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
16.8.81753664774171848863873.1	x^16 - 3x^15 - 8x^14 + 58x^13 - 72x^12 - 209x^11 + 729x^10 - 606x^9 - 953x^8 + 2757x^7 - 2253x^6 - 500x^5 + 2265x^4 - 1593x^3 + 325x^2 + 130x - 67	\( 13^{4}\cdot 17^{15} \)	$C_2^3.C_8$ (as 16T104)	Trivial (GRH)
16.8.187591757103747287810048.3	x^16 - 34x^12 + 187x^8 - 34x^6 - 255x^4 + 51x^2 + 17	\( 2^{16}\cdot 17^{15} \)	$C_2^3.C_8$ (as 16T104)	Trivial (GRH)
16.8.13967711378414469438602033.2	x^16 - 5x^15 + 25x^14 - 91x^13 + 183x^12 - 269x^11 - 882x^10 + 4002x^9 - 12071x^8 + 26355x^7 - 16226x^6 - 15464x^5 + 18449x^4 - 19451x^3 + 36514x^2 - 27904x + 6767	\( 17^{15}\cdot 47^{4} \)	$C_2^3.C_8$ (as 16T104)	Trivial (GRH)
16.0.20928938182187993309151488.1	x^16 - 3x^15 + 26x^14 - 61x^13 + 302x^12 - 481x^11 + 1800x^10 - 1694x^9 + 6221x^8 - 1408x^7 + 12724x^6 + 4447x^5 + 29261x^4 + 14047x^3 + 63157x^2 + 36221x + 38659	\( 2^{8}\cdot 13^{4}\cdot 17^{15} \)	$C_2^3.C_8$ (as 16T104)	$[2, 2, 50]$ (GRH)
16.16.20928938182187993309151488.1	x^16 - 5x^15 - 26x^14 + 164x^13 + 183x^12 - 2054x^11 + 546x^10 + 12026x^9 - 12139x^8 - 31190x^7 + 50618x^6 + 21443x^5 - 70291x^4 + 18850x^3 + 23458x^2 - 12808x + 1123	\( 2^{8}\cdot 13^{4}\cdot 17^{15} \)	$C_2^3.C_8$ (as 16T104)	Trivial (GRH)
16.8.57681033264163530732453953.4	x^16 - 3x^15 + 9x^14 + 24x^13 - 106x^12 - 243x^11 - 461x^10 + 4375x^9 - 4727x^8 - 4995x^7 + 30047x^6 - 70727x^5 + 97907x^4 - 53868x^3 - 44487x^2 + 42154x + 2381	\( 17^{15}\cdot 67^{4} \)	$C_2^3.C_8$ (as 16T104)	Trivial (GRH)
16.8.179594836941784276350012113.1	x^16 - 4x^15 + 16x^14 - 13x^13 - 305x^12 + 1526x^11 - 4710x^10 + 9235x^9 - 5745x^8 - 19350x^7 + 74102x^6 - 173243x^5 + 385986x^4 - 615472x^3 + 440486x^2 + 3302x - 98429	\( 17^{15}\cdot 89^{4} \)	$C_2^3.C_8$ (as 16T104)	Trivial (GRH)
16.0.3780184196000221150082102263808.1	x^16 + 153x^14 + 9146x^12 + 279905x^10 + 4752843x^8 + 44966581x^6 + 224207594x^4 + 506184129x^2 + 342569057	\( 2^{16}\cdot 17^{15}\cdot 67^{4} \)	$C_2^3.C_8$ (as 16T104)	$[2, 2, 2, 2, 2, 2228]$ (GRH)
16.16.3780184196000221150082102263808.1	x^16 - 153x^14 + 9146x^12 - 279905x^10 + 4752843x^8 - 44966581x^6 + 224207594x^4 - 506184129x^2 + 342569057	\( 2^{16}\cdot 17^{15}\cdot 67^{4} \)	$C_2^3.C_8$ (as 16T104)	Trivial (GRH)
16.8.66688975910627504451630153142433.2	x^16 - x^15 - 84x^14 + 526x^13 - 1461x^12 + 1070x^11 + 11918x^10 - 50814x^9 + 95150x^8 - 83318x^7 - 55402x^6 - 449804x^5 + 2075106x^4 - 1186125x^3 - 2215830x^2 + 2558448x + 1672427	\( 13^{12}\cdot 17^{15} \)	$C_2^3.C_8$ (as 16T104)	$[2, 4]$ (GRH)
