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 all 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.255326682647558617373989666816.1	x^16 + 56x^14 + 1176x^12 + 11368x^10 + 49392x^8 + 79576x^6 + 57624x^4 + 19208x^2 + 2401	\( 2^{64}\cdot 7^{12} \)	$OD_{16}.C_2$ (as 16T40)	$[2, 30, 30]$ (GRH)
16.16.255326682647558617373989666816.1	x^16 - 56x^14 + 1176x^12 - 11368x^10 + 49392x^8 - 79576x^6 + 57624x^4 - 19208x^2 + 2401	\( 2^{64}\cdot 7^{12} \)	$OD_{16}.C_2$ (as 16T40)	Trivial (GRH)
16.8.255326682647558617373989666816.1	x^16 + 56x^14 - 392x^12 - 392x^10 + 5488x^8 - 2744x^6 - 19208x^4 + 19208x^2 + 2401	\( 2^{64}\cdot 7^{12} \)	$OD_{16}.C_2$ (as 16T40)	$[2]$ (GRH)
16.8.255326682647558617373989666816.2	x^16 - 56x^14 - 392x^12 + 392x^10 + 5488x^8 + 2744x^6 - 19208x^4 - 19208x^2 + 2401	\( 2^{64}\cdot 7^{12} \)	$OD_{16}.C_2$ (as 16T40)	$[2]$ (GRH)
16.8.3922880935919264967742950184849.2	x^16 - 2x^15 - 11x^14 + 133x^13 - 457x^12 - 31x^11 + 1247x^10 - 10079x^9 + 7175x^8 - 8721x^7 + 104159x^6 + 37621x^5 - 268923x^4 + 44999x^3 + 36567x^2 - 35088x - 3247	\( 13^{12}\cdot 17^{14} \)	$OD_{16}.C_2$ (as 16T40)	$[2, 2]$ (GRH)
16.0.147108257121214334362554931640625.1	x^16 - 2x^15 + 23x^14 - 174x^13 + 1000x^12 + 496x^11 - 8597x^10 + 52088x^9 + 106831x^8 + 537290x^7 + 3491765x^6 + 12847940x^5 + 39264590x^4 + 74177940x^3 + 92969235x^2 + 82809270x + 40054095	\( 3^{4}\cdot 5^{14}\cdot 29^{14} \)	$OD_{16}.C_2$ (as 16T40)	$[2, 2, 2, 2, 12, 12]$ (GRH)
16.16.147108257121214334362554931640625.1	x^16 - 2x^15 - 122x^14 + 406x^13 + 3900x^12 - 13424x^11 - 53257x^10 + 164608x^9 + 375226x^8 - 961140x^7 - 1450125x^6 + 2843520x^5 + 3030830x^4 - 4046660x^3 - 3118060x^2 + 2163460x + 1223095	\( 3^{4}\cdot 5^{14}\cdot 29^{14} \)	$OD_{16}.C_2$ (as 16T40)	$[4]$ (GRH)
16.16.60283401692879138764114019775390625.1	x^16 - 6x^15 - 182x^14 + 1148x^13 + 12506x^12 - 84296x^11 - 394695x^10 + 2956884x^9 + 5316819x^8 - 49762742x^7 - 14339755x^6 + 343311742x^5 - 150618369x^4 - 583498754x^3 + 438205392x^2 + 18646992x - 486704	\( 5^{14}\cdot 61^{14} \)	$OD_{16}.C_2$ (as 16T40)	$[4]$ (GRH)
16.0.1171598758708107367475386427203165009.3	x^16 - 3x^15 + 35x^14 - 111x^13 + 1722x^12 + 8963x^11 + 112504x^10 + 557525x^9 + 2911429x^8 + 10065610x^7 + 29242029x^6 + 61121472x^5 + 94081513x^4 + 77034741x^3 - 48509444x^2 - 224991882x + 118910117	\( 13^{14}\cdot 29^{14} \)	$OD_{16}.C_2$ (as 16T40)	$[2, 54, 108]$ (GRH)
16.16.203962831252212947906041415777587890625.1	x^16 - 7x^15 - 202x^14 + 901x^13 + 13545x^12 - 28129x^11 - 337032x^10 + 50243x^9 + 1550036x^8 - 984145x^7 - 2098230x^6 + 3089875x^5 - 1557975x^4 + 309625x^3 - 2000x^2 - 6875x + 625	\( 5^{14}\cdot 109^{14} \)	$OD_{16}.C_2$ (as 16T40)	$[4]$ (GRH)
16.0.16225116300501260546649351778570556640625.3	x^16 - 6x^15 + 277x^14 - 1628x^13 + 34595x^12 - 184482x^11 + 2756157x^10 - 14048154x^9 + 164477936x^8 - 693240910x^7 + 6595225475x^6 - 25233283590x^5 + 220917959275x^4 - 763530138840x^3 + 6088967690620x^2 - 16618897630070x + 94392688351355	\( 5^{14}\cdot 149^{14} \)	$OD_{16}.C_2$ (as 16T40)	$[2, 182, 364]$ (GRH)
16.8.41587707333348149512906399539663989371009.1	x^16 - 2x^15 - 49x^14 + 89x^13 - 8849x^12 + 78999x^11 - 455761x^10 - 16878x^9 + 71363414x^8 - 504128958x^7 + 1709408121x^6 - 12816699466x^5 + 54011941451x^4 + 14877745689x^3 - 491053716521x^2 + 1002903417071x - 804002796719	\( 17^{14}\cdot 89^{12} \)	$OD_{16}.C_2$ (as 16T40)	$[2, 2]$ (GRH)
16.8.249686282242731792647174886492450339042241.2	x^16 - 2x^15 - 32x^14 + 71x^13 - 6102x^12 + 27466x^11 + 146765x^10 - 790746x^9 + 10245030x^8 - 67215741x^7 - 113711176x^6 + 1810848260x^5 - 3185922987x^4 - 8754113842x^3 + 36703872896x^2 - 34702486496x - 11574258736	\( 37^{12}\cdot 41^{14} \)	$OD_{16}.C_2$ (as 16T40)	$[2, 2]$ (GRH)
