Global number field search results

Further refine search

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 314)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.145220537353515625.2	x^16 - 3x^15 + 5x^14 - 2x^13 - x^12 + 6x^11 + 4x^10 - 9x^9 + 26x^8 - 12x^7 + 6x^6 + 12x^5 + 4x^4 - 6x^3 + 5x^2 + 4x + 1	\( 5^{12}\cdot 29^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	Trivial
16.0.28992335455322265625.3	x^16 - 5x^15 + 2x^14 + 25x^13 - 27x^12 - 45x^11 + 34x^10 + 530x^8 - 1305x^7 + 904x^6 + 465x^5 - 1027x^4 + 435x^3 + 207x^2 - 270x + 81	\( 5^{14}\cdot 41^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2]$
16.0.121333322988525390625.2	x^16 - x^15 + x^14 + 2x^13 - 9x^12 + 12x^11 - 20x^9 + 57x^8 - 40x^7 + 96x^5 - 144x^4 + 64x^3 + 64x^2 - 128x + 256	\( 5^{12}\cdot 89^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	Trivial
16.0.259160193017822265625.6	x^16 - 3x^15 + 15x^14 - 40x^13 + 101x^12 - 200x^11 + 246x^10 - 275x^9 + 11x^8 + 80x^7 - 75x^6 + 133x^5 + 416x^4 + 505x^3 + 315x^2 + 100x + 25	\( 5^{12}\cdot 101^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2]$
16.0.314455409918212890625.4	x^16 - 3x^15 - 3x^14 - 9x^13 + 91x^12 + 2x^11 - 285x^10 - 227x^9 + 544x^8 + 764x^7 - 305x^6 - 1006x^5 + 151x^4 + 698x^3 - 102x^2 - 311x + 121	\( 5^{14}\cdot 61^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2]$
16.8.952791945576416015625.3	x^16 - 2x^15 - 15x^14 + 12x^13 + 114x^12 + 14x^11 - 546x^10 - 206x^9 + 1196x^8 + 477x^7 - 964x^6 - 292x^5 + 229x^4 + 26x^3 - 15x^2 + x + 1	\( 3^{8}\cdot 5^{12}\cdot 29^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	Trivial (GRH)
16.8.952791945576416015625.4	x^16 - 2x^15 - 9x^14 + 11x^13 + 33x^12 + 21x^11 - 117x^10 - 126x^9 + 206x^8 + 59x^7 + 151x^6 + 41x^5 - 555x^4 + 57x^3 + 200x^2 - 91x + 31	\( 3^{8}\cdot 5^{12}\cdot 29^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	Trivial (GRH)
16.0.5528355987585453765625.1	x^16 + 19x^14 + 120x^12 + 312x^10 + 342x^8 + 403x^6 + 721x^4 + 54x^2 + 1	\( 5^{6}\cdot 29^{12} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[3]$
16.0.10236206731207275390625.1	x^16 - 4x^15 + 19x^14 - 54x^13 + 166x^12 - 302x^11 + 781x^10 - 662x^9 + 2867x^8 - 238x^7 + 9681x^6 + 2282x^5 + 18806x^4 + 7394x^3 + 13879x^2 + 5684x + 661	\( 5^{14}\cdot 109^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	Trivial (GRH)
16.0.66787881998297119140625.1	x^16 - 3x^15 - 6x^14 + 67x^13 - 92x^12 - 388x^11 + 1171x^10 - 884x^9 - 1842x^8 + 7987x^7 - 10546x^6 - 154x^5 + 23133x^4 - 41026x^3 + 35166x^2 - 14964x + 2501	\( 5^{14}\cdot 149^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[5]$ (GRH)
16.16.83564717538041455968256.2	x^16 - 20x^14 + 150x^12 - 544x^10 + 1044x^8 - 1088x^6 + 600x^4 - 160x^2 + 16	\( 2^{44}\cdot 41^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	Trivial (GRH)
16.0.95038694188787201488441.1	x^16 - x^14 - 28x^12 + 163x^10 - 333x^8 - 20x^6 + 1142x^4 + 92x^2 + 1	\( 13^{14}\cdot 17^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	Trivial (GRH)
16.0.102711726879931884765625.5	x^16 - 6x^15 + 14x^14 - 21x^13 + 93x^12 - 127x^11 - 191x^10 + 737x^9 - 1034x^8 + 1052x^7 + 104x^6 - 4075x^5 + 9045x^4 - 10079x^3 + 6953x^2 - 2841x + 631	\( 5^{12}\cdot 29^{10} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[4]$ (GRH)
