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 39 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.8.483749495705158869017.1	x^16 - 7x^15 + 15x^14 - 3x^13 - 47x^12 + 74x^11 + 9x^10 - 12x^9 - 52x^8 - 44x^7 + 19x^6 + 37x^5 + 30x^4 - 6x^3 - 9x^2 - 5x + 1	\( 13^{2}\cdot 17^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	Trivial
16.12.732780301186512843008.1	x^16 - 3x^15 - 8x^14 + 24x^13 + 30x^12 - 56x^11 - 121x^10 + 23x^9 + 441x^8 - 48x^7 - 842x^6 + 384x^5 + 616x^4 - 488x^3 - 32x^2 + 96x - 16	\( 2^{8}\cdot 17^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	Trivial (GRH)
16.12.6323092520785183086737.1	x^16 - 4x^15 - x^14 + 38x^13 - 101x^12 - 21x^11 + 594x^10 - 540x^9 - 1359x^8 + 1560x^7 + 1614x^6 - 1526x^5 - 951x^4 + 506x^3 + 152x^2 - 64x + 1	\( 17^{15}\cdot 47^{2} \)	$(C_2\times C_8).D_4$ (as 16T306)	Trivial (GRH)
16.12.12849417078227563094777.1	x^16 - 3x^15 - 8x^14 + 41x^13 - 21x^12 - 175x^11 + 287x^10 + 244x^9 - 596x^8 - 116x^7 + 365x^6 - 7x^5 - 132x^4 + 5x^3 + 36x^2 + 11x + 1	\( 17^{15}\cdot 67^{2} \)	$(C_2\times C_8).D_4$ (as 16T306)	Trivial (GRH)
16.8.22673252991009250896353.1	x^16 - 6x^15 + 19x^14 - 12x^13 - 81x^12 + 316x^11 - 723x^10 + 1176x^9 - 1378x^8 + 992x^7 - 138x^6 - 600x^5 + 795x^4 - 486x^3 + 145x^2 - 20x + 1	\( 17^{15}\cdot 89^{2} \)	$(C_2\times C_8).D_4$ (as 16T306)	Trivial (GRH)
16.4.123839870900520670468352.1	x^16 - 5x^15 + 8x^14 + 11x^13 - 106x^12 + 360x^11 - 950x^10 + 2421x^9 - 5781x^8 + 12126x^7 - 21088x^6 + 29212x^5 - 32024x^4 + 27112x^3 - 16968x^2 + 7456x - 1648	\( 2^{8}\cdot 13^{2}\cdot 17^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2]$ (GRH)
16.8.123839870900520670468352.1	x^16 - 5x^15 - 9x^14 + 62x^13 + 30x^12 - 269x^11 - 270x^10 + 1044x^9 + 985x^8 - 3769x^7 + 1675x^6 + 2641x^5 - 3549x^4 + 1714x^3 - 36x^2 - 551x + 239	\( 2^{8}\cdot 13^{2}\cdot 17^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	Trivial (GRH)
16.4.123839870900520670468352.2	x^16 + 17x^14 + 68x^12 - 289x^10 - 2873x^8 - 7157x^6 - 4386x^4 + 4199x^2 + 2873	\( 2^{8}\cdot 13^{2}\cdot 17^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2]$
16.8.123839870900520670468352.2	x^16 - 5x^15 + 8x^14 + 28x^13 - 242x^12 + 853x^11 - 1698x^10 + 1673x^9 + 390x^8 - 4313x^7 + 7914x^6 - 7967x^5 + 4509x^4 - 513x^3 - 1362x^2 + 724x - 67	\( 2^{8}\cdot 13^{2}\cdot 17^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	Trivial (GRH)
16.8.13816369346835042457994537.1	x^16 - 5x^15 + 8x^14 + 28x^13 - 225x^12 + 887x^11 - 3211x^10 + 7096x^9 - 7651x^8 + 328x^7 + 20885x^6 - 50365x^5 + 49797x^4 + 17830x^3 - 67305x^2 + 42102x - 8329	\( 13^{6}\cdot 17^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2]$ (GRH)
16.0.31703006950533291639898112.1	x^16 + 34x^14 + 425x^12 + 2584x^10 + 8670x^8 + 16898x^6 + 19040x^4 + 11492x^2 + 2873	\( 2^{16}\cdot 13^{2}\cdot 17^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2, 2, 50]$ (GRH)
16.16.31703006950533291639898112.1	x^16 - 34x^14 + 425x^12 - 2584x^10 + 8670x^8 - 16898x^6 + 19040x^4 - 11492x^2 + 2873	\( 2^{16}\cdot 13^{2}\cdot 17^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	Trivial (GRH)
