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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
8.0.2326500163918495744.9	x^8 - 4x^7 + 862x^6 - 2572x^5 + 280793x^4 - 557304x^3 + 40962248x^2 - 40684024x + 2258152126	\( 2^{22}\cdot 863^{4} \)	$C_4\times C_2$ (as 8T2)	$[2, 6, 10248]$ (GRH)
8.0.2991726925849821184.14	x^8 - 4x^7 + 918x^6 - 2740x^5 + 318313x^4 - 632064x^3 + 49406768x^2 - 49091192x + 2896594238	\( 2^{22}\cdot 919^{4} \)	$C_4\times C_2$ (as 8T2)	$[121828]$ (GRH)
8.0.3667463505637801984.15	x^8 - 4x^7 + 966x^6 - 2884x^5 + 352345x^4 - 699888x^3 + 57507920x^2 - 57158456x + 3544060958	\( 2^{22}\cdot 967^{4} \)	$C_4\times C_2$ (as 8T2)	$[17, 9724]$ (GRH)
8.0.3916282174986256384.10	x^8 - 4x^7 + 982x^6 - 2932x^5 + 364073x^4 - 723264x^3 + 60393008x^2 - 60031864x + 3782251966	\( 2^{22}\cdot 983^{4} \)	$C_4\times C_2$ (as 8T2)	$[9, 12204]$ (GRH)
8.0.4045335284672364544.10	x^8 - 4x^7 + 990x^6 - 2956x^5 + 370009x^4 - 735096x^3 + 61871048x^2 - 61503992x + 3905751998	\( 2^{22}\cdot 991^{4} \)	$C_4\times C_2$ (as 8T2)	$[2, 2, 26520]$ (GRH)
8.0.4887897553254744064.14	x^8 - 4x^7 + 1038x^6 - 3100x^5 + 406633x^4 - 808104x^3 + 71248328x^2 - 70844792x + 4711451678	\( 2^{22}\cdot 1039^{4} \)	$C_4\times C_2$ (as 8T2)	$[4, 20, 2300]$ (GRH)
8.0.5355412928692486144.10	x^8 - 4x^7 + 1062x^6 - 3172x^5 + 425593x^4 - 845904x^3 + 76272848x^2 - 75850424x + 5158114526	\( 2^{22}\cdot 1063^{4} \)	$C_4\times C_2$ (as 8T2)	$[156180]$ (GRH)
8.0.5855690051597369344.18	x^8 - 4x^7 + 1086x^6 - 3244x^5 + 444985x^4 - 884568x^3 + 81528200x^2 - 81086456x + 5635807358	\( 2^{22}\cdot 1087^{4} \)	$C_4\times C_2$ (as 8T2)	$[4, 4, 9792]$ (GRH)
8.0.5990152398130118656.6	x^8 + 1544x^6 + 744980x^4 + 115024912x^2 + 5665723441	\( 2^{24}\cdot 773^{4} \)	$C_4\times C_2$ (as 8T2)	$[101218]$ (GRH)
8.0.6208146464334413824.11	x^8 - 4x^7 + 1102x^6 - 3292x^5 + 458153x^4 - 910824x^3 + 85162568x^2 - 84707704x + 5972200606	\( 2^{22}\cdot 1103^{4} \)	$C_4\times C_2$ (as 8T2)	$[2, 2, 44896]$ (GRH)
8.0.6769446830888452096.8	x^8 + 1592x^6 + 792020x^4 + 126089584x^2 + 6399840001	\( 2^{24}\cdot 797^{4} \)	$C_4\times C_2$ (as 8T2)	$[17, 6630]$ (GRH)
8.0.7244326837868822528.41	x^8 + 1928x^6 + 1161620x^4 + 223960336x^2 + 6746805122	\( 2^{31}\cdot 241^{4} \)	$C_8$ (as 8T1)	$[6, 6, 6, 534]$ (GRH)
8.0.7361413259884232704.13	x^8 - 4x^7 + 1150x^6 - 3436x^5 + 498809x^4 - 991896x^3 + 96710408x^2 - 96215032x + 7072139518	\( 2^{22}\cdot 1151^{4} \)	$C_4\times C_2$ (as 8T2)	$[8, 8, 1640]$ (GRH)
8.0.7923882339384426496.8	x^8 + 1656x^6 + 856980x^4 + 141915888x^2 + 7486921729	\( 2^{24}\cdot 829^{4} \)	$C_4\times C_2$ (as 8T2)	$[146454]$ (GRH)
8.0.8518685995854462976.14	x^8 + 1696x^6 + 924472x^4 + 180424008x^2 + 7933644574	\( 2^{31}\cdot 1583^{3} \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2, 2, 29762]$ (GRH)
8.0.9383518892996952064.15	x^8 - 4x^7 + 1222x^6 - 3652x^5 + 563033x^4 - 1119984x^3 + 115918928x^2 - 115359544x + 8998422046	\( 2^{22}\cdot 1223^{4} \)	$C_4\times C_2$ (as 8T2)	$[7, 25340]$ (GRH)
