26230853x^3 + 1467647092x^2 - 869994585x + 39456176629	\( -\,3^{5}\cdot 11^{8}\cdot 173^{5} \)	$C_{10}$ (as 10T1)	$[162090]$ (GRH)
10.0.8150011085120819200000.1	x^10 - 2x^9 + 643x^8 - 1026x^7 + 167456x^6 - 200492x^5 + 22072947x^4 - 17679454x^3 + 1472396383x^2 - 593461186x + 39761899451	\( -\,2^{15}\cdot 5^{5}\cdot 11^{8}\cdot 13^{5} \)	$C_{10}$ (as 10T1)	$[2, 89122]$ (GRH)
10.0.8387835905457895514683.2	x^10 - 3x^9 + 649x^8 - 1552x^7 + 170310x^6 - 304484x^5 + 22583084x^4 - 26841873x^3 + 1513017121x^2 - 896970629x + 40978460293	\( -\,11^{8}\cdot 523^{5} \)	$C_{10}$ (as 10T1)	$[5, 49775]$ (GRH)
10.0.8713538558196399395567.1	x^10 - 3x^9 + 654x^8 - 1564x^7 + 172930x^6 - 309184x^5 + 23103426x^4 - 27462309x^3 + 1559430974x^2 - 924569189x + 42547369523	\( -\,11^{8}\cdot 17^{5}\cdot 31^{5} \)	$C_{10}$ (as 10T1)	$[198090]$ (GRH)
10.0.8951656010087854604288.1	x^10 + 902x^8 + 295856x^6 + 42455336x^4 + 2486669680x^2 + 40781382752	\( -\,2^{15}\cdot 11^{9}\cdot 41^{5} \)	$C_{10}$ (as 10T1)	$[2, 120274]$ (GRH)
10.0.9088948783634770663459.1	x^10 - x^9 + 903x^8 - 903x^7 + 296759x^6 - 296759x^5 + 42752095x^4 - 42752095x^3 + 2529421775x^2 - 2529421775x + 43310804527	\( -\,7^{5}\cdot 11^{9}\cdot 47^{5} \)	$C_{10}$ (as 10T1)	$[2, 69726]$ (GRH)
10.0.9134812610097024750592.1	x^10 - 2x^9 + 658x^8 - 1050x^7 + 175310x^6 - 209906x^5 + 23634087x^4 - 18929332x^3 + 1611981682x^2 - 649611640x + 44498397329	\( -\,2^{10}\cdot 7^{5}\cdot 11^{8}\cdot 19^{5} \)	$C_{10}$ (as 10T1)	$[2, 60302]$ (GRH)
10.0.9395294360545792084375.1	x^10 - 3x^9 + 664x^8 - 1588x^7 + 178230x^6 - 318692x^5 + 24167966x^4 - 28731717x^3 + 1655453824x^2 - 981671945x + 45829332361	\( -\,5^{5}\cdot 11^{8}\cdot 107^{5} \)	$C_{10}$ (as 10T1)	$[185570]$ (GRH)
10.0.9483429712577339949056.1	x^10 - 2x^9 + 663x^8 - 1058x^7 + 177968x^6 - 213092x^5 + 24170371x^4 - 19358686x^3 + 1660643511x^2 - 669185018x + 46173766231	\( -\,2^{15}\cdot 11^{8}\cdot 67^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 2, 17570]$ (GRH)
10.0.9510965031851013440512.1	x^10 + 913x^8 + 303116x^6 + 44027599x^4 + 2610207655x^2 + 43329447073	\( -\,2^{10}\cdot 11^{9}\cdot 83^{5} \)	$C_{10}$ (as 10T1)	$[2, 52086]$ (GRH)
10.0.10119070675735060734783.1	x^10 - 3x^9 + 674x^8 - 1612x^7 + 183610x^6 - 328344x^5 + 25264714x^4 - 30039653x^3 + 1755844186x^2 - 1041379749x + 49310761543	\( -\,3^{5}\cdot 11^{8}\cdot 181^{5} \)	$C_{10}$ (as 10T1)	$[240852]$ (GRH)