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 matches 1-50 of 3014)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.18446744073709551616.1	x^16 + 1	\( 2^{64} \)	$C_8\times C_2$ (as 16T5)	Trivial
16.0.1104726920056229495169.1	x^16 - x^15 + 8x^14 - 5x^13 + 40x^12 - 22x^11 + 111x^10 - 36x^9 + 206x^8 - 59x^7 + 212x^6 - 14x^5 + 125x^4 - 20x^3 + 26x^2 + 4x + 1	\( 3^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[5]$
16.0.11034809241396899282944.1	x^16 + 15x^14 + 91x^12 + 286x^10 + 495x^8 + 462x^6 + 210x^4 + 36x^2 + 1	\( 2^{16}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[8]$
16.0.30257271966902092038144.1	x^16 + 8x^14 + 44x^12 + 128x^10 + 270x^8 + 288x^6 + 216x^4 + 32x^2 + 4	\( 2^{62}\cdot 3^{8} \)	$C_8\times C_2$ (as 16T5)	$[3, 3]$ (GRH)
16.0.30257271966902092038144.2	x^16 - 8x^14 + 44x^12 - 128x^10 + 270x^8 - 288x^6 + 216x^4 - 32x^2 + 4	\( 2^{62}\cdot 3^{8} \)	$C_8\times C_2$ (as 16T5)	Trivial (GRH)
16.16.65772588499765987890625.1	x^16 - x^15 - 22x^14 + 17x^13 + 172x^12 - 92x^11 - 601x^10 + 196x^9 + 1014x^8 - 189x^7 - 844x^6 + 74x^5 + 325x^4 - 46x^2 - 4x + 1	\( 5^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	Trivial (GRH)
16.0.121029087867608368152576.1	x^16 + 16x^14 + 104x^12 + 352x^10 + 660x^8 + 672x^6 + 336x^4 + 64x^2 + 1	\( 2^{64}\cdot 3^{8} \)	$C_8\times C_2$ (as 16T5)	$[3, 6]$ (GRH)
16.16.121029087867608368152576.1	x^16 - 16x^14 + 104x^12 - 352x^10 + 660x^8 - 672x^6 + 336x^4 - 64x^2 + 1	\( 2^{64}\cdot 3^{8} \)	$C_8\times C_2$ (as 16T5)	Trivial (GRH)
16.0.121029087867608368152576.2	x^16 + 6561	\( 2^{64}\cdot 3^{8} \)	$C_8\times C_2$ (as 16T5)	$[3, 6]$ (GRH)
16.0.970664662927461034900129.1	x^16 - x^15 + 23x^14 - 16x^13 + 247x^12 - 128x^11 + 1478x^10 - 512x^9 + 5217x^8 - 1206x^7 + 10340x^6 - 1072x^5 + 10480x^4 - 960x^3 + 3968x^2 + 512x + 256	\( 7^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[3, 15]$ (GRH)
16.0.1801439850948198400000000.1	x^16 + 24x^14 + 204x^12 + 768x^10 + 1390x^8 + 1248x^6 + 536x^4 + 96x^2 + 4	\( 2^{62}\cdot 5^{8} \)	$C_8\times C_2$ (as 16T5)	$[17]$ (GRH)
16.16.1801439850948198400000000.1	x^16 - 24x^14 + 204x^12 - 768x^10 + 1390x^8 - 1248x^6 + 536x^4 - 96x^2 + 4	\( 2^{62}\cdot 5^{8} \)	$C_8\times C_2$ (as 16T5)	Trivial (GRH)
16.0.2824911165797606216433664.1	x^16 + 30x^14 + 364x^12 + 2288x^10 + 7920x^8 + 14784x^6 + 13440x^4 + 4608x^2 + 256	\( 2^{24}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[3, 24]$ (GRH)
16.16.2824911165797606216433664.1	x^16 - 30x^14 + 364x^12 - 2288x^10 + 7920x^8 - 14784x^6 + 13440x^4 - 4608x^2 + 256	\( 2^{24}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	Trivial (GRH)
