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 46 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.88230205055486500383227904.1	x^16 + 48x^14 + 588x^12 + 2592x^10 + 4068x^8 + 2736x^6 + 900x^4 + 144x^2 + 9	\( 2^{64}\cdot 3^{14} \)	$C_8.C_4$ (as 16T49)	$[82]$ (GRH)
16.16.88230205055486500383227904.1	x^16 - 48x^14 + 588x^12 - 2592x^10 + 4068x^8 - 2736x^6 + 900x^4 - 144x^2 + 9	\( 2^{64}\cdot 3^{14} \)	$C_8.C_4$ (as 16T49)	Trivial (GRH)
16.8.88230205055486500383227904.3	x^16 - 180x^12 - 96x^10 + 1764x^8 + 2016x^6 + 324x^4 - 144x^2 + 9	\( 2^{64}\cdot 3^{14} \)	$C_8.C_4$ (as 16T49)	Trivial (GRH)
16.8.88230205055486500383227904.4	x^16 - 180x^12 + 96x^10 + 1764x^8 - 2016x^6 + 324x^4 + 144x^2 + 9	\( 2^{64}\cdot 3^{14} \)	$C_8.C_4$ (as 16T49)	Trivial (GRH)
16.0.19799315994393973883056640625.1	x^16 - 6x^15 + 53x^14 - 147x^13 + 616x^12 - 966x^11 + 5180x^10 - 13866x^9 + 38704x^8 - 60987x^7 + 64505x^6 - 455553x^5 + 629776x^4 - 425649x^3 + 932012x^2 + 80847x + 42331	\( 3^{14}\cdot 5^{14}\cdot 7^{14} \)	$C_8.C_4$ (as 16T49)	$[2, 6, 12]$ (GRH)
16.16.19799315994393973883056640625.1	x^16 - 6x^15 - 52x^14 + 273x^13 + 1246x^12 - 4431x^11 - 17815x^10 + 28449x^9 + 142864x^8 - 20247x^7 - 533260x^6 - 388458x^5 + 679966x^4 + 995106x^3 + 122987x^2 - 364563x - 149609	\( 3^{14}\cdot 5^{14}\cdot 7^{14} \)	$C_8.C_4$ (as 16T49)	$[2]$ (GRH)
16.16.1816151322484127584722900390625.1	x^16 - 7x^15 - 37x^14 + 351x^13 + 165x^12 - 5994x^11 + 6508x^10 + 42278x^9 - 81859x^8 - 120715x^7 + 358055x^6 + 66660x^5 - 657550x^4 + 249570x^3 + 412000x^2 - 305460x + 36605	\( 5^{14}\cdot 29^{14} \)	$C_8.C_4$ (as 16T49)	$[2]$ (GRH)
16.0.1816151322484127584722900390625.3	x^16 - 5x^15 + 23x^14 - 20x^13 + 218x^12 - 520x^11 + 2936x^10 - 85x^9 + 19125x^8 - 4545x^7 + 114546x^6 + 83880x^5 + 798933x^4 + 836180x^3 + 2107098x^2 + 1340385x + 957431	\( 5^{14}\cdot 29^{14} \)	$C_8.C_4$ (as 16T49)	$[2, 2, 164]$ (GRH)
16.8.231501630828342033704595947265625.2	x^16 - 2x^15 - 57x^14 + 166x^13 + 1000x^12 - 4679x^11 - 12232x^10 + 101483x^9 - 54879x^8 - 1396365x^7 + 5011730x^6 - 6772345x^5 + 2304100x^4 + 3221670x^3 - 3142655x^2 + 796850x - 50455	\( 5^{14}\cdot 41^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.231501630828342033704595947265625.3	x^16 - 2x^15 - 57x^14 + 166x^13 + 1205x^12 - 2219x^11 - 15512x^10 - 12497x^9 + 138641x^8 + 39660x^7 - 996205x^6 + 3584050x^5 + 8988535x^4 - 7132265x^3 - 15247495x^2 + 500420x + 1115995	\( 5^{14}\cdot 41^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.662966878170355779548558581239481.1	x^16 - 3x^15 + 24x^14 - 230x^13 + 1237x^12 + 2043x^11 + 279x^10 - 73306x^9 - 762393x^8 + 1865554x^7 + 4370455x^6 - 293238x^5 + 22835637x^4 - 116506574x^3 - 3454475x^2 + 105429551x - 11550751	\( 13^{14}\cdot 17^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.662966878170355779548558581239481.2	x^16 - 4x^15 - x^14 + 21x^13 - 424x^12 + 2767x^11 - 5645x^10 - 6762x^9 + 78779x^8 - 326727x^7 + 1031729x^6 - 2463602x^5 + 3719006x^4 - 2537101x^3 - 811071x^2 + 2329344x - 1021019	\( 13^{14}\cdot 17^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.662966878170355779548558581239481.3	x^16 - 6x^15 - 40x^14 + 200x^13 - 13x^12 + 3887x^11 - 38363x^10 + 110448x^9 + 2743x^8 - 478075x^7 + 351039x^6 + 846560x^5 + 41314x^4 - 742224x^3 - 495964x^2 + 238045x + 216037	\( 13^{14}\cdot 17^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.662966878170355779548558581239481.4	x^16 - 2x^15 - 55x^14 - 164x^13 + 1586x^12 + 7111x^11 - 13169x^10 - 111033x^9 - 214461x^8 - 84916x^7 + 846586x^6 + 4107675x^5 + 11276590x^4 + 19008036x^3 + 18151962x^2 + 8356311x + 1214071	\( 13^{14}\cdot 17^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.16.45259126231720831581016789061101452813693889.1	x^16 - 3x^15 - 536x^14 + 1240x^13 + 102277x^12 - 251544x^11 - 9100211x^10 + 25863349x^9 + 396034194x^8 - 1291290002x^7 - 7676264155x^6 + 27899474246x^5 + 46801723935x^4 - 185786927618x^3 - 58277636264x^2 + 285507154591x + 61589352119	\( 13^{14}\cdot 101^{14} \)	$C_8.C_4$ (as 16T49)	$[2]$ (GRH)
16.0.45259126231720831581016789061101452813693889.2	x^16 - x^15 + 120x^14 - 2105x^13 + 123x^12 - 251782x^11 + 677985x^10 - 4367626x^9 + 178861490x^8 + 422045666x^7 + 9472812670x^6 + 9793290973x^5 + 142759809978x^4 - 653503073861x^3 + 2727122691361x^2 - 17032173590210x + 30833678218877	\( 13^{14}\cdot 101^{14} \)	$C_8.C_4$ (as 16T49)	$[2, 2, 1824964]$ (GRH)
16.8.341820520390299824133982419608164514148827929.1	x^16 - 3x^15 + 144x^14 - 4412x^13 - 65432x^12 - 728094x^11 - 1657428x^10 + 100353656x^9 + 999608855x^8 + 5120653975x^7 - 14134091903x^6 - 388988455119x^5 - 1924503835524x^4 - 2927083507477x^3 + 6015138745506x^2 + 20205755303303x - 13163633135399	\( 37^{14}\cdot 41^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.341820520390299824133982419608164514148827929.2	x^16 - 4x^15 - 13x^14 + 63x^13 - 7321x^12 + 59103x^11 - 115080x^10 - 772381x^9 + 10492820x^8 - 29022674x^7 - 5402229x^6 + 113723601x^5 - 384839693x^4 + 1250599119x^3 - 10796424454x^2 + 23032733237x + 3644035361	\( 37^{14}\cdot 41^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.341820520390299824133982419608164514148827929.3	x^16 - 389x^14 - 6068x^13 - 191213x^12 - 2073739x^11 - 14781949x^10 - 92178988x^9 - 31765557x^8 + 1085395296x^7 - 2811627137x^6 - 1928515073x^5 + 43477867525x^4 - 24006418810x^3 - 151944870564x^2 + 74815544047x + 180850298131	\( 37^{14}\cdot 41^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.341820520390299824133982419608164514148827929.4	x^16 - x^15 + 130x^14 + 6156x^13 - 80382x^12 + 866668x^11 - 1885874x^10 - 108427352x^9 + 1612862067x^8 - 14155155281x^7 + 69586907661x^6 - 108889517130x^5 - 380843328948x^4 + 2008596388551x^3 - 1937686049708x^2 - 7126041807578x + 1513355408767	\( 37^{14}\cdot 41^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.16.84693947642368239934810426203628826170679406001.1	x^16 - x^15 - 919x^14 + 330x^13 + 333504x^12 + 207407x^11 - 62605754x^10 - 104127446x^9 + 6520100240x^8 + 17009155785x^7 - 369548628666x^6 - 1243559750672x^5 + 10246556574051x^4 + 39953039198538x^3 - 102338147908928x^2 - 451442241263186x - 151797202614301	\( 13^{14}\cdot 173^{14} \)	$C_8.C_4$ (as 16T49)	$[5, 10]$ (GRH)
16.0.84693947642368239934810426203628826170679406001.3	x^16 - 3x^15 + 206x^14 + 2682x^13 + 7659x^12 + 676587x^11 - 1062900x^10 + 25016421x^9 + 568783688x^8 - 11274491499x^7 + 115359230062x^6 - 1299529050323x^5 + 10084531101885x^4 - 50798315471152x^3 + 386408516466130x^2 - 776582504211170x + 5843269449320273	\( 13^{14}\cdot 173^{14} \)	$C_8.C_4$ (as 16T49)	$[2, 10, 34439060]$ (GRH)
