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
8.0.144568462126260158464.4	x^8 - 4x^7 + 2422x^6 - 7252x^5 + 2205833x^4 - 4399584x^3 + 895316528x^2 - 893117944x + 136648520446	\( 2^{22}\cdot 2423^{4} \)	$C_4\times C_2$ (as 8T2)	$[11, 98340]$ (GRH)
8.0.150381974238709940224.4	x^8 - 4x^7 + 2446x^6 - 7324x^5 + 2249705x^4 - 4487208x^3 + 922122440x^2 - 919880056x + 142122972958	\( 2^{22}\cdot 2447^{4} \)	$C_4\times C_2$ (as 8T2)	$[4, 20, 12580]$ (GRH)
8.0.374245522326980990449.2	x^8 - 2x^7 + 170x^6 - 308x^5 + 16593x^4 - 8850x^3 + 940388x^2 + 123912x + 21525984	\( 73^{6}\cdot 223^{4} \)	$C_4\times C_2$ (as 8T2)	$[2, 8, 65520]$ (GRH)
8.0.444690528501640462336.4	x^8 + 4536x^6 + 6429780x^4 + 2916548208x^2 + 416343691009	\( 2^{24}\cdot 2269^{4} \)	$C_4\times C_2$ (as 8T2)	$[1044870]$ (GRH)
8.0.467050538034157060096.4	x^8 + 4592x^6 + 6589520x^4 + 3025907584x^2 + 437250240001	\( 2^{24}\cdot 2297^{4} \)	$C_4\times C_2$ (as 8T2)	$[14, 80080]$ (GRH)
8.0.539209428477134503936.4	x^8 + 4760x^6 + 7080500x^4 + 3370318000x^2 + 504712205761	\( 2^{24}\cdot 2381^{4} \)	$C_4\times C_2$ (as 8T2)	$[1010990]$ (GRH)
8.0.550162127014976290816.4	x^8 + 4784x^6 + 7152080x^4 + 3421555072x^2 + 514951195201	\( 2^{24}\cdot 2393^{4} \)	$C_4\times C_2$ (as 8T2)	$[5, 10, 20400]$ (GRH)
8.0.627503801799075168256.4	x^8 + 4944x^6 + 7638480x^4 + 3776464512x^2 + 587247875041	\( 2^{24}\cdot 2473^{4} \)	$C_4\times C_2$ (as 8T2)	$[10, 131360]$ (GRH)
8.0.724035990444278098129.1	x^8 - 2x^7 + 210x^6 - 368x^5 + 23373x^4 - 14510x^3 + 1466208x^2 + 76192x + 37558784	\( 73^{6}\cdot 263^{4} \)	$C_4\times C_2$ (as 8T2)	$[1091961]$ (GRH)
8.0.816233329019587465009.1	x^8 - 2x^7 + 218x^6 - 380x^5 + 24873x^4 - 15786x^3 + 1590908x^2 + 60840x + 41606784	\( 73^{6}\cdot 271^{4} \)	$C_4\times C_2$ (as 8T2)	$[1354309]$ (GRH)
8.0.928994798648812371968.4	x^8 + 6488x^6 + 13154420x^4 + 8534587696x^2 + 865193827682	\( 2^{31}\cdot 811^{4} \)	$C_8$ (as 8T1)	$[1016306]$ (GRH)
8.0.975668972415025676288.4	x^8 + 6568x^6 + 13480820x^4 + 8854202576x^2 + 908662539362	\( 2^{31}\cdot 821^{4} \)	$C_8$ (as 8T1)	$[1151954]$ (GRH)
8.0.985210896300709511168.4	x^8 + 6584x^6 + 13546580x^4 + 8919068272x^2 + 917549148482	\( 2^{31}\cdot 823^{4} \)	$C_8$ (as 8T1)	$[2, 610706]$ (GRH)
8.0.1004504539652390125568.4	x^8 + 6616x^6 + 13678580x^4 + 9049748528x^2 + 935517754082	\( 2^{31}\cdot 827^{4} \)	$C_8$ (as 8T1)	$[1440002]$ (GRH)
8.0.1136909748160207781888.4	x^8 + 6824x^6 + 14552180x^4 + 9930407632x^2 + 1058829713762	\( 2^{31}\cdot 853^{4} \)	$C_8$ (as 8T1)	$[9, 120402]$ (GRH)
8.0.1158385608388612456448.4	x^8 + 6856x^6 + 14688980x^4 + 10070764688x^2 + 1078830667202	\( 2^{31}\cdot 857^{4} \)	$C_8$ (as 8T1)	$[2, 539746]$ (GRH)