16.8.31703006950533291639898112.1	x^16 + 17x^14 - 68x^12 - 1700x^10 + 255x^8 + 26248x^6 - 4828x^4 - 77571x^2 + 2873	\( 2^{16}\cdot 13^{2}\cdot 17^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2]$ (GRH)
16.16.842099397638721574979305472.3	x^16 - 68x^14 + 1496x^12 - 15232x^10 + 80767x^8 - 230826x^6 + 350285x^4 - 263109x^2 + 76313	\( 2^{16}\cdot 17^{15}\cdot 67^{2} \)	$(C_2\times C_8).D_4$ (as 16T306)	Trivial (GRH)
16.4.30854674434917562989871890897.9	x^16 - 6x^15 + 87x^14 - 488x^13 + 3268x^12 - 13386x^11 + 51042x^10 - 142950x^9 + 288795x^8 - 393476x^7 - 100557x^6 + 1254102x^5 - 3337665x^4 + 4289566x^3 - 2665081x^2 + 766748x + 2904383	\( 17^{15}\cdot 47^{6} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2, 2]$ (GRH)
16.8.31236842166910780816202985728.3	x^16 - 4x^15 + 50x^14 - 217x^13 + 290x^12 - 361x^11 - 12632x^10 + 54370x^9 - 25924x^8 - 116063x^7 + 333964x^6 - 210048x^5 + 56339x^4 - 274843x^3 - 4310198x^2 - 3508966x - 546719	\( 2^{8}\cdot 17^{15}\cdot 6529^{2} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2, 2]$ (GRH)
16.4.258930158322830089457985795017.16	x^16 - 3x^15 + 77x^14 - 163x^13 + 2189x^12 - 3558x^11 + 25243x^10 - 44177x^9 + 10386x^8 - 478326x^7 - 2486412x^6 - 3692832x^5 - 20644371x^4 - 18441153x^3 - 11710839x^2 - 64012350x + 9493447	\( 17^{15}\cdot 67^{6} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2, 2, 4, 4]$ (GRH)
16.0.905469581514181342527129976832.1	x^16 + 136x^14 + 7174x^12 + 186524x^10 + 2536859x^8 + 18002218x^6 + 66518569x^4 + 119927639x^2 + 82055753	\( 2^{16}\cdot 13^{6}\cdot 17^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2, 2, 2, 6, 870]$ (GRH)
16.8.1422570703415873252968445947073.1	x^16 - 4x^15 - 35x^14 + 55x^13 - 1461x^12 + 2750x^11 + 13565x^10 + 5257x^9 + 376993x^8 - 1009787x^7 + 1488111x^6 - 10705746x^5 - 3090174x^4 + 6621394x^3 + 36211563x^2 + 120137644x + 12813683	\( 17^{15}\cdot 89^{6} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2]$ (GRH)
16.8.66688975910627504451630153142433.1	x^16 - 8x^15 + 30x^14 - 70x^13 - 936x^12 + 6162x^11 - 29406x^10 + 89830x^9 - 143598x^8 + 104338x^7 + 207532x^6 - 679458x^5 + 755326x^4 - 401668x^3 - 75136x^2 + 167061x + 31417	\( 13^{12}\cdot 17^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2, 4]$ (GRH)
16.8.66688975910627504451630153142433.3	x^16 - 4x^15 - x^14 + 21x^13 - 424x^12 + 999x^11 - 1667x^10 - 1016x^9 + 73917x^8 - 67715x^7 + 99993x^6 + 778026x^5 - 2204236x^4 - 5407891x^3 - 5505995x^2 + 8743206x + 21153679	\( 13^{12}\cdot 17^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2, 4]$ (GRH)
16.12.1170881448713923574794017240042457.1	x^16 - 5x^15 - 58x^14 + 416x^13 - 277x^12 - 5200x^11 + 33906x^10 - 136300x^9 + 291294x^8 - 199352x^7 - 244894x^6 + 520392x^5 - 367938x^4 - 167467x^3 + 328416x^2 + 61588x - 13969	\( 43^{2}\cdot 97^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2]$ (GRH)
16.12.1398851876803167753769596583695937.1	x^16 - 6x^15 - 68x^14 + 410x^13 + 1604x^12 - 10484x^11 - 13138x^10 + 150813x^9 - 135236x^8 - 1496025x^7 + 3584534x^6 + 9914265x^5 - 24578465x^4 - 34561989x^3 + 53908555x^2 + 39677155x - 20855909	\( 47^{2}\cdot 97^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2]$ (GRH)