16.8.1099877147396767625299704166328746389549375427801.1	x^16 - 2x^15 - 701x^14 - 628x^13 + 252311x^12 + 661327x^11 - 85402450x^10 + 456652722x^9 + 9389893780x^8 - 95757847887x^7 + 53744166666x^6 - 1698734028116x^5 + 51666615448253x^4 - 246602526605672x^3 - 165474707995824x^2 + 3450107191595130x - 6139708248207609	\( 37^{14}\cdot 73^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.1099877147396767625299704166328746389549375427801.2	x^16 - 4x^15 - 29x^14 + 119x^13 - 18187x^12 + 23439x^11 - 331733x^10 - 5090319x^9 + 95292171x^8 - 177168789x^7 - 282326958x^6 + 20777765544x^5 - 93063891411x^4 - 221952921930x^3 + 259076011275x^2 + 2244417237747x + 550007954217	\( 37^{14}\cdot 73^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.1099877147396767625299704166328746389549375427801.3	x^16 - 6x^15 - 663x^14 + 6072x^13 - 138630x^12 + 6385537x^11 - 6123213x^10 - 1683482107x^9 + 4616835965x^8 + 307874361192x^7 - 2707188392044x^6 - 12394664061501x^5 + 320379262260514x^4 - 2174612665157564x^3 + 7438959624205646x^2 - 13129043796800163x + 9516392527011651	\( 37^{14}\cdot 73^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.1099877147396767625299704166328746389549375427801.4	x^16 - 2x^15 - 678x^14 + 8110x^13 + 176560x^12 - 5072721x^11 - 62583259x^10 + 1268065652x^9 + 21309733002x^8 - 154648818706x^7 - 2677277154937x^6 + 6006374183562x^5 + 143362781560899x^4 - 409151283885081x^3 - 6759690646580883x^2 + 21965648393476953x + 221064824525695641	\( 37^{14}\cdot 73^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.16.9943583883093737930218051237711077235104795837841.1	x^16 - x^15 - 1288x^14 - 16925x^13 + 265395x^12 + 6325863x^11 + 7509025x^10 - 662101208x^9 - 4489506330x^8 + 16087587618x^7 + 256010445822x^6 + 389263434099x^5 - 4693197033536x^4 - 18212997720900x^3 + 14395417397350x^2 + 163997627966411x + 208148520549407	\( 29^{14}\cdot 109^{14} \)	$C_8.C_4$ (as 16T49)	$[2]$ (GRH)
16.0.9943583883093737930218051237711077235104795837841.5	x^16 - 3x^15 + 289x^14 - 5715x^13 + 198068x^12 - 2405520x^11 + 20097237x^10 + 16350756x^9 - 1447386238x^8 + 13050043542x^7 + 253622592936x^6 - 3906739562893x^5 + 49584050475435x^4 - 337409531350162x^3 + 1555861018641102x^2 - 3935185278274183x + 5698054976725061	\( 29^{14}\cdot 109^{14} \)	$C_8.C_4$ (as 16T49)	$[2, 2, 29636612]$ (GRH)
16.8.1205418165202307934078936492069912344967184840483369.1	x^16 - 2x^15 - 1151x^14 + 16767x^13 + 649621x^12 - 18427412x^11 - 177549808x^10 + 9762162282x^9 - 33442665892x^8 - 2778720508658x^7 + 31617335805990x^6 + 426501635882804x^5 - 6666671433405269x^4 - 34592170126209414x^3 + 593366179212502821x^2 + 1049166479823709608x - 18530020609680400767	\( 61^{14}\cdot 73^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.1205418165202307934078936492069912344967184840483369.3	x^16 - 67x^14 - 8906x^13 - 243786x^12 + 418582x^11 + 34740094x^10 + 1097370602x^9 + 15244519653x^8 - 62119510308x^7 - 2434234654366x^6 - 33456378639173x^5 - 146350495119186x^4 + 2670926156166982x^3 + 20824625479139251x^2 + 57598242321428699x + 485904167550453131	\( 61^{14}\cdot 73^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.2699742028062005762663832012742665627137111010645529.1	