16.8.4734759874359678578687627415368937.1	x^16 - 8x^15 + 30x^14 - 70x^13 - 598x^12 + 4134x^11 - 8498x^10 + 3880x^9 + 69102x^8 - 253070x^7 + 339220x^6 - 162276x^5 - 97045x^4 + 184874x^3 - 113712x^2 + 34036x - 4157	\( 3^{12}\cdot 73^{15} \)	$C_2^3.C_8$ (as 16T104)	Trivial (GRH)
16.8.9491566863962023381888433837890625.1	x^16 - 8x^15 + 30x^14 - 70x^13 - 450x^12 + 3246x^11 - 14558x^10 + 42320x^9 - 83050x^8 + 115130x^7 - 47368x^6 - 119996x^5 + 288595x^4 - 309070x^3 - 99740x^2 + 224988x - 55949	\( 5^{14}\cdot 41^{15} \)	$C_2^3.C_8$ (as 16T104)	$[8]$ (GRH)
16.8.9491566863962023381888433837890625.2	x^16 - 8x^15 + 30x^14 - 70x^13 - 450x^12 + 3246x^11 - 4308x^10 - 8930x^9 + 45690x^8 - 92330x^7 + 39962x^6 + 128874x^5 - 383805x^4 + 481410x^3 - 346560x^2 + 137248x - 16384	\( 5^{14}\cdot 41^{15} \)	$C_2^3.C_8$ (as 16T104)	$[8]$ (GRH)
16.8.2164959798672044689794137876838502993.1	x^16 - 4x^15 - 41x^14 - 130x^13 - 2186x^12 + 10546x^11 + 124718x^10 + 77955x^9 + 18509x^8 + 8606523x^7 + 27735607x^6 + 128700291x^5 + 1368635976x^4 + 4658216687x^3 + 3073249780x^2 - 7839808132x - 9179159021	\( 43^{4}\cdot 97^{15} \)	$C_2^3.C_8$ (as 16T104)	$[2, 2]$ (GRH)
16.8.3090063795858197568077038853384324833.3	x^16 - 3x^15 - 17x^14 - 652x^13 - 2640x^12 + 4292x^11 - 2603x^10 + 577894x^9 + 166968x^8 + 4917135x^7 + 4209376x^6 - 8766217x^5 + 15633220x^4 - 86630330x^3 - 10934242x^2 + 5095648x + 631471	\( 47^{4}\cdot 97^{15} \)	$C_2^3.C_8$ (as 16T104)	$[2, 2]$ (GRH)
16.8.8767895277848913089642817986417897713.1	x^16 - 6x^15 - 68x^14 - 75x^13 - 2082x^12 + 23660x^11 + 97345x^10 - 688528x^9 + 384199x^8 - 3788717x^7 + 3798904x^6 + 392424841x^5 + 341740386x^4 + 161939835x^3 - 7687245606x^2 + 6779883369x - 791777377	\( 61^{4}\cdot 97^{15} \)	$C_2^3.C_8$ (as 16T104)	$[4, 4]$ (GRH)
16.16.1062747667303462437668657811578369140625.1	x^16 - x^15 - 197x^14 - 102x^13 + 10926x^12 + 5579x^11 - 264375x^10 - 11771x^9 + 3149729x^8 - 1649977x^7 - 17580825x^6 + 17914002x^5 + 36131021x^4 - 53976394x^3 - 3024783x^2 + 29665257x - 10313939	\( 5^{14}\cdot 89^{15} \)	$C_2^3.C_8$ (as 16T104)	$[2, 2]$ (GRH)
16.0.1062747667303462437668657811578369140625.2	x^16 - 7x^15 + 48x^14 + 881x^13 - 2450x^12 + 4931x^11 + 110498x^10 - 129737x^9 + 410366x^8 - 600295x^7 - 997465x^6 + 3926065x^5 - 3011335x^4 + 6342040x^3 - 657200x^2 - 20284665x + 22137835	\( 5^{14}\cdot 89^{15} \)	$C_2^3.C_8$ (as 16T104)	$[4, 25876]$ (GRH)
16.8.706991024666918541719408792174287819307153.1	x^16 - x^15 + 188x^14 + 7377x^13 - 17594x^12 - 1381795x^11 - 5293289x^10 + 69162204x^9 + 480433550x^8 - 1037559794x^7 - 13587856083x^6 + 10794765535x^5 + 255680761873x^4 - 71370632807x^3 - 3911934284598x^2 - 8682678868227x - 5465405110997	\( 17^{15}\cdot 89^{12} \)	$C_2^3.C_8$ (as 16T104)	$[2, 4]$ (GRH)