16.8.2356327674777993305467029827040553.1	x^16 - x^15 + 52x^14 - 193x^13 - 223x^12 + 2279x^11 - 31773x^10 + 8184x^9 + 186871x^8 - 188533x^7 + 2009890x^6 + 742099x^5 - 15046663x^4 + 5401798x^3 + 23108071x^2 - 12535249x - 4070861	\( 61^{2}\cdot 97^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2]$ (GRH)
16.4.4003010667744610631429360934274392034057.4	x^16 - 4x^15 + 250x^14 - 421x^13 + 8969x^12 + 66321x^11 - 1139968x^10 + 8421507x^9 - 45091632x^8 + 114656041x^7 - 71808218x^6 - 620145820x^5 + 2803253366x^4 - 552382365x^3 - 7887221570x^2 - 1289438969x - 1711681339	\( 43^{6}\cdot 97^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2, 6, 6]$ (GRH)
16.4.6825950925050758427882178827125973556097.7	x^16 - 2x^15 + 14x^14 + 1269x^13 - 37712x^12 + 379060x^11 - 4073673x^10 + 15481249x^9 - 92090702x^8 + 80128862x^7 - 831919255x^6 - 1323459410x^5 + 25241662310x^4 + 52344317495x^3 + 541452941068x^2 + 553864288512x + 2220423519641	\( 47^{6}\cdot 97^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2, 2, 10]$ (GRH)
16.8.32625338328875805606560925727460997390073.5	x^16 - 2x^15 + 305x^14 - 2029x^13 - 63708x^12 + 133747x^11 - 1977115x^10 - 11521320x^9 + 64929697x^8 - 653861602x^7 + 4834485125x^6 + 17850285859x^5 - 42242950419x^4 - 45734794022x^3 - 1240783907555x^2 + 1087153097008x + 6042624679631	\( 61^{6}\cdot 97^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2, 4]$ (GRH)
16.8.706991024666918541719408792174287819307153.2	x^16 - 4x^15 - x^14 + 21x^13 - 26298x^12 + 60091x^11 - 365263x^10 + 1891798x^9 + 168854201x^8 - 277864511x^7 + 3402810507x^6 - 10149468346x^5 - 65890867646x^4 - 253210003245x^3 - 1915541871643x^2 - 2616854225292x - 863507151949	\( 17^{15}\cdot 89^{12} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2, 4]$ (GRH)
16.8.706991024666918541719408792174287819307153.3	x^16 - 8x^15 + 30x^14 - 70x^13 - 41872x^12 + 251778x^11 - 2342188x^10 + 9402260x^9 + 171044192x^8 - 737819626x^7 + 2958541378x^6 - 6256536692x^5 - 142014209188x^4 + 293577770820x^3 - 241662173554x^2 + 93956112739x - 10012855669	\( 17^{15}\cdot 89^{12} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2, 4]$ (GRH)
16.8.14014641336002292789493279203934745080101945089.1	x^16 - x^15 + 94x^14 - 2156x^13 - 39678x^12 - 67631x^11 + 1274883x^10 + 52941213x^9 + 363015846x^8 - 2252123415x^7 - 25151684794x^6 - 96196910865x^5 + 103874593488x^4 + 7056647500815x^3 + 19640886189987x^2 - 105017935194008x - 265429377926851	\( 37^{14}\cdot 41^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[8]$ (GRH)
16.8.14014641336002292789493279203934745080101945089.2	x^16 - x^15 + 94x^14 - 2156x^13 - 29059x^12 - 123760x^11 + 1863479x^10 + 41129851x^9 + 314500669x^8 - 858373597x^7 - 50306428611x^6 - 98834863124x^5 + 1753792080987x^4 + 7302425346538x^3 - 10440602463500x^2 - 127935155601144x - 225600707201264	\( 37^{14}\cdot 41^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[8]$ (GRH)