x^16 - 2x^15 - 1215x^14 + 5961x^13 + 471345x^12 - 18245116x^11 - 714832698x^10 - 8455181166x^9 - 17719251843x^8 + 1043907848018x^7 + 20752520925940x^6 + 185632816258606x^5 + 1367334826234034x^4 + 16479084532307579x^3 + 119340689913643006x^2 + 247314848830313952x - 90570842522372189	\( 53^{14}\cdot 89^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.2699742028062005762663832012742665627137111010645529.2	x^16 - 4x^15 - 37x^14 + 147x^13 - 93130x^12 - 604947x^11 + 2379681x^10 + 30799334x^9 + 83871983x^8 - 43358097x^7 - 391932779x^6 + 1360249204x^5 + 9655116950x^4 + 20571597915x^3 + 17514522367x^2 + 2572687806x - 1766411567	\( 53^{14}\cdot 89^{14} \)	$C_8.C_4$ (as 16T49)	$[3, 12]$ (GRH)
16.8.9008789808170658548806656862365268212872206896031561.1	x^16 - 1304x^14 - 10282x^13 + 1114084x^12 + 13402587x^11 - 618113010x^10 - 14840411598x^9 + 135910932348x^8 + 6818143175898x^7 + 15967753823857x^6 - 915313131098278x^5 - 2974204871463126x^4 + 54988959641645836x^3 + 149332680084096920x^2 - 946683758562289055x - 2821473341718922999	\( 53^{14}\cdot 97^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.9008789808170658548806656862365268212872206896031561.3	x^16 - 4x^15 - 41x^14 + 161x^13 - 404736x^12 - 1484709x^11 - 13645887x^10 - 139487100x^9 + 43904988053x^8 + 345679229513x^7 + 3340517012461x^6 + 18731643146726x^5 - 1430607533707472x^4 - 12848087213470847x^3 - 30969923082952135x^2 - 11643515053935122x + 26882036630663087	\( 53^{14}\cdot 97^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.64479545841814254728122854912988442937092177855107129.1	x^16 - 4x^15 - 23x^14 + 98x^13 - 1000472x^12 - 4647376x^11 + 2357862x^10 + 18163842x^9 + 10642508325x^8 - 19389915190x^7 - 130866147686x^6 + 878429017229x^5 - 2180629500814x^4 - 16295183935748x^3 - 13035184353877x^2 + 16445814982743x + 15827972949927	\( 61^{14}\cdot 97^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.64479545841814254728122854912988442937092177855107129.2	x^16 - 4x^15 - 41x^14 + 161x^13 - 57670x^12 - 252809x^11 - 2417749x^10 - 26801036x^9 + 498030477x^8 + 2903909665x^7 + 37856782679x^6 + 250305707770x^5 - 1689580081024x^4 - 14946713792227x^3 - 23777866905041x^2 + 23287671874118x + 59045036290459	\( 61^{14}\cdot 97^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.64479545841814254728122854912988442937092177855107129.3	x^16 - 4x^15 - 23x^14 + 98x^13 - 840713x^12 - 3901834x^11 - 7269097x^10 - 72342590x^9 + 15836693522x^8 + 100014470272x^7 + 588540102377x^6 + 3620444460103x^5 - 77387700251526x^4 - 528998767606638x^3 + 72859130170740x^2 + 3402687025817982x + 8634653323364421	\( 61^{14}\cdot 97^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.8.64479545841814254728122854912988442937092177855107129.4	x^16 - 3x^15 + 554x^14 - 7595x^13 - 557765x^12 - 21555312x^11 - 964537235x^10 - 17203793113x^9 - 201693621442x^8 + 2693259145663x^7 + 174686723625779x^6 + 3073967109999834x^5 + 36797324745255904x^4 + 194886203868804103x^3 - 1617614637177574531x^2 - 13771872983608380722x + 22791644861288076339	\( 61^{14}\cdot 97^{14} \)	$C_8.C_4$ (as 16T49)	$[4]$ (GRH)
