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 29 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.275188285440000000000.1	x^16 + 6x^14 + 20x^12 + 58x^10 + 129x^8 + 190x^6 + 180x^4 + 100x^2 + 25	\( 2^{32}\cdot 3^{8}\cdot 5^{10} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	Trivial (GRH)
16.0.275188285440000000000.2	x^16 - 6x^14 + 20x^12 - 58x^10 + 129x^8 - 190x^6 + 180x^4 - 100x^2 + 25	\( 2^{32}\cdot 3^{8}\cdot 5^{10} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	Trivial (GRH)
16.4.869730877440000000000.1	x^16 - 8x^14 - 4x^13 + 30x^12 + 32x^11 - 96x^10 - 40x^9 + 79x^8 + 272x^7 - 412x^6 + 40x^5 - 28x^4 + 504x^3 - 576x^2 + 236x - 31	\( 2^{40}\cdot 3^{4}\cdot 5^{10} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	Trivial (GRH)
16.4.869730877440000000000.2	x^16 + 4x^14 - 4x^13 - 60x^10 - 36x^9 - 140x^8 - 64x^7 - 124x^6 - 132x^5 - 184x^4 + 96x^3 - 12x^2 - 20x - 1	\( 2^{40}\cdot 3^{4}\cdot 5^{10} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	Trivial (GRH)
16.0.9756589522702500000000.1	x^16 - 5x^15 + 48x^13 - 96x^12 - 91x^11 + 569x^10 - 402x^9 - 1519x^8 + 2935x^7 + 873x^6 - 7511x^5 + 8017x^4 - 2700x^3 - 180x^2 - 224x + 304	\( 2^{8}\cdot 3^{8}\cdot 5^{10}\cdot 29^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	$[2]$
16.0.9756589522702500000000.2	x^16 - x^15 - 7x^14 + 4x^13 + 8x^12 + 87x^11 - 6x^10 - 574x^9 + 597x^8 + 748x^7 - 2322x^6 + 2127x^5 + 1204x^4 - 4490x^3 + 4305x^2 - 2125x + 475	\( 2^{8}\cdot 3^{8}\cdot 5^{10}\cdot 29^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	$[2]$
16.4.13915694039040000000000.1	x^16 + 4x^14 - 18x^12 + 56x^10 + 331x^8 + 360x^6 - 1530x^4 - 2700x^2 + 2025	\( 2^{44}\cdot 3^{4}\cdot 5^{10} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	Trivial (GRH)
16.4.13915694039040000000000.2	x^16 - 4x^14 - 18x^12 - 56x^10 + 331x^8 - 360x^6 - 1530x^4 + 2700x^2 + 2025	\( 2^{44}\cdot 3^{4}\cdot 5^{10} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	Trivial (GRH)
16.0.2201295421769100124225536.1	x^16 - 40x^14 + 682x^12 - 6420x^10 + 36466x^8 - 131784x^6 + 319464x^4 - 499392x^2 + 374544	\( 2^{50}\cdot 3^{4}\cdot 17^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	$[2]$ (GRH)
16.0.11144058072706069378891776.1	x^16 + 8x^14 + 18x^12 - 416x^10 + 1517x^8 - 3704x^6 + 6420x^4 - 4624x^2 + 1156	\( 2^{46}\cdot 3^{8}\cdot 17^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	$[2, 2]$ (GRH)
16.0.11144058072706069378891776.2	x^16 - 8x^14 + 18x^12 + 416x^10 + 1517x^8 + 3704x^6 + 6420x^4 + 4624x^2 + 1156	\( 2^{46}\cdot 3^{8}\cdot 17^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	$[2, 2]$ (GRH)
16.0.12452113261527040000000000.5	x^16 - 8x^14 + 32x^12 + 416x^10 + 2294x^8 + 1640x^6 + 42025	\( 2^{28}\cdot 5^{10}\cdot 41^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	$[2]$ (GRH)
16.0.19021991394672640000000000.4	x^16 - 18x^14 + 152x^12 - 744x^10 + 3039x^8 - 5700x^6 + 9700x^4 - 8250x^2 + 3025	\( 2^{40}\cdot 5^{10}\cdot 11^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	$[2]$ (GRH)
16.0.19757093783472562500000000.1	x^16 - 3x^15 - 14x^14 + 84x^13 - 62x^12 - 651x^11 + 2188x^10 - 489x^9 - 11819x^8 + 23001x^7 + 11356x^6 - 94281x^5 + 129040x^4 - 73992x^3 + 31750x^2 - 33489x + 17551	\( 2^{8}\cdot 3^{12}\cdot 5^{12}\cdot 29^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	$[2, 4]$ (GRH)
16.8.24948698345635840000000000.1	x^16 - 18x^14 - 12x^13 + 64x^12 + 8x^11 - 308x^10 + 832x^9 + 3990x^8 + 32x^7 + 878x^6 + 3704x^5 - 23865x^4 - 200x^3 + 20184x^2 + 580x - 3631	\( 2^{32}\cdot 5^{10}\cdot 29^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	Trivial (GRH)
16.8.24948698345635840000000000.2	x^16 - 28x^14 - 32x^13 + 180x^12 + 336x^11 - 224x^10 - 1084x^9 - 139x^8 + 1072x^7 - 2720x^6 - 156x^5 + 5280x^4 - 928x^3 - 1452x^2 + 3964x - 751	\( 2^{32}\cdot 5^{10}\cdot 29^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	Trivial (GRH)