8.0.1191168083926269820928.4	x^8 + 6904x^6 + 14895380x^4 + 10283770352x^2 + 1109361726722	\( 2^{31}\cdot 863^{4} \)	$C_8$ (as 8T1)	$[2, 2, 4, 62948]$ (GRH)
8.0.1256092108114942364489.2	x^8 - x^7 + 1608x^6 - 3250x^5 + 188893x^4 + 474767x^3 + 6289010x^2 + 15728420x + 66111848	\( 73^{4}\cdot 89^{7} \)	$C_8$ (as 8T1)	$[2, 2, 2, 157522]$ (GRH)
8.0.1270364178351933882368.4	x^8 + 7016x^6 + 15382580x^4 + 10792418128x^2 + 1183118837282	\( 2^{31}\cdot 877^{4} \)	$C_8$ (as 8T1)	$[19, 57494]$ (GRH)
8.0.1293699764917064695808.4	x^8 + 7048x^6 + 15523220x^4 + 10940765456x^2 + 1204851795842	\( 2^{31}\cdot 881^{4} \)	$C_8$ (as 8T1)	$[2, 2, 6, 54966]$ (GRH)
8.0.1329304102000476028928.4	x^8 + 7096x^6 + 15735380x^4 + 11165825648x^2 + 1238010918722	\( 2^{31}\cdot 887^{4} \)	$C_8$ (as 8T1)	$[2, 571394]$ (GRH)
8.0.1415724398828591148049.1	x^8 - 2x^7 + 258x^6 - 440x^5 + 33093x^4 - 22886x^3 + 2322648x^2 - 50240x + 66904064	\( 73^{6}\cdot 311^{4} \)	$C_4\times C_2$ (as 8T2)	$[7, 186732]$ (GRH)
8.0.1453312516300627509248.4	x^8 + 7256x^6 + 16452980x^4 + 11938282288x^2 + 1353502754402	\( 2^{31}\cdot 907^{4} \)	$C_8$ (as 8T1)	$[1243954]$ (GRH)
8.0.1479119877504046727168.4	x^8 + 7288x^6 + 16598420x^4 + 12096928496x^2 + 1377537732482	\( 2^{31}\cdot 911^{4} \)	$C_8$ (as 8T1)	$[2, 2, 2, 177986]$ (GRH)
8.0.1599531221475066380288.4	x^8 + 7432x^6 + 17260820x^4 + 12828241424x^2 + 1489679535362	\( 2^{31}\cdot 929^{4} \)	$C_8$ (as 8T1)	$[2, 2, 2, 203524]$ (GRH)
8.0.1619334413678782351489.1	x^8 - 2x^7 + 84x^6 - 322x^5 + 8967x^4 + 16100x^3 + 604596x^2 + 1085296x + 12178432	\( 113^{6}\cdot 167^{4} \)	$C_4\times C_2$ (as 8T2)	$[1290179]$ (GRH)
8.0.1621554850562885994001.1	x^8 - 2x^7 + 174x^6 - 148x^5 + 18561x^4 - 35530x^3 + 1250448x^2 - 2033504x + 31533568	\( 89^{6}\cdot 239^{4} \)	$C_4\times C_2$ (as 8T2)	$[5, 5, 5, 11895]$ (GRH)
8.0.1683791680202162044928.4	x^8 + 7528x^6 + 17709620x^4 + 13331801936x^2 + 1568153202722	\( 2^{31}\cdot 941^{4} \)	$C_8$ (as 8T1)	$[3, 600342]$ (GRH)
8.0.1727148905014061170688.4	x^8 + 7576x^6 + 17936180x^4 + 13588449968x^2 + 1608532764962	\( 2^{31}\cdot 947^{4} \)	$C_8$ (as 8T1)	$[3, 594582]$ (GRH)
8.0.1877741314886554615808.4	x^8 + 7736x^6 + 18701780x^4 + 14467697008x^2 + 1748782875842	\( 2^{31}\cdot 967^{4} \)	$C_8$ (as 8T1)	$[2, 665026]$ (GRH)
8.0.2005136473592963268608.4	x^8 + 7864x^6 + 19325780x^4 + 15197793392x^2 + 1867428863042	\( 2^{31}\cdot 983^{4} \)	$C_8$ (as 8T1)	$[2, 769778]$ (GRH)
8.0.2071211665752250646528.4	x^8 + 7928x^6 + 19641620x^4 + 15571876336x^2 + 1928966181122	\( 2^{31}\cdot 991^{4} \)	$C_8$ (as 8T1)	$[2, 2, 4, 108868]$ (GRH)
8.0.2121829576586704191488.4	x^8 + 7976x^6 + 19880180x^4 + 15856431568x^2 + 1976107784162	\( 2^{31}\cdot 997^{4} \)	$C_8$ (as 8T1)	$[1529218]$ (GRH)