16.0.102711726879931884765625.8	x^16 - 4x^15 + 33x^14 - 100x^13 + 408x^12 - 896x^11 + 2491x^10 - 4256x^9 + 10142x^8 - 14592x^7 + 28752x^6 - 30049x^5 + 43444x^4 - 24683x^3 + 26254x^2 - 1635x + 6211	\( 5^{12}\cdot 29^{10} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[4]$ (GRH)
16.0.102711726879931884765625.9	x^16 - 4x^15 - 6x^14 + 53x^13 + 78x^12 - 388x^11 - 498x^10 + 1622x^9 + 2426x^8 - 4767x^7 - 7911x^6 + 6008x^5 + 11890x^4 - 6636x^3 - 3020x^2 + 23352x + 19321	\( 5^{12}\cdot 29^{10} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2, 2]$ (GRH)
16.16.434823787016118543056896.2	x^16 - 8x^15 + 120x^13 - 116x^12 - 736x^11 + 824x^10 + 2384x^9 - 2444x^8 - 4384x^7 + 3536x^6 + 4544x^5 - 2384x^4 - 2432x^3 + 576x^2 + 512x + 8	\( 2^{54}\cdot 17^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	Trivial (GRH)
16.0.434823787016118543056896.3	x^16 - 8x^15 + 24x^14 - 24x^13 - 8x^12 - 160x^11 + 1080x^10 - 2672x^9 + 3236x^8 - 2064x^7 + 5872x^6 - 28720x^5 + 77392x^4 - 132224x^3 + 151152x^2 - 108640x + 37636	\( 2^{54}\cdot 17^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2, 2, 2]$ (GRH)
16.0.516387172268851080441049.4	x^16 - 2x^15 - 4x^14 - 16x^13 + 92x^12 - 60x^11 + 98x^10 - 1042x^9 + 2050x^8 - 1478x^7 + 3073x^6 - 4719x^5 - 99x^4 - 1809x^3 + 8505x^2 - 3888x + 729	\( 13^{12}\cdot 53^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[4]$ (GRH)
16.0.616308629868476806640625.1	x^16 + 14x^14 - 19x^13 + 20x^12 - 192x^11 - 88x^10 - 339x^9 + 706x^8 + 1248x^7 + 4624x^6 + 5077x^5 + 5763x^4 + 5464x^3 + 1060x^2 - 224x + 2416	\( 3^{12}\cdot 5^{12}\cdot 41^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2, 10]$ (GRH)
16.0.1200326067404665657109641.6	x^16 - 8x^15 + 54x^14 - 238x^13 + 849x^12 - 2364x^11 + 5252x^10 - 9309x^9 + 12611x^8 - 12586x^7 + 7564x^6 - 125x^5 - 3621x^4 + 2618x^3 + 30x^2 - 728x + 211	\( 13^{12}\cdot 61^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2]$ (GRH)
16.0.2342043297768627990318769.2	x^16 - 2x^15 + 8x^14 - 11x^13 + 31x^12 + 142x^11 - 79x^10 - 719x^9 + 464x^8 + 759x^7 + 451x^6 - 2244x^5 + 1601x^4 - 807x^3 + 538x^2 - 126x + 9	\( 13^{14}\cdot 29^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2]$ (GRH)
16.0.3455222492240908603515625.2	x^16 - 3x^15 + 29x^14 - 39x^13 + 268x^12 - 59x^11 + 1214x^10 + 217x^9 + 4750x^8 - 3382x^7 + 13331x^6 - 13531x^5 + 8584x^4 - 301x^3 + 2273x^2 - 182x + 49	\( 5^{10}\cdot 29^{12} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[12]$ (GRH)
16.0.3455222492240908603515625.4	x^16 - 8x^15 + 52x^14 - 224x^13 + 811x^12 - 2318x^11 + 5781x^10 - 12042x^9 + 21965x^8 - 33670x^7 + 43848x^6 - 46567x^5 + 40381x^4 - 27165x^3 + 14386x^2 - 5231x + 1379	\( 5^{10}\cdot 29^{12} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2, 6]$ (GRH)
16.0.3455222492240908603515625.9	x^16 - 4x^15 + 29x^14 - 88x^13 + 386x^12 - 916x^11 + 2866x^10 - 5307x^9 + 12495x^8 - 16545x^7 + 29363x^6 - 17395x^5 + 24954x^4 + 30159x^3 - 16340x^2 + 53788x + 132119	\( 5^{10}\cdot 29^{12} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[12]$ (GRH)
16.8.12913449667746331350360169.1	x^16 - 18x^14 + 67x^12 - 449x^10 + 2777x^8 - 5011x^6 + 23349x^4 - 24300x^2 + 5776	\( 17^{12}\cdot 53^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	Trivial (GRH)
16.0.24731386827930948650761081.1	x^16 + 22x^14 + 183x^12 + 427x^10 - 1303x^8 + 6366x^6 + 10183x^4 + 3465x^2 + 289	\( 13^{12}\cdot 101^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[5]$ (GRH)