16.8.14014641336002292789493279203934745080101945089.3	x^16 - 8x^15 + 30x^14 - 70x^13 - 84459x^12 + 507300x^11 - 9169571x^10 + 41196890x^9 - 131779642x^8 + 285518672x^7 + 1858998781x^6 - 6408866240x^5 + 5420592940x^4 + 93759936x^3 - 1266360960x^2 + 115686400x + 77696000	\( 37^{14}\cdot 41^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[8]$ (GRH)
16.8.14014641336002292789493279203934745080101945089.4	x^16 - 8x^15 + 30x^14 - 70x^13 - 63221x^12 + 379872x^11 + 2532567x^10 - 16145710x^9 + 24934043x^8 + 1317824x^7 - 1253263249x^6 + 3683185606x^5 - 7240728990x^4 + 8378734076x^3 + 25665275297x^2 - 29246158068x + 8761246720	\( 37^{14}\cdot 41^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[8]$ (GRH)
16.8.80291031759964036646878404141998486437104406229473.1	x^16 - 8x^15 + 30x^14 - 70x^13 - 126158x^12 + 757494x^11 - 1225116x^10 - 818830x^9 + 663628006x^8 - 2641265466x^7 + 15713408910x^6 - 37907570302x^5 - 122390139278x^4 + 304883890488x^3 + 12774229580x^2 - 171094769281x + 55890105463	\( 37^{14}\cdot 73^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[8]$ (GRH)
16.8.80291031759964036646878404141998486437104406229473.2	x^16 - 4x^15 - 29x^14 + 119x^13 - 107320x^12 - 46787x^11 + 8593x^10 + 3398924x^9 + 2625021761x^8 - 3023072037x^7 - 53629386313x^6 + 232338128224x^5 - 3924866163908x^4 - 32893267183391x^3 - 53609796972279x^2 + 37731456819936x + 167287637065831	\( 37^{14}\cdot 73^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[8]$ (GRH)
16.8.80291031759964036646878404141998486437104406229473.3	x^16 - 4x^15 - 29x^14 + 119x^13 - 145134x^12 + 234117x^11 + 9329744x^10 + 67725940x^9 + 5939864526x^8 - 14853519562x^7 - 744609210817x^6 - 595121748833x^5 - 34266716442x^4 + 163951671539017x^3 + 1279771953158790x^2 - 8572126998875658x + 21318855083198401	\( 37^{14}\cdot 73^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[8]$ (GRH)
16.8.80291031759964036646878404141998486437104406229473.4	x^16 - 4x^15 - 29x^14 + 119x^13 - 185649x^12 + 1330723x^11 - 7413755x^10 + 134162437x^9 + 7467374561x^8 - 35610842313x^7 - 109039674744x^6 - 3976708155048x^5 - 75494837260791x^4 + 608115581856810x^3 + 2681157447026307x^2 - 18957448548520857x + 31014141249191103	\( 37^{14}\cdot 73^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[8]$ (GRH)
16.8.1680869644357963641125481571233506843563004905118353.1	x^16 - 7x^15 - 2205x^14 + 34778x^13 + 251441x^12 - 2431318x^11 + 838802231x^10 - 32204712967x^9 + 439598737165x^8 - 5536048330415x^7 + 69548060234944x^6 - 210196292452445x^5 - 3983226416739629x^4 + 41084287044150071x^3 - 204922171861025793x^2 + 784199220962810898x - 1512274356748426639	\( 61^{12}\cdot 97^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2, 2, 4]$ (GRH)
16.8.1680869644357963641125481571233506843563004905118353.3	x^16 - 3x^15 - 2248x^14 + 20785x^13 + 1485243x^12 - 21614001x^11 - 373958264x^10 + 8144026557x^9 + 15042335559x^8 - 78298872864x^7 + 3236328597138x^6 - 626802607944064x^5 + 4581066558613275x^4 + 111422777813856136x^3 - 1849537571150881115x^2 - 5596555580957524159x + 165600259875929075027	\( 61^{12}\cdot 97^{15} \)	$(C_2\times C_8).D_4$ (as 16T306)	$[2, 2, 20]$ (GRH)