16.0.7205759403792793600000000.1	x^16 + 16x^14 + 104x^12 + 352x^10 + 660x^8 + 672x^6 + 336x^4 + 64x^2 + 2209	\( 2^{64}\cdot 5^{8} \)	$C_8\times C_2$ (as 16T5)	$[34]$ (GRH)
16.0.7205759403792793600000000.2	x^16 + 390625	\( 2^{64}\cdot 5^{8} \)	$C_8\times C_2$ (as 16T5)	$[34]$ (GRH)
16.0.7205759403792793600000000.3	x^16 - 16x^14 + 104x^12 - 352x^10 + 660x^8 - 672x^6 + 336x^4 - 64x^2 + 2209	\( 2^{64}\cdot 5^{8} \)	$C_8\times C_2$ (as 16T5)	$[2]$ (GRH)
16.0.26585452170716224216367104.1	x^16 + 24x^14 + 276x^12 + 1776x^10 + 6850x^8 + 14784x^6 + 17024x^4 + 6144x^2 + 1024	\( 2^{62}\cdot 7^{8} \)	$C_8\times C_2$ (as 16T5)	$[136]$ (GRH)
16.0.26585452170716224216367104.2	x^16 - 8x^15 + 60x^14 - 280x^13 + 1126x^12 - 3480x^11 + 9068x^10 - 19160x^9 + 33497x^8 - 47584x^7 + 54432x^6 - 49136x^5 + 34192x^4 - 17680x^3 + 6408x^2 - 1456x + 158	\( 2^{62}\cdot 7^{8} \)	$C_8\times C_2$ (as 16T5)	$[4]$ (GRH)
16.0.36093282486485263170800449.1	x^16 - 6x^15 + 24x^14 - 68x^13 + 229x^12 - 610x^11 + 1652x^10 - 3427x^9 + 8268x^8 - 14574x^7 + 31149x^6 - 43150x^5 + 84686x^4 - 84235x^3 + 155680x^2 - 83057x + 153851	\( 11^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[17, 17]$ (GRH)
16.0.41107867812353742431640625.1	x^16 - x^15 + 12x^14 - 17x^13 + 2x^12 - 75x^11 - 142x^10 - 399x^9 + 470x^8 - 121x^7 + 3168x^6 + 5225x^5 + 8927x^4 + 11662x^3 + 12432x^2 + 7816x + 4336	\( 5^{12}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[146]$ (GRH)
16.0.72399383432805056195395584.1	x^16 - 11x^14 + 20x^12 + 115x^10 - 297x^8 - 729x^6 + 5496x^4 + 4993x^2 + 2209	\( 2^{16}\cdot 3^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 2]$ (GRH)
16.16.72399383432805056195395584.1	x^16 - 2x^15 - 37x^14 + 68x^13 + 508x^12 - 836x^11 - 3189x^10 + 4518x^9 + 9089x^8 - 10408x^7 - 10057x^6 + 8378x^5 + 2786x^4 - 1462x^3 - 37x^2 + 32x + 1	\( 2^{16}\cdot 3^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	Trivial (GRH)
16.0.72399383432805056195395584.2	x^16 - 17x^14 + 221x^12 - 986x^10 + 3162x^8 - 5202x^6 + 6069x^4 - 1445x^2 + 289	\( 2^{16}\cdot 3^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 10]$ (GRH)
16.0.72399383432805056195395584.3	x^16 - 19x^14 + 108x^12 - 173x^10 + 155x^8 + 955x^6 + 720x^4 - 9739x^2 + 10609	\( 2^{16}\cdot 3^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 8]$ (GRH)
16.0.106341808682864896865468416.1	x^16 + 32x^14 + 416x^12 + 2816x^10 + 10560x^8 + 21504x^6 + 21504x^4 + 8192x^2 + 961	\( 2^{64}\cdot 7^{8} \)	$C_8\times C_2$ (as 16T5)	$[2, 34]$ (GRH)
16.16.106341808682864896865468416.1	x^16 - 32x^14 + 416x^12 - 2816x^10 + 10560x^8 - 21504x^6 + 21504x^4 - 8192x^2 + 961	\( 2^{64}\cdot 7^{8} \)	$C_8\times C_2$ (as 16T5)	Trivial (GRH)
