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 34 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.1824028217829228544.1	x^16 - 4x^15 + 12x^14 - 32x^13 + 66x^12 - 112x^11 + 180x^10 - 224x^9 + 264x^8 - 248x^7 + 220x^6 - 144x^5 + 92x^4 - 48x^3 + 24x^2 - 8x + 2	\( 2^{46}\cdot 7^{2}\cdot 23^{2} \)	16T860	Trivial
16.0.2523470413267206144.1	x^16 - 6x^15 + 20x^14 - 44x^13 + 62x^12 - 84x^11 + 116x^10 - 84x^9 + 88x^8 - 84x^7 + 16x^6 - 40x^5 + 12x^4 + 8x^3 + 16x^2 + 8x + 4	\( 2^{28}\cdot 3^{12}\cdot 7^{2}\cdot 19^{2} \)	16T860	Trivial
16.0.3520699409764825344.2	x^16 - 2x^15 - 2x^14 - 3x^13 + 9x^12 + 19x^11 - 18x^10 - 30x^9 - 8x^8 + 43x^7 + 202x^6 + 362x^5 + 405x^4 + 357x^3 + 218x^2 + 85x + 25	\( 2^{8}\cdot 3^{12}\cdot 7^{8}\cdot 67^{2} \)	16T860	Trivial
16.0.4580284825600000000.1	x^16 - 6x^15 + 14x^14 - 6x^13 - 38x^12 + 76x^11 - 8x^10 - 142x^9 + 143x^8 + 92x^7 - 228x^6 + 22x^5 + 172x^4 - 70x^3 - 70x^2 + 48x + 29	\( 2^{28}\cdot 5^{8}\cdot 11^{2}\cdot 19^{2} \)	16T860	Trivial
16.0.10670414233600000000.1	x^16 - 6x^15 + 20x^14 - 54x^13 + 104x^12 - 148x^11 + 220x^10 - 302x^9 + 291x^8 - 300x^7 + 384x^6 - 338x^5 + 250x^4 - 278x^3 + 216x^2 - 60x + 29	\( 2^{28}\cdot 5^{8}\cdot 11^{2}\cdot 29^{2} \)	16T860	Trivial (GRH)
16.0.10670414233600000000.2	x^16 - 4x^15 + 26x^13 - 32x^12 - 66x^11 + 142x^10 + 76x^9 - 317x^8 - 34x^7 + 450x^6 + 24x^5 - 416x^4 - 86x^3 + 234x^2 + 154x + 29	\( 2^{28}\cdot 5^{8}\cdot 11^{2}\cdot 29^{2} \)	16T860	Trivial
16.12.6052981596828100000000.1	x^16 - 5x^15 - 2x^14 + 49x^13 - 70x^12 - 79x^11 + 250x^10 - 116x^9 - 87x^8 + 114x^7 - 362x^6 + 345x^5 + 203x^4 - 255x^3 - 21x^2 + 37x - 1	\( 2^{8}\cdot 5^{8}\cdot 11^{2}\cdot 29^{8} \)	16T860	Trivial (GRH)
16.0.66183076013297341825024.4	x^16 - 4x^15 - 4x^14 + 28x^13 + 10x^12 - 96x^11 - 50x^10 + 228x^9 + 219x^8 - 420x^7 - 462x^6 + 424x^5 + 546x^4 - 224x^3 - 164x^2 - 32x + 64	\( 2^{32}\cdot 17^{8}\cdot 47^{2} \)	16T860	Trivial (GRH)
16.0.66183076013297341825024.5	x^16 - 4x^15 + 10x^14 - 40x^13 + 157x^12 - 404x^11 + 772x^10 - 1216x^9 + 1544x^8 - 1520x^7 + 1152x^6 - 208x^5 - 660x^4 + 432x^3 + 128x^2 - 32x + 16	\( 2^{32}\cdot 17^{8}\cdot 47^{2} \)	16T860	Trivial (GRH)
16.8.67791400715173078515625.1	x^16 - 3x^15 - 9x^14 + 33x^13 + 28x^12 - 137x^11 - 60x^10 + 282x^9 + 207x^8 - 267x^7 - 600x^6 - 225x^5 + 1143x^4 + 834x^3 - 1089x^2 - 568x + 149	\( 5^{8}\cdot 19^{2}\cdot 29^{8}\cdot 31^{2} \)	16T860	Trivial (GRH)
16.12.231260683111582301945856.1	x^16 - 22x^14 - 6x^13 + 151x^12 + 162x^11 - 376x^10 - 936x^9 - 242x^8 + 1572x^7 + 2048x^6 + 288x^5 - 1196x^4 - 936x^3 - 184x^2 + 48x + 16	\( 2^{24}\cdot 3^{12}\cdot 11^{10} \)	16T860	Trivial (GRH)