8.0.2225843012532885782528.4	x^8 + 8072x^6 + 20361620x^4 + 16435899664x^2 + 2072977845122	\( 2^{31}\cdot 1009^{4} \)	$C_8$ (as 8T1)	$[2, 2, 2, 169586]$ (GRH)
8.0.2261349279535651094528.4	x^8 + 8104x^6 + 20523380x^4 + 16632147152x^2 + 2106045633122	\( 2^{31}\cdot 1013^{4} \)	$C_8$ (as 8T1)	$[3, 617574]$ (GRH)
8.0.2315403053053151019008.4	x^8 + 8152x^6 + 20767220x^4 + 16929437744x^2 + 2156387132642	\( 2^{31}\cdot 1019^{4} \)	$C_8$ (as 8T1)	$[3, 417894]$ (GRH)
8.0.2333634485193631858688.4	x^8 + 8168x^6 + 20848820x^4 + 17029316176x^2 + 2173366476962	\( 2^{31}\cdot 1021^{4} \)	$C_8$ (as 8T1)	$[3, 459462]$ (GRH)
8.0.2377732718215764579121.2	x^8 - 2x^7 + 198x^6 - 184x^5 + 22701x^4 - 40990x^3 + 1600620x^2 - 2481416x + 43151872	\( 89^{6}\cdot 263^{4} \)	$C_4\times C_2$ (as 8T2)	$[2, 2, 453960]$ (GRH)
8.0.2426411897054044356608.4	x^8 + 8248x^6 + 21259220x^4 + 17534604656x^2 + 2259772175042	\( 2^{31}\cdot 1031^{4} \)	$C_8$ (as 8T1)	$[14, 90734]$ (GRH)
8.0.2513708739303702600529.2	x^8 - 2x^7 + 306x^6 - 512x^5 + 44541x^4 - 32990x^3 + 3464208x^2 - 271712x + 110642432	\( 73^{6}\cdot 359^{4} \)	$C_4\times C_2$ (as 8T2)	$[13, 157092]$ (GRH)
8.0.2600350069471783682048.4	x^8 + 8392x^6 + 22008020x^4 + 18469130384x^2 + 2421764721602	\( 2^{31}\cdot 1049^{4} \)	$C_8$ (as 8T1)	$[2, 1116754]$ (GRH)
8.0.2620237933574774325248.4	x^8 + 8408x^6 + 22092020x^4 + 18574970416x^2 + 2440286738402	\( 2^{31}\cdot 1051^{4} \)	$C_8$ (as 8T1)	$[3, 585174]$ (GRH)
8.0.2680508590349431332241.1	x^8 - 2x^7 + 206x^6 - 196x^5 + 24177x^4 - 42906x^3 + 1730816x^2 - 2642784x + 47649536	\( 89^{6}\cdot 271^{4} \)	$C_4\times C_2$ (as 8T2)	$[2, 26, 38896]$ (GRH)
8.0.2721393863698015059968.4	x^8 + 8488x^6 + 22514420x^4 + 19110239696x^2 + 2534495539682	\( 2^{31}\cdot 1061^{4} \)	$C_8$ (as 8T1)	$[21, 80682]$ (GRH)
8.0.2745373376333238568369.3	x^8 - 2x^7 + 314x^6 - 524x^5 + 46617x^4 - 34842x^3 + 3685100x^2 - 319320x + 119608128	\( 73^{6}\cdot 367^{4} \)	$C_4\times C_2$ (as 8T2)	$[2, 6, 232992]$ (GRH)
8.0.2804404700831346065408.4	x^8 + 8552x^6 + 22855220x^4 + 19545784144x^2 + 2611805406242	\( 2^{31}\cdot 1069^{4} \)	$C_8$ (as 8T1)	$[3, 433878]$ (GRH)
8.0.2850736989716891767937.1	x^8 - x^7 + 1646x^6 + 3374x^5 + 675121x^4 + 1559767x^3 + 64010176x^2 - 139767108x + 480344032	\( 59^{4}\cdot 113^{7} \)	$C_8$ (as 8T1)	$[1316786]$ (GRH)
8.0.2998113306417853104128.4	x^8 + 8696x^6 + 23631380x^4 + 20549848048x^2 + 2792210603522	\( 2^{31}\cdot 1087^{4} \)	$C_8$ (as 8T1)	$[4, 4, 252, 252]$ (GRH)
8.0.3042487957614365769728.4	x^8 + 8728x^6 + 23805620x^4 + 20777545136x^2 + 2833537717922	\( 2^{31}\cdot 1091^{4} \)	$C_8$ (as 8T1)	$[2380498]$ (GRH)
8.0.3064859098449862197248.4	x^8 + 8744x^6 + 23892980x^4 + 20892021712x^2 + 2854372466402	\( 2^{31}\cdot 1093^{4} \)	$C_8$ (as 8T1)	$[1727074]$ (GRH)

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