16.0.38982341165056000000000000.1	x^16 - 6x^15 + 54x^13 + 113x^12 - 1526x^11 + 3730x^10 + 400x^9 - 10048x^8 - 45882x^7 + 319616x^6 - 824978x^5 + 1227621x^4 - 1152650x^3 + 684110x^2 - 238380x + 37845	\( 2^{28}\cdot 5^{12}\cdot 29^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	$[4]$ (GRH)
16.0.39760898555704370993823744.1	x^16 + 12x^14 + 70x^12 + 236x^10 + 514x^8 + 708x^6 + 630x^4 + 324x^2 + 81	\( 2^{46}\cdot 3^{4}\cdot 17^{8} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	$[8]$ (GRH)
16.8.178304929163297110062268416.1	x^16 - 4x^14 - 192x^12 - 184x^10 + 2592x^8 + 680x^6 - 6256x^4 + 1156	\( 2^{50}\cdot 3^{8}\cdot 17^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	Trivial (GRH)
16.8.202312640342759040000000000.1	x^16 - 2x^15 - 17x^14 - 60x^13 + 60x^12 + 460x^11 + 627x^10 + 180x^9 + 1465x^8 + 9658x^7 + 22537x^6 + 22262x^5 - 1782x^4 - 20268x^3 - 14377x^2 - 3896x - 359	\( 2^{16}\cdot 3^{12}\cdot 5^{10}\cdot 29^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	Trivial (GRH)
16.16.31949641098354480906240000000000.2	x^16 - 60x^14 + 1264x^12 - 11400x^10 + 47859x^8 - 97680x^6 + 93280x^4 - 36300x^2 + 3025	\( 2^{48}\cdot 3^{8}\cdot 5^{10}\cdot 11^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	Trivial (GRH)
16.8.70499058785862276874240000000000.1	x^16 - 40x^14 - 268x^13 - 1811x^12 + 20656x^11 + 43294x^10 - 104488x^9 + 244651x^8 - 7558680x^7 + 234858x^6 + 41315996x^5 - 89381223x^4 + 503482600x^3 - 90353990x^2 - 261568276x + 277986479	\( 2^{32}\cdot 5^{10}\cdot 29^{6}\cdot 41^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	$[2]$ (GRH)
16.0.1762476469646556921856000000000000.1	x^16 + 120x^14 - 80x^13 + 5779x^12 - 4080x^11 + 139950x^10 - 36380x^9 + 1710046x^8 + 894240x^7 + 11172540x^6 + 16447560x^5 + 56975359x^4 + 108407120x^3 + 225613310x^2 + 283026660x + 151994111	\( 2^{32}\cdot 5^{12}\cdot 29^{6}\cdot 41^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	$[2, 2, 2, 12]$ (GRH)
16.16.3865906572900892189655040000000000.1	x^16 - 140x^14 + 7196x^12 - 177320x^10 + 2262139x^8 - 15149200x^6 + 51403220x^4 - 80525500x^2 + 44289025	\( 2^{48}\cdot 3^{8}\cdot 5^{10}\cdot 11^{8} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	Trivial (GRH)
16.8.5347975059777049895895040000000000.1	x^16 - 54x^14 - 159x^12 - 3080x^11 - 18048x^10 - 124520x^9 - 333886x^8 - 759000x^7 - 8160964x^6 + 2291740x^5 + 98870734x^4 + 22356840x^3 - 53694970x^2 - 5479100x + 5427475	\( 2^{32}\cdot 5^{10}\cdot 11^{8}\cdot 29^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	$[2]$ (GRH)
16.0.8356211030901640462336000000000000.1	x^16 - 32x^14 + 119x^12 + 3692x^10 + 69261x^8 - 773720x^6 + 3490440x^4 + 2018400x^2 + 336400	\( 2^{28}\cdot 5^{12}\cdot 11^{8}\cdot 29^{6} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	$[2, 4, 16]$ (GRH)
16.0.2531650413679670693032099840000000000.1	x^16 + 560x^14 + 122936x^12 + 13877280x^10 + 881319704x^8 + 32138356800x^6 + 653031584480x^4 + 6665553136000x^2 + 25162463088400	\( 2^{48}\cdot 5^{10}\cdot 11^{6}\cdot 151^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	$[2, 2, 2, 2, 2, 569700]$ (GRH)
16.8.7936109291110060736213155840000000000.1	x^16 + 52x^14 - 324x^13 - 27589x^12 + 34408x^11 - 1384598x^10 + 7185744x^9 + 194964715x^8 - 205481584x^7 + 7975385568x^6 - 8528696844x^5 - 438868218257x^4 - 570322900656x^3 - 13351517441880x^2 - 26945103359324x + 14401865752759	\( 2^{32}\cdot 5^{10}\cdot 29^{6}\cdot 751^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	$[14]$ (GRH)
16.0.63291260341991767325802496000000000000.1	x^16 + 560x^14 + 109988x^12 + 9846560x^10 + 431415164x^8 + 9477533120x^6 + 104285207312x^4 + 533244250880x^2 + 1006498523536	\( 2^{48}\cdot 5^{12}\cdot 11^{6}\cdot 151^{4} \)	$C_2^3.C_2^4.C_2$ (as 16T456)	$[2, 4, 4, 569700]$ (GRH)