16.8.19719055677142144882125300632796548005703977.1	x^16 - 8x^15 + 30x^14 - 70x^13 - 32134x^12 + 193350x^11 - 2198790x^10 + 9220860x^9 - 10053370x^8 - 12983686x^7 + 814005396x^6 - 2359973708x^5 - 3456857577x^4 + 10814479334x^3 - 15509537492x^2 + 9713737864x - 823982021	\( 19^{12}\cdot 73^{15} \)	$C_2^3.C_8$ (as 16T104)	Trivial (GRH)
16.8.62141154520506997217088824525941184562505001.1	x^16 - 8x^15 + 30x^14 - 70x^13 - 28535x^12 + 171756x^11 - 1363335x^10 + 5241530x^9 + 96731439x^8 - 416484476x^7 + 5419873627x^6 - 14781801288x^5 - 10127121036x^4 + 44395141190x^3 - 2031620275545x^2 + 2007029914720x + 8241104367689	\( 41^{15}\cdot 43^{12} \)	$C_2^3.C_8$ (as 16T104)	Trivial (GRH)
16.8.195243657193163639221629075064503172225659097.1	x^16 - 4x^15 - 29x^14 - 1560x^13 - 49358x^12 + 43368x^11 - 2592178x^10 - 4534424x^9 + 83558589x^8 + 499725828x^7 + 5448645279x^6 + 40146705456x^5 + 206054540288x^4 + 621629449624x^3 + 721476532032x^2 - 243288205952x - 716371879936	\( 23^{12}\cdot 73^{15} \)	$C_2^3.C_8$ (as 16T104)	Trivial (GRH)
16.8.5600075906386661768959437042812533816731958913.1	x^16 - x^15 - 662x^14 + 2719x^13 + 78065x^12 - 715973x^11 + 10413130x^10 - 41911767x^9 - 1159905613x^8 + 7553415536x^7 + 37089111838x^6 - 393273090724x^5 + 493775735297x^4 + 3751528448186x^3 - 13423616432713x^2 + 14170208488667x - 4125171948377	\( 17^{15}\cdot 89^{14} \)	$C_2^3.C_8$ (as 16T104)	$[2, 8]$ (GRH)
16.8.5600075906386661768959437042812533816731958913.2	x^16 - x^15 - 662x^14 - 9385x^13 - 65670x^12 - 687226x^11 - 5633748x^10 - 20006553x^9 - 345111236x^8 - 5406999958x^7 - 28256937548x^6 + 9956127740x^5 + 670089369972x^4 + 2925833801882x^3 + 6158845500328x^2 + 7013223282254x + 3596679729757	\( 17^{15}\cdot 89^{14} \)	$C_2^3.C_8$ (as 16T104)	$[2, 8]$ (GRH)
16.16.15359445630083788418852698524374845584773320185041.1	x^16 - 5x^15 - 1709x^14 + 5733x^13 + 1025838x^12 - 2578770x^11 - 260470219x^10 + 537783345x^9 + 27172084547x^8 - 27058405023x^7 - 1122845915066x^6 + 475008820192x^5 + 14316222629824x^4 - 14649824518528x^3 - 10929645040640x^2 + 7374113275904x + 3477032665088	\( 41^{15}\cdot 61^{14} \)	$C_2^3.C_8$ (as 16T104)	$[2, 2]$ (GRH)
16.0.15359445630083788418852698524374845584773320185041.6	x^16 - 3x^15 - 466x^14 + 8167x^13 + 204662x^12 + 89446x^11 + 26545517x^10 + 1241998870x^9 + 20144084946x^8 + 243389781077x^7 + 2107575937554x^6 + 12621694069014x^5 + 82741220348795x^4 - 276270386009564x^3 + 2766467958123332x^2 - 3706153303430478x + 1463534766472091	\( 41^{15}\cdot 61^{14} \)	$C_2^3.C_8$ (as 16T104)	$[4, 11975140]$ (GRH)
