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 32 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.1401249857536000000.1	x^16 - 6x^15 + 10x^14 + 6x^13 - 38x^12 + 50x^11 - 22x^10 - 46x^9 + 120x^8 - 98x^7 - 18x^6 + 74x^5 - 30x^4 - 10x^3 + 14x^2 - 6x + 1	\( 2^{30}\cdot 5^{6}\cdot 17^{4} \)	16T1276	Trivial
16.0.8385407879109765625.1	x^16 - 4x^15 + 7x^14 + 3x^13 - 26x^12 + 42x^11 + 15x^10 - 143x^9 + 305x^8 - 361x^7 + 297x^6 - 114x^5 - 20x^4 + 75x^3 - 17x^2 - 8x + 19	\( 5^{8}\cdot 11^{6}\cdot 59^{4} \)	16T1276	Trivial
16.0.11979351654400000000.1	x^16 - 6x^15 + 16x^14 - 20x^13 + 4x^12 - 8x^11 + 104x^10 - 196x^9 + 44x^8 + 272x^7 - 316x^6 + 24x^5 + 168x^4 - 92x^3 - 4x^2 + 8x + 2	\( 2^{30}\cdot 5^{8}\cdot 13^{4} \)	16T1276	Trivial
16.0.72011464084359765625.1	x^16 - 3x^15 + 11x^14 - 17x^13 + 40x^12 - 37x^11 + 66x^10 + 25x^9 - 30x^8 + 254x^7 - 180x^6 + 443x^5 - 120x^4 + 127x^3 + 575x^2 - 527x + 551	\( 5^{8}\cdot 11^{6}\cdot 101^{4} \)	16T1276	Trivial
16.4.119842600295694598144.8	x^16 - x^14 + 2x^12 + 6x^10 - 2x^8 - 25x^6 + 22x^4 - 8x^2 + 1	\( 2^{34}\cdot 17^{8} \)	16T1276	Trivial (GRH)
16.0.119842600295694598144.23	x^16 + x^14 + 2x^12 - 6x^10 - 2x^8 + 25x^6 + 22x^4 + 8x^2 + 1	\( 2^{34}\cdot 17^{8} \)	16T1276	Trivial
16.4.1917481604731113570304.12	x^16 - 6x^14 + 18x^12 - 64x^10 + 153x^8 - 202x^6 + 132x^4 - 56x^2 + 16	\( 2^{38}\cdot 17^{8} \)	16T1276	Trivial (GRH)
16.8.7669926418924454281216.8	x^16 - 8x^14 + 46x^12 - 164x^10 + 269x^8 - 132x^6 - 68x^4 + 48x^2 + 4	\( 2^{40}\cdot 17^{8} \)	16T1276	Trivial (GRH)
16.4.7669926418924454281216.13	x^16 + 8x^14 + 46x^12 + 164x^10 + 269x^8 + 132x^6 - 68x^4 - 48x^2 + 4	\( 2^{40}\cdot 17^{8} \)	16T1276	Trivial (GRH)
16.4.29189604827181094140625.1	x^16 - 3x^15 + 2x^14 + 9x^13 - 31x^12 + 3x^11 + 34x^10 - 36x^9 + 127x^8 + 180x^7 - 65x^6 - 408x^5 - 607x^4 - 42x^3 + 455x^2 + 330x + 76	\( 5^{8}\cdot 11^{6}\cdot 59^{6} \)	16T1276	Trivial (GRH)
16.0.45007165052724853515625.1	x^16 - 5x^15 + 2x^14 + 43x^13 - 128x^12 - 8x^11 + 799x^10 - 1406x^9 - 1400x^8 + 7846x^7 - 4338x^6 - 18116x^5 + 22632x^4 + 15712x^3 - 34793x^2 - 1481x + 22031	\( 5^{12}\cdot 11^{6}\cdot 101^{4} \)	16T1276	$[2]$ (GRH)
16.8.122718822702791268499456.8	x^16 - 8x^14 - 12x^12 + 144x^10 - 138x^8 - 168x^6 + 148x^4 - 32x^2 + 1	\( 2^{44}\cdot 17^{8} \)	16T1276	Trivial (GRH)
16.4.734588945124553969140625.1	x^16 - 5x^15 + 16x^14 - 27x^13 + 35x^12 - 49x^11 + 115x^10 - 133x^9 + 104x^8 + 226x^7 + 129x^6 + 123x^5 - 777x^4 - 625x^3 - 252x^2 - 186x + 29	\( 5^{8}\cdot 11^{6}\cdot 101^{6} \)	16T1276	$[2]$ (GRH)