16.16.410614370925299326221754150224933859206386689.1	x^16 - 6x^15 - 954x^14 + 11888x^13 + 220836x^12 - 4207992x^11 - 4080691x^10 + 439415370x^9 - 2229690096x^8 - 5603494212x^7 + 61671443021x^6 - 61744943186x^5 - 302059720208x^4 + 381451049084x^3 + 246801227608x^2 - 422001336482x + 105590872531	\( 29^{14}\cdot 53^{14} \)	$OD_{16}.C_2$ (as 16T40)	$[4]$ (GRH)
16.8.803416469975725073264940954221144185207724929.1	x^16 - 5x^15 - 934x^14 + 2223x^13 + 245657x^12 + 712517x^11 - 19740121x^10 - 222937160x^9 - 16641328x^8 + 15221652842x^7 + 49129870727x^6 - 154664551218x^5 - 2055904962519x^4 - 14072956021738x^3 + 25781607633385x^2 + 82626919055977x - 179786105721269	\( 37^{12}\cdot 73^{14} \)	$OD_{16}.C_2$ (as 16T40)	$[2, 2]$ (GRH)
16.8.2753761490493877153393821007665572209609402129.3	x^16 - 4x^15 - 390x^14 - 844x^13 - 118952x^12 + 1209554x^11 + 8567282x^10 + 166021436x^9 + 4637668682x^8 - 26650450836x^7 + 250720847712x^6 - 1881824439314x^5 - 48125809891x^4 + 6649957871712x^3 + 5867704308348x^2 + 8083094211792x + 940107776688	\( 41^{12}\cdot 73^{14} \)	$OD_{16}.C_2$ (as 16T40)	$[2, 2, 6]$ (GRH)
16.16.12436160298838170417198712919084997051554477041.1	x^16 - 6x^15 - 1220x^14 + 3400x^13 + 567046x^12 + 450094x^11 - 126688589x^10 - 529773288x^9 + 13086980592x^8 + 97377694420x^7 - 423891709799x^6 - 5748766657820x^5 - 7225988019316x^4 + 92029351276520x^3 + 377047001834358x^2 + 431756362246264x + 8585514871439	\( 37^{14}\cdot 53^{14} \)	$OD_{16}.C_2$ (as 16T40)	$[4]$ (GRH)
16.0.21767174858780577201904716993499183222663790161.3	x^16 - 3x^15 + 187x^14 - 627x^13 + 28306x^12 - 340621x^11 + 11768472x^10 - 163195065x^9 + 1476282219x^8 - 6294591692x^7 + 15572551375x^6 - 249046344x^5 + 456414116225x^4 + 5076352091595x^3 - 3454592429488x^2 - 38055428105350x + 82946223837577	\( 13^{14}\cdot 157^{14} \)	$OD_{16}.C_2$ (as 16T40)	$[2, 1230, 2460]$ (GRH)
16.8.17328553034618181867273005889005225191371184588849.5	x^16 - 7x^15 - 2022x^14 + 12208x^13 + 1582461x^12 - 8736888x^11 - 621467375x^10 + 3540601088x^9 + 130023633221x^8 - 902801827044x^7 - 12312300080542x^6 + 118985616572265x^5 + 28489887648616x^4 - 1639799050910109x^3 - 7553763870360839x^2 + 51111767470296455x + 100142470449872159	\( 61^{12}\cdot 97^{14} \)	$OD_{16}.C_2$ (as 16T40)	$[2, 2, 2]$ (GRH)
16.0.103591320678630890586725126366901805607295040854289.2	x^16 - 7x^15 + 369x^14 + 8198x^13 + 118511x^12 + 2243990x^11 + 59677021x^10 + 795562016x^9 + 12919660196x^8 + 184403499414x^7 + 2497035252601x^6 + 28925010527445x^5 + 288007893045025x^4 + 1891810596789859x^3 + 14048409623804496x^2 + 65945974579414745x + 157304641041896641	\( 37^{14}\cdot 101^{14} \)	$OD_{16}.C_2$ (as 16T40)	$[2, 5022, 50220]$ (GRH)
16.16.791005910030165719912925444172568170567213001250881.1	x^16 - 6x^15 - 2706x^14 + 33440x^13 + 2418348x^12 - 43338060x^11 - 785911195x^10 + 20629844262x^9 + 34138973916x^8 - 3724774186692x^7 + 20267517960617x^6 + 183380655430714x^5 - 2133469310847068x^4 + 4398309541608152x^3 + 20698040251059424x^2 - 90854176564154546x + 79952241592615927	\( 29^{14}\cdot 149^{14} \)	$OD_{16}.C_2$ (as 16T40)	$[20]$ (GRH)
16.0.6400551765976000463282291896137640731464336249990929.3	x^16 - 6x^15 + 1873x^14 - 31410x^13 + 1465823x^12 - 13245362x^11 + 373695495x^10 - 4141244433x^9 + 110959531595x^8 - 1370337802129x^7 + 11615377868028x^6 - 130418478207074x^5 + 2753263432891772x^4 - 16318805569604653x^3 - 8951931674854952x^2 - 1427922201066519125x + 11763847569050485421	\( 29^{14}\cdot 173^{14} \)	$OD_{16}.C_2$ (as 16T40)	$[2, 7414, 14828]$ (GRH)