16.8.20231328175647090122615673426308895930590180621609.1	x^16 - 4x^15 - 37x^14 - 4036x^13 - 186046x^12 + 1318432x^11 + 19436086x^10 + 195916584x^9 + 5460971989x^8 - 61011866388x^7 - 252544335297x^6 + 2645214889372x^5 - 53240095283656x^4 + 27704092920824x^3 + 178672951198304x^2 - 2193741464668160x - 3108481636851712	\( 47^{12}\cdot 89^{15} \)	$C_2^3.C_8$ (as 16T104)	Trivial (GRH)
16.8.72902183182742832065008845132818265359946436492777.1	x^16 - 8x^15 + 30x^14 - 70x^13 - 348370x^12 + 2090766x^11 - 41550754x^10 + 188587700x^9 + 5889687494x^8 - 24667276606x^7 + 758427128184x^6 - 2188176847700x^5 - 2945197729257x^4 + 9508212706382x^3 - 1164602131361688x^2 + 1159487494913896x + 513540167205851	\( 67^{12}\cdot 73^{15} \)	$C_2^3.C_8$ (as 16T104)	Trivial (GRH)
16.8.526463173424807410745021702403427128295303807818937.1	x^16 - 4x^15 - 29x^14 + 5886x^13 - 850971x^12 + 2780x^11 + 204791405x^10 - 41499142x^9 + 61421290143x^8 - 7995133208x^7 - 12918699536515x^6 - 45621986975278x^5 - 2108604337447076x^4 - 386139934252072x^3 + 266577755600244992x^2 + 1432339139767432576x + 20138270326434543616	\( 73^{15}\cdot 79^{12} \)	$C_2^3.C_8$ (as 16T104)	Trivial (GRH)
16.8.1680869644357963641125481571233506843563004905118353.2	x^16 - 4x^15 - 41x^14 - 11673x^13 - 454109x^12 + 2184995x^11 + 78893665x^10 + 3434567043x^9 + 57917196094x^8 - 481785086219x^7 - 12675582312061x^6 - 202418022839255x^5 - 1423478158368283x^4 + 18985774070078141x^3 + 250647316750174834x^2 + 1331571217615502528x + 4011939306776803313	\( 61^{12}\cdot 97^{15} \)	$C_2^3.C_8$ (as 16T104)	$[2, 2, 4]$ (GRH)
16.8.2857263440495560367103411585720766893299521110665609.1	x^16 - 4x^15 - 37x^14 - 6172x^13 - 527806x^12 + 1651648x^11 - 61310410x^10 + 688001144x^9 + 37964908341x^8 - 460309412308x^7 + 4828308042143x^6 - 15136486766876x^5 - 98143453715880x^4 + 844893035355224x^3 - 2797368182141824x^2 + 1561832763993728x + 1333629299617792	\( 71^{12}\cdot 89^{15} \)	$C_2^3.C_8$ (as 16T104)	Trivial (GRH)
16.8.13854815685101981032101054249860279864869741101695057.1	x^16 - 7x^15 - 1380x^14 + 4314x^13 + 668694x^12 - 280415x^11 - 196778428x^10 - 1081392193x^9 + 37182839562x^8 + 640346059654x^7 - 1039599254791x^6 - 124062279034770x^5 - 848384823179655x^4 + 5872021418457196x^3 + 83906088161932922x^2 + 210034438044426092x - 261511764516720983	\( 41^{15}\cdot 73^{15} \)	$C_2^3.C_8$ (as 16T104)	$[48]$ (GRH)