8.0.9631459800550211584.11	x^8 - 4x^7 + 1230x^6 - 3676x^5 + 570409x^4 - 1134696x^3 + 118198088x^2 - 117631352x + 9234443678	\( 2^{22}\cdot 1231^{4} \)	$C_4\times C_2$ (as 8T2)	$[2, 2, 31968]$ (GRH)
8.0.10159260410122837729.1	x^8 - 2x^7 - 36x^6 - 142x^5 + 1767x^4 + 11360x^3 + 69276x^2 + 150736x + 431872	\( 47^{4}\cdot 113^{6} \)	$C_4\times C_2$ (as 8T2)	$[112355]$ (GRH)
8.0.11223855906552807424.18	x^8 - 4x^7 + 1278x^6 - 3820x^5 + 615673x^4 - 1224984x^3 + 132503048x^2 - 131891192x + 10749544958	\( 2^{22}\cdot 1279^{4} \)	$C_4\times C_2$ (as 8T2)	$[4, 8, 7360]$ (GRH)
8.0.11244469883406123008.6	x^8 + 2152x^6 + 1447220x^4 + 311441744x^2 + 10472228642	\( 2^{31}\cdot 269^{4} \)	$C_8$ (as 8T1)	$[147922]$ (GRH)
8.0.12050141564144451584.57	x^8 + 2120x^6 + 1144388x^4 + 202094656x^2 + 11222568866	\( 2^{31}\cdot 1777^{3} \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2, 2, 25628]$ (GRH)
8.0.12052084020012384256.14	x^8 + 1724x^6 + 935902x^4 + 180472356x^2 + 11224377919	\( 2^{30}\cdot 2239^{3} \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[4, 8, 3768]$ (GRH)
8.0.12090313646459060224.10	x^8 - 4x^7 + 1302x^6 - 3892x^5 + 638953x^4 - 1271424x^3 + 140069168x^2 - 139434104x + 11573459006	\( 2^{22}\cdot 1303^{4} \)	$C_4\times C_2$ (as 8T2)	$[153780]$ (GRH)
8.0.12227533478366872576.1	x^8 + 883x^6 + 289746x^4 + 41924192x^2 + 2264237056	\( 2^{10}\cdot 17^{4}\cdot 103^{2}\cdot 3671^{2} \)	$C_2^2 \wr C_2$ (as 8T18)	$[2, 2, 2, 18564]$ (GRH)
8.0.12496337667773956096.19	x^8 + 1856x^6 + 1076480x^4 + 199794688x^2 + 11788964929	\( 2^{24}\cdot 929^{4} \)	$C_4\times C_2$ (as 8T2)	$[2, 2, 2, 13140]$ (GRH)
8.0.12642965179772960768.6	x^8 + 2216x^6 + 1534580x^4 + 340062928x^2 + 11774678882	\( 2^{31}\cdot 277^{4} \)	$C_8$ (as 8T1)	$[146098]$ (GRH)
8.0.12695186543459958784.14	x^8 - 4x^7 + 1318x^6 - 3940x^5 + 654713x^4 - 1302864x^3 + 145269968x^2 - 144619192x + 12148451038	\( 2^{22}\cdot 1319^{4} \)	$C_4\times C_2$ (as 8T2)	$[5, 5, 6660]$ (GRH)
8.0.12843942828228739072.10	x^8 + 1804x^6 + 955966x^4 + 188293284x^2 + 11961853903	\( 2^{30}\cdot 2287^{3} \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2, 2, 30166]$ (GRH)
8.0.12901851046848014329.4	x^8 - 2x^7 + 58x^6 - 1124x^5 + 5836x^4 - 47870x^3 + 481563x^2 - 1872810x + 2972700	\( 13^{4}\cdot 277^{6} \)	$D_4$ (as 8T4)	$[87, 1740]$ (GRH)
8.0.12932374110536728576.30	x^8 + 1872x^6 + 1095120x^4 + 205006464x^2 + 12198981601	\( 2^{24}\cdot 937^{4} \)	$C_4\times C_2$ (as 8T2)	$[10, 14000]$ (GRH)
8.0.13005995399880638464.12	x^8 - 4x^7 + 1326x^6 - 3964x^5 + 662665x^4 - 1318728x^3 + 147917960x^2 - 147259256x + 12443851358	\( 2^{22}\cdot 1327^{4} \)	$C_4\times C_2$ (as 8T2)	$[2, 6, 26160]$ (GRH)
8.0.13010376709705302016.15	x^8 + 1704x^6 + 933376x^4 + 186106424x^2 + 12116857534	\( 2^{31}\cdot 1823^{3} \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2, 2, 27288]$ (GRH)
8.0.13774492524565495808.14	x^8 + 2264x^6 + 1601780x^4 + 362642992x^2 + 12828495842	\( 2^{31}\cdot 283^{4} \)	$C_8$ (as 8T1)	$[138146]$ (GRH)