16.4.1054319845659111328515625.1	x^16 - x^15 - 3x^14 + 4x^13 - 66x^12 + 283x^11 - 862x^10 + 2229x^9 - 4913x^8 + 10813x^7 - 21199x^6 + 31801x^5 - 37510x^4 + 38582x^3 - 32884x^2 + 18613x - 5099	\( 5^{8}\cdot 11^{10}\cdot 101^{4} \)	16T1276	Trivial (GRH)
16.4.32667140577724797996255625.1	x^16 - x^15 - 9x^14 + 11x^13 - 13x^12 - 57x^11 + 123x^10 + 349x^9 + 297x^8 - 773x^7 - 1086x^6 + 802x^5 + 712x^4 + 945x^3 - 2195x^2 + 1200x - 225	\( 5^{4}\cdot 13^{6}\cdot 101^{8} \)	16T1276	Trivial (GRH)
16.4.816678514443119949906390625.1	x^16 - 7x^15 + 25x^14 - 98x^13 + 387x^12 - 1039x^11 + 1778x^10 - 2615x^9 + 4902x^8 - 4225x^7 - 11766x^6 + 25877x^5 - 84x^4 - 19771x^3 - 3679x^2 + 2050x + 625	\( 5^{6}\cdot 13^{6}\cdot 101^{8} \)	16T1276	$[4]$ (GRH)
16.16.1604279675444921972578515625.1	x^16 - 4x^15 - 45x^14 + 179x^13 + 791x^12 - 3142x^11 - 6921x^10 + 27489x^9 + 32002x^8 - 126127x^7 - 76921x^6 + 291115x^5 + 87056x^4 - 288997x^3 - 26268x^2 + 74332x - 12661	\( 5^{8}\cdot 29^{6}\cdot 1621^{4} \)	16T1276	Trivial (GRH)
16.0.405651805355453454745600000000.1	x^16 - 4x^15 + 50x^14 - 88x^13 + 865x^12 - 378x^11 + 10336x^10 + 3922x^9 + 78330x^8 + 68372x^7 + 413060x^6 + 412040x^5 + 1121134x^4 + 724230x^3 + 833204x^2 + 254796x + 152479	\( 2^{24}\cdot 5^{8}\cdot 29^{6}\cdot 101^{4} \)	16T1276	$[2, 2, 868]$ (GRH)
16.16.405651805355453454745600000000.1	x^16 - 4x^15 - 60x^14 + 148x^13 + 1448x^12 - 1330x^11 - 15338x^10 - 1892x^9 + 61256x^8 + 28872x^7 - 96724x^6 - 53134x^5 + 67075x^4 + 31622x^3 - 22918x^2 - 6152x + 3379	\( 2^{24}\cdot 5^{8}\cdot 29^{6}\cdot 101^{4} \)	16T1276	Trivial (GRH)
16.0.1002674797153076232861572265625.1	x^16 - 3x^15 + 110x^14 - 205x^13 + 4689x^12 - 3878x^11 + 101693x^10 + 19015x^9 + 1258001x^8 + 1498347x^7 + 9604628x^6 + 19095936x^5 + 49007769x^4 + 100830379x^3 + 159770709x^2 + 203130409x + 194676821	\( 5^{12}\cdot 29^{6}\cdot 1621^{4} \)	16T1276	$[2, 2, 6906]$ (GRH)
16.0.1435330823196597981282304000000.1	x^16 - 8x^15 + 64x^14 - 302x^13 + 1319x^12 - 4374x^11 + 13442x^10 - 33304x^9 + 81289x^8 - 135444x^7 + 319922x^6 - 236196x^5 + 1151393x^4 - 87862x^3 + 3213860x^2 + 1704014x + 343311	\( 2^{24}\cdot 5^{6}\cdot 13^{4}\cdot 61^{8} \)	16T1276	$[2]$ (GRH)
16.0.1435330823196597981282304000000.2	x^16 - 2x^15 - 8x^14 - 146x^13 + 557x^12 + 1818x^11 - 3724x^10 - 9986x^9 + 7570x^8 - 26398x^7 + 119892x^6 - 39392x^5 + 127084x^4 - 139886x^3 - 34402x^2 + 30056x + 13421	\( 2^{24}\cdot 5^{6}\cdot 13^{4}\cdot 61^{8} \)	16T1276	$[2]$ (GRH)