16.8.13854815685101981032101054249860279864869741101695057.2	x^16 - 8x^15 + 30x^14 - 70x^13 - 433123x^12 + 2599284x^11 - 64876517x^10 + 300555100x^9 - 39325421x^8 - 1617435648x^7 + 99309516517x^6 - 291033786670x^5 - 420732794356x^4 + 1324048078030x^3 - 8192417846781x^2 + 7482245749632x + 11036826128683	\( 41^{15}\cdot 73^{15} \)	$C_2^3.C_8$ (as 16T104)	$[48]$ (GRH)
16.8.13854815685101981032101054249860279864869741101695057.3	x^16 - 125706x^12 - 8613854x^10 + 4061186735x^8 + 450184977646x^6 - 11542208172049x^4 - 1507021151328107x^2 + 10792143313968857	\( 41^{15}\cdot 73^{15} \)	$C_2^3.C_8$ (as 16T104)	$[48]$ (GRH)
16.8.13854815685101981032101054249860279864869741101695057.4	x^16 - x^15 + 94x^14 + 6208x^13 - 246687x^12 - 145121x^11 - 10993465x^10 - 1114369992x^9 + 15068632831x^8 - 1048567964x^7 - 404880849047x^6 + 40524218769108x^5 - 238409158886151x^4 - 1546925722655262x^3 + 7605509253401021x^2 + 28165196463819167x + 20617776290452519	\( 41^{15}\cdot 73^{15} \)	$C_2^3.C_8$ (as 16T104)	$[48]$ (GRH)
16.8.87995526059768479187762363921103601182604493355285937.1	x^16 - 4x^15 - 29x^14 + 9025x^13 - 564592x^12 + 600723x^11 + 106534135x^10 - 2295493716x^9 + 41697009299x^8 + 210269586483x^7 - 8329715762855x^6 + 42632626532812x^5 - 69676368352736x^4 - 258874459402297x^3 + 945131876919130x^2 - 148420382825981x - 2223621705617209	\( 61^{14}\cdot 73^{15} \)	$C_2^3.C_8$ (as 16T104)	$[8]$ (GRH)
16.8.87995526059768479187762363921103601182604493355285937.2	x^16 - 4x^15 - 29x^14 - 8787x^13 - 466626x^12 + 2577855x^11 + 104450131x^10 + 1646275166x^9 + 21202851621x^8 - 374714718069x^7 - 7222778406903x^6 - 23859158339510x^5 + 192307300221262x^4 + 4255857054532135x^3 + 29656924089445914x^2 + 79631144220170561x + 97623421972208003	\( 61^{14}\cdot 73^{15} \)	$C_2^3.C_8$ (as 16T104)	$[8]$ (GRH)
16.8.240277040497518512877081049134097240815202879947452081.1	x^16 - 4x^15 - 37x^14 + 9581x^13 - 621434x^12 + 3159219x^11 - 122064213x^10 - 1318149458x^9 + 17745867159x^8 - 185731157449x^7 + 1070375916313x^6 + 8721064590146x^5 - 22238144524836x^4 + 153070746965979x^3 + 852542410999822x^2 + 263445165203961x - 1115465623645375	\( 53^{14}\cdot 89^{15} \)	$C_2^3.C_8$ (as 16T104)	$[8]$ (GRH)
16.8.240277040497518512877081049134097240815202879947452081.2	x^16 - 4x^15 - 37x^14 - 9287x^13 - 489358x^12 + 2895067x^11 + 123682053x^10 + 1561814892x^9 + 21247871733x^8 - 299097667517x^7 - 4577780534713x^6 - 6633762668540x^5 + 145824602336670x^4 + 1096700690244239x^3 + 3639176903823396x^2 + 5963757538824515x + 3903857622444659	\( 53^{14}\cdot 89^{15} \)	$C_2^3.C_8$ (as 16T104)	$[8]$ (GRH)