8.0.13838579036739076096.31	x^8 + 1904x^6 + 1132880x^4 + 215700352x^2 + 13051006081	\( 2^{24}\cdot 953^{4} \)	$C_4\times C_2$ (as 8T2)	$[2, 86080]$ (GRH)
8.0.13952683962766721024.9	x^8 + 1804x^6 + 973314x^4 + 198979236x^2 + 12994449551	\( 2^{30}\cdot 2351^{3} \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2, 2, 26016]$ (GRH)
8.0.14110525818002210816.27	x^8 + 1488x^6 + 771676x^4 + 168390192x^2 + 13141451234	\( 2^{31}\cdot 1873^{3} \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2, 2, 27602]$ (GRH)
8.0.14475238875817050112.63	x^8 + 1448x^6 + 763156x^4 + 171279408x^2 + 13481116738	\( 2^{31}\cdot 1889^{3} \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[4, 4, 8200]$ (GRH)
8.0.14646503606723805184.14	x^8 - 4x^7 + 1366x^6 - 4084x^5 + 703145x^4 - 1399488x^3 + 161641520x^2 - 160942456x + 14002464958	\( 2^{22}\cdot 1367^{4} \)	$C_4\times C_2$ (as 8T2)	$[235900]$ (GRH)
8.0.15286151192988614656.27	x^8 + 1952x^6 + 1190720x^4 + 232428544x^2 + 14411762401	\( 2^{24}\cdot 977^{4} \)	$C_4\times C_2$ (as 8T2)	$[2, 2, 2, 15260]$ (GRH)
8.0.15947832799105384448.13	x^8 + 1992x^6 + 1248640x^4 + 274060872x^2 + 14852576702	\( 2^{31}\cdot 1951^{3} \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2, 2, 29712]$ (GRH)
8.0.16066850867227131904.13	x^8 - 4x^7 + 1398x^6 - 4180x^5 + 736393x^4 - 1465824x^3 + 173212208x^2 - 172479992x + 15351212798	\( 2^{22}\cdot 1399^{4} \)	$C_4\times C_2$ (as 8T2)	$[148500]$ (GRH)
8.0.16576793567083626496.8	x^8 + 1992x^6 + 1240020x^4 + 247011984x^2 + 15624750001	\( 2^{24}\cdot 997^{4} \)	$C_4\times C_2$ (as 8T2)	$[101682]$ (GRH)
8.0.17032800494280310609.1	x^8 - 2x^7 + 50x^6 - 128x^5 + 3453x^4 + 930x^3 + 138128x^2 + 77472x + 1891584	\( 73^{6}\cdot 103^{4} \)	$C_4\times C_2$ (as 8T2)	$[5, 29725]$ (GRH)
8.0.17154112262978404352.14	x^8 + 1792x^6 + 1039480x^4 + 223776056x^2 + 15976011998	\( 2^{31}\cdot 1999^{3} \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2, 2, 29102]$ (GRH)
8.0.17198061789028286464.16	x^8 - 4x^7 + 1422x^6 - 4252x^5 + 761833x^4 - 1516584x^3 + 182243528x^2 - 181485944x + 16424988446	\( 2^{22}\cdot 1423^{4} \)	$C_4\times C_2$ (as 8T2)	$[2, 72, 1224]$ (GRH)
8.0.17389398535413170176.25	x^8 + 2016x^6 + 1270080x^4 + 256048128x^2 + 16388352289	\( 2^{24}\cdot 1009^{4} \)	$C_4\times C_2$ (as 8T2)	$[2, 2, 6, 5460]$ (GRH)
8.0.17621690135424794624.32	x^8 + 2128x^6 + 1444172x^4 + 325463120x^2 + 16411477826	\( 2^{31}\cdot 2017^{3} \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2, 2, 28192]$ (GRH)
8.0.17666791246372274176.8	x^8 + 2024x^6 + 1280180x^4 + 259108432x^2 + 16648998961	\( 2^{24}\cdot 1013^{4} \)	$C_4\times C_2$ (as 8T2)	$[134810]$ (GRH)
8.0.17984695135752945664.16	x^8 - 4x^7 + 1438x^6 - 4300x^5 + 779033x^4 - 1550904x^3 + 188435528x^2 - 187660792x + 17171484478	\( 2^{22}\cdot 1439^{4} \)	$C_4\times C_2$ (as 8T2)	$[4, 4, 15600]$ (GRH)
8.0.18231519415575248896.7	x^8 + 2040x^6 + 1300500x^4 + 265302000x^2 + 17179607041	\( 2^{24}\cdot 1021^{4} \)	$C_4\times C_2$ (as 8T2)	$[172150]$ (GRH)

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