16.0.106341808682864896865468416.2	x^16 + 5764801	\( 2^{64}\cdot 7^{8} \)	$C_8\times C_2$ (as 16T5)	$[2, 34]$ (GRH)
16.16.137350965859713069141239809.1	x^16 - 6x^15 - 24x^14 + 184x^13 + 145x^12 - 2062x^11 + 500x^10 + 10181x^9 - 7614x^8 - 20610x^7 + 22809x^6 + 10286x^5 - 19654x^4 + 4745x^3 + 2122x^2 - 1001x + 101	\( 13^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	Trivial (GRH)
16.0.248853659625840981300978321.1	x^16 - x^15 - 2x^14 + 19x^13 - 46x^12 + 108x^11 + 348x^10 - 795x^9 + 1681x^8 + 6119x^7 - 1809x^6 - 6620x^5 + 12333x^4 + 18226x^3 + 16573x^2 + 9440x + 3481	\( 3^{8}\cdot 41^{14} \)	$C_8\times C_2$ (as 16T5)	$[17]$ (GRH)
16.0.431533953146964646550390625.1	x^16 - 6x^15 + 32x^14 - 110x^13 + 439x^12 - 1250x^11 + 4000x^10 - 9195x^9 + 25370x^8 - 47784x^7 + 115811x^6 - 170636x^5 + 371982x^4 - 388515x^3 + 779262x^2 - 435519x + 838099	\( 3^{8}\cdot 5^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[816]$ (GRH)
16.0.431533953146964646550390625.2	x^16 - 6x^15 + 26x^14 - 70x^13 + 153x^12 - 128x^11 - 428x^10 + 3149x^9 - 4488x^8 + 1516x^7 + 12743x^6 - 24194x^5 + 64192x^4 - 48869x^3 + 100862x^2 - 32207x + 16999	\( 3^{8}\cdot 5^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 34]$ (GRH)
16.0.431533953146964646550390625.3	x^16 - x^15 + 25x^14 - 22x^13 + 448x^12 - 447x^11 + 3528x^10 - 5340x^9 + 21507x^8 - 30030x^7 + 69368x^6 - 91287x^5 + 155828x^4 - 158392x^3 + 147875x^2 - 72501x + 28561	\( 3^{8}\cdot 5^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 170]$ (GRH)
16.0.431533953146964646550390625.4	x^16 - x^15 + 19x^14 - 4x^13 + 187x^12 + 24x^11 + 1146x^10 + 1455x^9 + 4962x^8 + 6399x^7 + 25490x^6 - 5124x^5 + 27353x^4 - 11794x^3 + 25043x^2 - 63579x + 41719	\( 3^{8}\cdot 5^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[48]$ (GRH)
16.0.723177258444187191407017984.1	x^16 + 153x^12 + 1768x^8 + 4913x^4 + 289	\( 2^{32}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 6, 24]$ (GRH)
16.0.723177258444187191407017984.2	x^16 - 4x^14 - 27x^12 + 44x^10 + 304x^8 + 1320x^6 + 5093x^4 - 14296x^2 + 10201	\( 2^{32}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 2, 8]$ (GRH)
16.0.723177258444187191407017984.3	x^16 + 4x^14 - 27x^12 - 44x^10 + 304x^8 - 1320x^6 + 5093x^4 + 14296x^2 + 10201	\( 2^{32}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[2, 6, 6]$ (GRH)
16.0.988555854433440250854375424.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 346x^12 - 984x^11 + 2640x^10 - 5896x^9 + 13211x^8 - 25432x^7 + 50016x^6 - 77960x^5 + 132922x^4 - 157696x^3 + 233836x^2 - 164920x + 214303	\( 2^{62}\cdot 11^{8} \)	$C_8\times C_2$ (as 16T5)	$[565]$ (GRH)