16.0.5167113728869511408443358969856.1	x^16 + 48x^14 + 684x^12 + 3744x^10 + 20406x^8 + 73296x^6 + 191916x^4 + 199584x^2 + 1089	\( 2^{66}\cdot 3^{14}\cdot 11^{4} \)	16T1276	$[2, 4]$ (GRH)
16.8.5167113728869511408443358969856.1	x^16 - 48x^14 - 48x^13 + 900x^12 + 1968x^11 - 6552x^10 - 25536x^9 + 942x^8 + 112032x^7 + 127728x^6 - 144432x^5 - 358920x^4 - 73008x^3 + 281664x^2 + 171936x - 21978	\( 2^{66}\cdot 3^{14}\cdot 11^{4} \)	16T1276	Trivial (GRH)
16.0.5167113728869511408443358969856.2	x^16 - 96x^13 - 468x^12 + 144x^11 + 5064x^10 + 15168x^9 + 35790x^8 + 91296x^7 + 190656x^6 + 286992x^5 + 362088x^4 + 475632x^3 + 589680x^2 + 496800x + 200934	\( 2^{66}\cdot 3^{14}\cdot 11^{4} \)	16T1276	$[2, 2]$ (GRH)
16.8.5167113728869511408443358969856.2	x^16 - 48x^14 - 48x^13 + 792x^12 + 1488x^11 - 4992x^10 - 15984x^9 - 2112x^8 + 38016x^7 + 38664x^6 - 23616x^5 - 60444x^4 - 10656x^3 + 36936x^2 + 12528x - 11007	\( 2^{66}\cdot 3^{14}\cdot 11^{4} \)	16T1276	Trivial (GRH)
16.0.548063673574853724539547811840000.1	x^16 - 14x^14 + 141x^12 - 1192x^10 + 8566x^8 - 40274x^6 + 218348x^4 - 395460x^2 + 1221025	\( 2^{24}\cdot 5^{4}\cdot 13^{6}\cdot 101^{8} \)	16T1276	$[2, 2, 18]$ (GRH)
16.8.548063673574853724539547811840000.1	x^16 - 48x^14 - 30x^12 + 9644x^10 + 48747x^8 + 2132x^6 - 33462x^4 - 3380x^2 + 4225	\( 2^{24}\cdot 5^{4}\cdot 13^{6}\cdot 101^{8} \)	16T1276	$[2, 2]$ (GRH)
16.0.548063673574853724539547811840000.2	x^16 + 14x^14 + 141x^12 + 1192x^10 + 8566x^8 + 40274x^6 + 218348x^4 + 395460x^2 + 1221025	\( 2^{24}\cdot 5^{4}\cdot 13^{6}\cdot 101^{8} \)	16T1276	$[2, 2, 18]$ (GRH)
16.8.548063673574853724539547811840000.2	x^16 + 48x^14 - 30x^12 - 9644x^10 + 48747x^8 - 2132x^6 - 33462x^4 + 3380x^2 + 4225	\( 2^{24}\cdot 5^{4}\cdot 13^{6}\cdot 101^{8} \)	16T1276	$[2]$ (GRH)
16.8.4134006486278719588795586854986572265625.1	x^16 - 4x^15 - 290x^14 + 1060x^13 + 12775x^12 - 42032x^11 + 1094828x^10 - 2557780x^9 + 20197965x^8 - 32604540x^7 + 117179468x^6 - 118981912x^5 + 97186535x^4 - 236386720x^3 - 414545290x^2 + 61506276x + 16346881	\( 5^{14}\cdot 29^{6}\cdot 101^{4}\cdot 149^{6} \)	16T1276	$[2, 4]$ (GRH)
16.0.42171000166529218525303781507718023681640625.1	x^16 - 5x^15 - 256x^14 + 1340x^13 + 23522x^12 - 114855x^11 - 611068x^10 + 2287230x^9 + 12681390x^8 - 119888075x^7 + 596167768x^6 - 1956930200x^5 + 9073021957x^4 - 18803061080x^3 + 49085212716x^2 - 24527109840x + 103425840496	\( 5^{14}\cdot 29^{6}\cdot 101^{6}\cdot 149^{6} \)	16T1276	$[2, 4, 8, 24]$ (GRH)