16.0.81925410828566900634765625.2	x^16 - 2x^15 + 18x^14 - 64x^13 + 120x^12 - 154x^11 + 548x^10 - 717x^9 + 4091x^8 - 4280x^7 + 14670x^6 - 15125x^5 + 38060x^4 - 32960x^3 + 49765x^2 - 25025x + 21605	\( 5^{14}\cdot 41^{10} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2, 4]$ (GRH)
16.0.81925410828566900634765625.3	x^16 - 2x^15 + 3x^14 + 6x^13 - 35x^12 + 6x^11 + 1033x^10 - 1787x^9 + 5916x^8 - 7725x^7 + 21925x^6 - 9715x^5 + 39510x^4 + 3160x^3 + 37865x^2 - 1225x + 22705	\( 5^{14}\cdot 41^{10} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2, 4]$ (GRH)
16.0.81925410828566900634765625.5	x^16 - x^15 + 52x^14 - 53x^13 + 1450x^12 + 13x^11 + 29552x^10 + 21851x^9 + 408181x^8 + 430260x^7 + 3953115x^6 + 4439000x^5 + 25816210x^4 + 24663705x^3 + 100016220x^2 + 58427950x + 173852905	\( 5^{14}\cdot 41^{10} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2, 2, 2]$ (GRH)
16.0.624592617158605666432592809.1	x^16 + 32x^14 + 104x^12 - 525x^10 - 660x^8 + 6681x^6 + 10738x^4 + 4203x^2 + 729	\( 13^{12}\cdot 173^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[7]$ (GRH)
16.0.1436256755503642932525262129.2	x^16 - 6x^15 + 22x^14 - 109x^13 + 504x^12 - 1854x^11 + 7377x^10 - 27415x^9 + 83734x^8 - 216549x^7 + 473915x^6 - 718469x^5 + 613596x^4 - 245902x^3 + 303248x^2 - 311475x + 119525	\( 13^{6}\cdot 29^{14} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[5, 5]$ (GRH)
16.0.2371212900396504113756570569.10	x^16 - 8x^15 + 58x^14 - 266x^13 + 1045x^12 - 3176x^11 + 7937x^10 - 15958x^9 + 24469x^8 - 27912x^7 + 21008x^6 - 7011x^5 + 15985x^4 - 33559x^3 + 30312x^2 - 12925x + 2209	\( 13^{6}\cdot 53^{12} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[8]$ (GRH)
16.8.3731986953978689760254088841.1	x^16 - 48x^14 + 804x^12 - 5908x^10 + 23808x^8 - 80581x^6 + 313296x^4 - 881664x^2 + 1048576	\( 17^{14}\cdot 53^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2]$ (GRH)
16.8.3859225055707220942242515625.1	x^16 - 5x^15 - 26x^14 + 143x^13 + 108x^12 - 1458x^11 + 2018x^10 + 4909x^9 - 17791x^8 + 13951x^7 + 26395x^6 - 80100x^5 + 85067x^4 - 37956x^3 + 4491x^2 + 220x + 97	\( 5^{6}\cdot 89^{12} \)	$(C_2\times C_4).D_4$ (as 16T121)	Trivial (GRH)
16.0.4353899607317398687744140625.1	x^16 - 2x^15 + 28x^14 - 54x^13 + 360x^12 - 394x^11 + 1448x^10 + 78x^9 + 1576x^8 + 5480x^7 - 3360x^6 + 17560x^5 + 18955x^4 - 4230x^3 + 47930x^2 + 72200x + 25855	\( 5^{14}\cdot 61^{10} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2, 8]$ (GRH)
16.0.4353899607317398687744140625.3	x^16 - 2x^15 - 8x^14 + 24x^13 + 96x^12 - 262x^11 + 145x^10 + 862x^9 - 736x^8 - 2004x^7 + 17625x^6 - 23674x^5 + 72006x^4 - 24728x^3 + 165308x^2 - 23064x + 140891	\( 5^{14}\cdot 61^{10} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[10, 40]$ (GRH)
16.0.4353899607317398687744140625.9	x^16 - 147x^14 + 8533x^12 - 242414x^10 + 3505530x^8 - 23532134x^6 + 48780893x^4 + 41074633x^2 + 283282561	\( 5^{14}\cdot 61^{10} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2, 10, 10]$ (GRH)
16.0.7612724592276900293212890625.4	x^16 + 42x^14 - 15x^13 + 1066x^12 + 170x^11 + 13121x^10 - 9895x^9 + 67004x^8 - 117105x^7 + 316503x^6 - 423225x^5 + 509814x^4 - 335340x^3 + 172044x^2 - 32805x + 6561	\( 5^{12}\cdot 89^{10} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[740]$ (GRH)