16.0.988555854433440250854375424.2	x^16 - 8x^15 + 68x^14 - 336x^13 + 1514x^12 - 5080x^11 + 14784x^10 - 34408x^9 + 67067x^8 - 105688x^7 + 133904x^6 - 133032x^5 + 100122x^4 - 54592x^3 + 20220x^2 - 4536x + 463	\( 2^{62}\cdot 11^{8} \)	$C_8\times C_2$ (as 16T5)	$[5]$ (GRH)
16.0.1125899906842624000000000000.1	x^16 + 40x^14 + 620x^12 + 4800x^10 + 19950x^8 + 44000x^6 + 47000x^4 + 20000x^2 + 2500	\( 2^{62}\cdot 5^{12} \)	$C_8\times C_2$ (as 16T5)	$[3, 246]$ (GRH)
16.16.1125899906842624000000000000.1	x^16 - 40x^14 + 620x^12 - 4800x^10 + 19950x^8 - 44000x^6 + 47000x^4 - 20000x^2 + 2500	\( 2^{62}\cdot 5^{12} \)	$C_8\times C_2$ (as 16T5)	Trivial (GRH)
16.0.2485729833445986061658423296.1	x^16 - 5x^14 + 75x^12 - 555x^10 + 4458x^8 - 14529x^6 + 11641x^4 + 7546x^2 + 3481	\( 2^{16}\cdot 41^{14} \)	$C_8\times C_2$ (as 16T5)	$[8]$ (GRH)
16.0.2859655432078149808865465089.6	x^16 - 6x^15 + 40x^14 - 152x^13 + 705x^12 - 2142x^11 + 7860x^10 - 19323x^9 + 60042x^8 - 119410x^7 + 322825x^6 - 498338x^5 + 1197274x^4 - 1299079x^3 + 2829154x^2 - 1635129x + 3329789	\( 17^{14}\cdot 19^{8} \)	$C_8\times C_2$ (as 16T5)	$[5, 520]$ (GRH)
16.0.3761893960837392421076598784.1	x^16 - 8x^15 + 20x^14 + 26x^12 - 520x^11 + 768x^10 + 1880x^9 - 853x^8 - 15304x^7 + 3152x^6 + 59544x^5 + 25482x^4 - 175600x^3 - 155892x^2 + 257304x + 353263	\( 2^{62}\cdot 13^{8} \)	$C_8\times C_2$ (as 16T5)	$[9, 9]$ (GRH)
16.16.3761893960837392421076598784.1	x^16 - 8x^15 - 12x^14 + 224x^13 - 182x^12 - 2184x^11 + 3600x^10 + 8312x^9 - 19381x^8 - 7240x^7 + 36768x^6 - 14600x^5 - 16214x^4 + 13904x^3 - 2564x^2 - 424x + 127	\( 2^{62}\cdot 13^{8} \)	$C_8\times C_2$ (as 16T5)	Trivial (GRH)
16.0.3954223417733761003417501696.1	x^16 + 214358881	\( 2^{64}\cdot 11^{8} \)	$C_8\times C_2$ (as 16T5)	$[226]$ (GRH)
16.16.3954223417733761003417501696.1	x^16 - 48x^14 + 936x^12 - 9504x^10 + 53460x^8 - 163296x^6 + 244944x^4 - 139968x^2 + 12769	\( 2^{64}\cdot 11^{8} \)	$C_8\times C_2$ (as 16T5)	Trivial (GRH)
16.0.3954223417733761003417501696.2	x^16 + 48x^14 + 936x^12 + 9504x^10 + 53460x^8 + 163296x^6 + 244944x^4 + 139968x^2 + 12769	\( 2^{64}\cdot 11^{8} \)	$C_8\times C_2$ (as 16T5)	$[226]$ (GRH)
16.0.4310472359920663782400000000.1	x^16 - 2x^15 + 27x^14 - 44x^13 + 452x^12 - 644x^11 + 5131x^10 - 6202x^9 + 42489x^8 - 42728x^7 + 257239x^6 - 204038x^5 + 1104650x^4 - 624150x^3 + 3070971x^2 - 944592x + 4250681	\( 2^{16}\cdot 5^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[40, 80]$ (GRH)
16.0.4310472359920663782400000000.2	x^16 + 41x^14 + 660x^12 + 5303x^10 + 22483x^8 + 49767x^6 + 54752x^4 + 25265x^2 + 2209	\( 2^{16}\cdot 5^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	$[8, 16]$ (GRH)