16.4.231260683111582301945856.1	x^16 + 2x^14 - 18x^13 + x^12 - 60x^11 + 89x^10 - 138x^9 + 412x^8 - 168x^7 + 935x^6 - 1590x^5 + 745x^4 - 1524x^3 + 2309x^2 - 1248x + 169	\( 2^{24}\cdot 3^{12}\cdot 11^{10} \)	16T860	Trivial (GRH)
16.4.231260683111582301945856.2	x^16 + 6x^14 - 6x^13 + 7x^12 - 54x^11 - 72x^10 - 72x^9 - 438x^8 - 276x^7 - 1416x^6 - 1344x^5 - 1196x^4 - 1896x^3 - 1032x^2 - 144x + 16	\( 2^{24}\cdot 3^{12}\cdot 11^{10} \)	16T860	$[2]$ (GRH)
16.12.404484175737229236240384.1	x^16 - 8x^14 - 32x^12 + 424x^10 - 1190x^8 + 952x^6 + 448x^4 - 728x^2 + 169	\( 2^{52}\cdot 3^{12}\cdot 13^{2} \)	16T860	Trivial (GRH)
16.4.404484175737229236240384.1	x^16 + 8x^14 - 32x^12 - 424x^10 - 1190x^8 - 952x^6 + 448x^4 + 728x^2 + 169	\( 2^{52}\cdot 3^{12}\cdot 13^{2} \)	16T860	Trivial (GRH)
16.12.404484175737229236240384.2	x^16 - 20x^14 - 16x^13 + 124x^12 + 264x^11 - 116x^10 - 1272x^9 - 1460x^8 + 1600x^7 + 4492x^6 + 1928x^5 - 2812x^4 - 3592x^3 - 1484x^2 - 160x + 25	\( 2^{52}\cdot 3^{12}\cdot 13^{2} \)	16T860	Trivial (GRH)
16.4.404484175737229236240384.2	x^16 + 12x^14 - 16x^13 + 44x^12 - 168x^11 - 624x^9 - 42x^8 - 16x^7 + 1200x^6 + 1272x^5 - 852x^4 - 1328x^3 - 48x^2 + 880x - 242	\( 2^{52}\cdot 3^{12}\cdot 13^{2} \)	16T860	Trivial (GRH)
16.8.627509100418278400000000.3	x^16 - x^14 - 24x^12 + 4x^10 + 162x^8 + 67x^6 - 204x^4 - 70x^2 + 49	\( 2^{16}\cdot 5^{8}\cdot 7^{2}\cdot 29^{8} \)	16T860	Trivial (GRH)
16.8.627509100418278400000000.4	x^16 + 6x^14 - 13x^12 - 102x^10 + 27x^8 + 438x^6 + 25x^4 - 252x^2 + 49	\( 2^{16}\cdot 5^{8}\cdot 7^{2}\cdot 29^{8} \)	16T860	Trivial (GRH)
16.8.627509100418278400000000.5	x^16 + x^14 - 24x^12 - 4x^10 + 162x^8 - 67x^6 - 204x^4 + 70x^2 + 49	\( 2^{16}\cdot 5^{8}\cdot 7^{2}\cdot 29^{8} \)	16T860	Trivial (GRH)
16.8.559392347252465689600000000.1	x^16 + 10x^14 - 174x^12 - 2000x^10 - 108x^8 + 28500x^6 - 16191x^4 - 58520x^2 + 43681	\( 2^{16}\cdot 5^{8}\cdot 11^{2}\cdot 19^{2}\cdot 29^{8} \)	16T860	Trivial (GRH)
16.8.691540078695480573937890625.1	x^16 - 5x^15 + 2x^14 + 38x^13 - 95x^12 + 78x^11 - 2606x^10 - 3437x^9 + 21742x^8 + 53403x^7 + 73070x^6 + 55760x^5 - 30743x^4 - 68356x^3 - 132106x^2 - 95081x + 56399	\( 5^{8}\cdot 19^{2}\cdot 29^{8}\cdot 31^{2}\cdot 101^{2} \)	16T860	$[2]$ (GRH)
16.8.805429631896971345844140625.1	x^16 - 3x^15 + 3x^14 - x^13 - 189x^12 + 486x^11 + 241x^10 - 1355x^9 - 2302x^8 - 10220x^7 + 83698x^6 - 55427x^5 - 319591x^4 + 607370x^3 + 66140x^2 - 661000x + 228400	\( 5^{8}\cdot 19^{2}\cdot 29^{8}\cdot 31^{2}\cdot 109^{2} \)	16T860	$[2]$ (GRH)
16.8.992533897870849042547265625.1	x^16 - 2x^15 - 2x^14 + 9x^13 - 118x^12 + 184x^11 - 512x^10 + 1596x^9 + 760x^8 - 576x^7 + 12482x^6 - 31296x^5 - 5460x^4 + 63447x^3 - 77480x^2 - 30821x + 89899	\( 5^{8}\cdot 11^{4}\cdot 19^{2}\cdot 29^{8}\cdot 31^{2} \)	16T860	$[2]$ (GRH)