16.16.193851685179255766530952003996759265201819225743449601.1	x^16 - 3x^15 - 2612x^14 + 7614x^13 + 2419205x^12 - 6535626x^11 - 935790958x^10 + 2176523968x^9 + 134048526390x^8 - 227735489612x^7 - 5858782940122x^6 + 18413561633240x^5 + 51593522344722x^4 - 277710740400021x^3 + 323798927354430x^2 - 54447078181100x - 1273986283439	\( 37^{14}\cdot 173^{14} \)	$C_8.C_4$ (as 16T49)	$[3, 3, 6]$ (GRH)
16.0.193851685179255766530952003996759265201819225743449601.5	x^16 - x^15 + 594x^14 + 2531x^13 + 47690x^12 - 5352141x^11 + 51739983x^10 + 192556636x^9 + 5083665532x^8 + 450226956190x^7 + 941787543275x^6 - 77428720044109x^5 - 764954674399913x^4 - 18683145716368537x^3 - 73879184588145834x^2 + 2427071999215910603x + 33380320760954558557	\( 37^{14}\cdot 173^{14} \)	$C_8.C_4$ (as 16T49)	$[6, 6, 1682050764]$ (GRH)
16.16.330056782202198660511172839698929216685213271046904401.1	x^16 - x^15 - 2706x^14 - 2359x^13 + 2824784x^12 + 6908002x^11 - 1451756694x^10 - 5433619055x^9 + 386060968586x^8 + 1889662834916x^7 - 49913000623296x^6 - 306922160402116x^5 + 2304642596194550x^4 + 18952504528520578x^3 + 27327366661749576x^2 - 19832907564347600x - 20956414760060291	\( 61^{14}\cdot 109^{14} \)	$C_8.C_4$ (as 16T49)	$[2]$ (GRH)
16.0.330056782202198660511172839698929216685213271046904401.4	x^16 - 3x^15 + 607x^14 - 12027x^13 + 323884x^12 + 4998536x^11 + 141652975x^10 + 1065246568x^9 - 16715660403x^8 + 245536064601x^7 + 24334833783094x^6 + 32537334329978x^5 + 301979753790703x^4 - 20341549562763644x^3 + 11150815222856179x^2 + 792523107994436141x + 7082452187739053435	\( 61^{14}\cdot 109^{14} \)	$C_8.C_4$ (as 16T49)	$[2, 2, 552275524]$ (GRH)
16.16.3668342962637889127310596327197122046055622675946369169.1	x^16 - 5x^15 - 3216x^14 - 16435x^13 + 3533194x^12 + 46612678x^11 - 1379884912x^10 - 28799442787x^9 + 94978012812x^8 + 5365653798128x^7 + 26357066282862x^6 - 153750994966120x^5 - 1057291387991512x^4 + 1776491162706154x^3 + 10306247757699384x^2 - 5002354276372688x - 25609000866480631	\( 53^{14}\cdot 149^{14} \)	$C_8.C_4$ (as 16T49)	$[2]$ (GRH)
16.0.3668342962637889127310596327197122046055622675946369169.4	x^16 - 7x^15 + 757x^14 + 17359x^13 + 505614x^12 + 12895156x^11 + 211899620x^10 + 7541456698x^9 - 1389972933x^8 + 1240781089975x^7 + 4371887866584x^6 - 55659562317467x^5 + 4297633387795179x^4 - 111896064809531971x^3 + 2220052595158974387x^2 - 20096776454760585706x + 78442230270956678147	\( 53^{14}\cdot 149^{14} \)	$C_8.C_4$ (as 16T49)	$[3, 6, 630, 1533420]$ (GRH)
16.16.26255811630589850827051927649928110197766220114319683841.1	x^16 - 7x^15 - 3676x^14 + 19982x^13 + 5392416x^12 - 23875039x^11 - 4058995913x^10 + 16436844988x^9 + 1683967369007x^8 - 7299192869405x^7 - 382817796251067x^6 + 2024106400885404x^5 + 43382677650078083x^4 - 300399178945081685x^3 - 1649219797768775897x^2 + 17337036358118728404x - 35542411485577782059	\( 61^{14}\cdot 149^{14} \)	$C_8.C_4$ (as 16T49)	$[2]$ (GRH)
16.0.26255811630589850827051927649928110197766220114319683841.3	x^16 - 5x^15 + 842x^14 + 28801x^13 + 657498x^12 + 7456671x^11 + 818111467x^10 - 3212165856x^9 + 356585283872x^8 - 4376626157712x^7 + 171426115905879x^6 - 1827680235740115x^5 + 32436664122096987x^4 - 268920195666810337x^3 + 2883739495205635060x^2 - 14238289298038957907x + 42985739425875246071	\( 61^{14}\cdot 149^{14} \)	$C_8.C_4$ (as 16T49)	$[2, 2, 2028971972]$ (GRH)