16.0.7612724592276900293212890625.16	x^16 - 6x^15 + 66x^14 - 290x^13 + 1682x^12 - 5688x^11 + 21596x^10 - 56654x^9 + 150277x^8 - 314240x^7 + 610374x^6 - 1009634x^5 + 1471135x^4 - 1837696x^3 + 1885989x^2 - 1486072x + 950771	\( 5^{12}\cdot 89^{10} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[20]$ (GRH)
16.0.7612724592276900293212890625.17	x^16 - 5x^15 - 10x^14 + 6x^13 + 436x^12 + 1665x^11 - 7659x^10 - 62838x^9 + 98681x^8 + 843231x^7 - 489347x^6 - 5502447x^5 + 850907x^4 + 7824574x^3 + 10797536x^2 + 22364064x + 21492496	\( 5^{12}\cdot 89^{10} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2, 74]$ (GRH)
16.0.7937726777341695855516080761.1	x^16 - 8x^15 + 26x^14 - 42x^13 - 123x^12 + 920x^11 - 1588x^10 - 541x^9 + 14638x^8 - 45186x^7 + 87563x^6 - 116912x^5 + 116423x^4 - 84579x^3 + 45084x^2 - 15676x + 3181	\( 13^{14}\cdot 17^{10} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[4]$ (GRH)
16.0.7937726777341695855516080761.3	x^16 - 8x^15 + 52x^14 - 224x^13 + 735x^12 - 1862x^11 + 4080x^10 - 7717x^9 + 15431x^8 - 28468x^7 + 49941x^6 - 69904x^5 + 95090x^4 - 97761x^3 + 141895x^2 - 101281x + 32353	\( 13^{14}\cdot 17^{10} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[4]$ (GRH)
16.0.7937726777341695855516080761.5	x^16 - 4x^15 + 13x^14 - 28x^13 + 297x^12 - 839x^11 + 2537x^10 - 1192x^9 + 12753x^8 - 34044x^7 + 192731x^6 - 96505x^5 + 999786x^4 - 881433x^3 + 2699541x^2 - 479196x + 5517801	\( 13^{14}\cdot 17^{10} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2, 2]$ (GRH)
16.0.11857795698361121271751807729.1	x^16 + 70x^14 + 1543x^12 + 13118x^10 + 44585x^8 + 62904x^6 + 34672x^4 + 5504x^2 + 256	\( 17^{6}\cdot 53^{12} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[5]$ (GRH)
16.0.12812035518280357547259227689.11	x^16 + 23x^14 + 242x^12 + 2895x^10 + 10612x^8 + 11110x^6 + 35584x^4 + 104363x^2 + 26569	\( 13^{6}\cdot 61^{12} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[18]$ (GRH)
16.0.17606641095812026885331265625.12	x^16 - 8x^15 + 94x^14 - 518x^13 + 2915x^12 - 11120x^11 + 40043x^10 - 109674x^9 + 276033x^8 - 548960x^7 + 988724x^6 - 1403525x^5 + 1790895x^4 - 1714545x^3 + 1504070x^2 - 814425x + 464375	\( 5^{6}\cdot 101^{12} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[5, 10]$ (GRH)
16.0.26968313608671985107666015625.18	x^16 - 3x^15 + 16x^14 - 42x^13 + 450x^12 - 1128x^11 + 6778x^10 - 39236x^9 + 147063x^8 - 440459x^7 + 1006203x^6 - 1489799x^5 + 1402694x^4 - 832761x^3 - 73468x^2 + 144471x + 497311	\( 5^{12}\cdot 101^{10} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2, 4, 8]$ (GRH)
16.0.26968313608671985107666015625.27	x^16 - 2x^15 + 30x^14 - 40x^13 + 536x^12 - 790x^11 + 7911x^10 - 15125x^9 + 93021x^8 - 166580x^7 + 673820x^6 - 927958x^5 + 2870551x^4 - 2418440x^3 + 6353305x^2 - 1890290x + 8629655	\( 5^{12}\cdot 101^{10} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2, 4, 8]$ (GRH)
16.0.26968313608671985107666015625.32	x^16 - 3x^15 + 80x^14 - 280x^13 + 3006x^12 - 9305x^11 + 56746x^10 - 124795x^9 + 621706x^8 - 329460x^7 + 4075490x^6 + 6631093x^5 + 23495891x^4 + 44048875x^3 + 48334335x^2 + 46880900x + 35940025	\( 5^{12}\cdot 101^{10} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[2, 2, 2, 2]$ (GRH)
16.0.58966431579683595226807139761.6	x^16 - 2x^15 + 16x^14 + x^13 + 188x^12 - 256x^11 + 2629x^10 - 1780x^9 + 16260x^8 - 5457x^7 + 132380x^6 - 5820x^5 + 368815x^4 - 706086x^3 + 352784x^2 - 341152x + 5333168	\( 13^{14}\cdot 157^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	$[26]$ (GRH)