16.8.992533897870849042547265625.2	x^16 - 6x^15 + 4x^14 + 29x^13 - 250x^12 + 1136x^11 - 2091x^10 - 1045x^9 + 19210x^8 - 41847x^7 + 66320x^6 - 66691x^5 - 40185x^4 + 82699x^3 - 226205x^2 + 176189x + 54391	\( 5^{8}\cdot 11^{4}\cdot 19^{2}\cdot 29^{8}\cdot 31^{2} \)	16T860	$[2]$ (GRH)
16.0.4442777237269582873600000000.1	x^16 + 55x^14 + 1229x^12 + 14475x^10 + 97712x^8 + 383925x^6 + 845081x^4 + 921785x^2 + 346921	\( 2^{16}\cdot 5^{8}\cdot 19^{2}\cdot 29^{8}\cdot 31^{2} \)	16T860	$[2, 2, 586]$ (GRH)
16.16.4442777237269582873600000000.1	x^16 - 55x^14 + 1229x^12 - 14475x^10 + 97712x^8 - 383925x^6 + 845081x^4 - 921785x^2 + 346921	\( 2^{16}\cdot 5^{8}\cdot 19^{2}\cdot 29^{8}\cdot 31^{2} \)	16T860	Trivial (GRH)
16.0.9670824485325868057600000000.1	x^16 + 56x^14 + 1281x^12 + 15589x^10 + 110298x^8 + 463897x^6 + 1129849x^4 + 1453837x^2 + 755161	\( 2^{16}\cdot 5^{8}\cdot 11^{2}\cdot 29^{8}\cdot 79^{2} \)	16T860	$[2, 2, 850]$ (GRH)
16.16.29939112302672824345600000000.1	x^16 - 65x^14 + 1729x^12 - 24485x^10 + 201492x^8 - 984815x^6 + 2778681x^4 - 4090075x^2 + 2337841	\( 2^{16}\cdot 5^{8}\cdot 11^{2}\cdot 29^{8}\cdot 139^{2} \)	16T860	Trivial (GRH)
16.0.57456715021727885253362581504.1	x^16 - 64x^14 + 1900x^12 - 33880x^10 + 381955x^8 - 2678996x^6 + 11464256x^4 - 27917400x^2 + 29964676	\( 2^{40}\cdot 7^{2}\cdot 17^{10}\cdot 23^{2} \)	16T860	$[2, 2]$ (GRH)
16.8.401462406422482169881600000000.1	x^16 - 27x^14 - 391x^12 + 12083x^10 + 14558x^8 - 954119x^6 - 406089x^4 + 20161999x^2 + 31348801	\( 2^{16}\cdot 5^{8}\cdot 11^{2}\cdot 29^{8}\cdot 509^{2} \)	16T860	Trivial (GRH)
16.0.632158804568484064343109765625.1	x^16 - 6x^15 + 7x^14 + 85x^13 - 327x^12 + 105x^11 + 2540x^10 - 7304x^9 - 1224x^8 + 45319x^7 - 39606x^6 - 42651x^5 + 160574x^4 - 99582x^3 + 36474x^2 - 7017x + 551	\( 5^{8}\cdot 29^{2}\cdot 89^{2}\cdot 149^{8} \)	16T860	$[2]$ (GRH)
16.8.645576055826149774217152338862890625.1	x^16 - x^15 - 62x^14 - 803x^13 - 6364x^12 + 28486x^11 + 560949x^10 + 4108102x^9 + 12524048x^8 - 80124311x^7 - 1020941616x^6 - 5169819990x^5 - 12573808799x^4 - 17661455410x^3 - 15689345750x^2 - 6979244050x - 406670525	\( 5^{8}\cdot 13^{2}\cdot 97^{4}\cdot 101^{10} \)	16T860	$[2, 6]$ (GRH)
16.8.645576055826149774217152338862890625.2	x^16 - 2x^15 - 186x^14 + 212x^13 - 3859x^12 - 64746x^11 + 469183x^10 - 1573763x^9 + 8042475x^8 + 20224282x^7 - 27498496x^6 + 46417704x^5 - 1273883888x^4 - 1784768672x^3 - 2403534464x^2 + 27785101440x - 18802865920	\( 5^{8}\cdot 13^{2}\cdot 97^{4}\cdot 101^{10} \)	16T860	$[2, 2]$ (GRH)