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 54)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.464775560904572928.1	x^16 - 4x^15 + 8x^14 - 12x^13 + 15x^12 - 12x^11 + 2x^10 + 4x^9 - 2x^8 - 2x^6 + 4x^5 - 2x^4 + 1	\( 2^{32}\cdot 3^{2}\cdot 17\cdot 29^{4} \)	16T1887	Trivial
16.2.649700179607289856.1	x^16 - 4x^13 + x^12 + 6x^10 - 4x^9 - x^8 - 4x^7 + 6x^6 + x^4 - 4x^3 + 1	\( -\,2^{32}\cdot 31\cdot 47^{4} \)	16T1887	Trivial
16.0.754661449441280000.1	x^16 - 6x^15 + 18x^14 - 38x^13 + 76x^12 - 134x^11 + 190x^10 - 242x^9 + 284x^8 - 288x^7 + 246x^6 - 180x^5 + 121x^4 - 70x^3 + 30x^2 - 8x + 1	\( 2^{16}\cdot 5^{4}\cdot 113^{5} \)	16T1887	Trivial
16.6.832833149900000000.1	x^16 - 2x^15 - 2x^14 - x^13 + 6x^12 + 9x^11 - 5x^10 - 16x^9 - 15x^8 + 19x^7 + 15x^6 + 4x^5 - 16x^4 - x^3 + x^2 + 3x - 1	\( -\,2^{8}\cdot 5^{8}\cdot 59\cdot 109^{4} \)	16T1887	Trivial
16.0.1425697426100000000.1	x^16 - 6x^15 + 18x^14 - 39x^13 + 68x^12 - 95x^11 + 119x^10 - 139x^9 + 130x^8 - 106x^7 + 85x^6 - 55x^5 + 30x^4 - 15x^3 + 8x^2 - x + 1	\( 2^{8}\cdot 5^{8}\cdot 101\cdot 109^{4} \)	16T1887	Trivial
16.2.2131488231100000000.1	x^16 - 3x^15 + 5x^14 - 4x^13 - 2x^12 + 13x^11 - 24x^10 + 32x^9 - 35x^8 + 32x^7 - 24x^6 + 13x^5 - 2x^4 - 4x^3 + 5x^2 - 3x + 1	\( -\,2^{8}\cdot 5^{8}\cdot 109^{4}\cdot 151 \)	16T1887	Trivial
16.0.2554962714100000000.1	x^16 - 2x^15 + 7x^14 - 13x^13 + 20x^12 - 22x^11 + 16x^10 - 8x^9 + 3x^8 - 8x^7 + 16x^6 - 22x^5 + 20x^4 - 13x^3 + 7x^2 - 2x + 1	\( 2^{8}\cdot 5^{8}\cdot 109^{4}\cdot 181 \)	16T1887	Trivial
16.6.2696120875100000000.1	x^16 - 4x^14 + 2x^12 - 14x^11 - 6x^10 + 40x^9 + 35x^8 - 30x^7 - 24x^6 + 8x^5 - 13x^4 - 8x^3 + 11x^2 + 4x - 1	\( -\,2^{8}\cdot 5^{8}\cdot 109^{4}\cdot 191 \)	16T1887	Trivial
16.4.24617983278400000000.1	x^16 - x^15 + 4x^14 - 10x^13 + 8x^12 - 17x^11 + 18x^10 + 7x^9 - 27x^8 + 36x^7 - 68x^6 + 110x^5 - 6x^4 - 28x^3 - 48x^2 - 12x + 4	\( 2^{12}\cdot 5^{8}\cdot 109^{5} \)	16T1887	Trivial
16.4.24617983278400000000.2	x^16 - x^15 - 3x^14 + 6x^13 + 5x^12 - 5x^11 + 3x^10 - 16x^9 - 42x^8 + 43x^7 + 105x^6 + 8x^5 - 75x^4 - 53x^3 - 37x^2 - 30x - 9	\( 2^{12}\cdot 5^{8}\cdot 109^{5} \)	16T1887	Trivial
16.8.364978541081600000000.1	x^16 - 6x^15 + 12x^14 - 4x^13 - 37x^12 + 86x^11 - 66x^10 - 32x^9 + 48x^8 + 110x^7 - 104x^6 - 62x^5 + 24x^4 + 48x^3 - 14x^2 - 4x + 1	\( 2^{16}\cdot 5^{8}\cdot 101\cdot 109^{4} \)	16T1887	Trivial
16.4.393887732454400000000.1	x^16 - 5x^15 + 12x^14 - 14x^13 - 25x^12 + 162x^11 - 448x^10 + 887x^9 - 1366x^8 + 1713x^7 - 1778x^6 + 1514x^5 - 1053x^4 + 582x^3 - 250x^2 + 81x - 9	\( 2^{16}\cdot 5^{8}\cdot 109^{5} \)	16T1887	Trivial
16.8.393887732454400000000.1	x^16 - x^15 - 11x^14 + 11x^13 + 33x^12 - 52x^11 - 20x^10 + 135x^9 - 31x^8 - 142x^7 + 98x^6 + 86x^5 - 82x^4 - 20x^3 + 52x^2 + 28x + 4	\( 2^{16}\cdot 5^{8}\cdot 109^{5} \)	16T1887	Trivial
16.4.393887732454400000000.2	x^16 - 2x^15 - 7x^14 + 15x^13 + 28x^12 - 83x^11 - 35x^10 + 263x^9 - 136x^8 - 320x^7 + 427x^6 - 13x^5 - 276x^4 + 185x^3 - 49x^2 + 7x - 1	\( 2^{16}\cdot 5^{8}\cdot 109^{5} \)	16T1887	Trivial
16.2.5761803985554132434944.1	x^16 - 2x^14 - 3x^12 + 46x^10 + 79x^8 + 50x^6 + 4x^4 - 16x^2 - 1	\( -\,2^{34}\cdot 761^{4} \)	16T1887	Trivial
16.6.5761803985554132434944.1	x^16 + 2x^14 - 3x^12 - 46x^10 + 79x^8 - 50x^6 + 4x^4 + 16x^2 - 1	\( -\,2^{34}\cdot 761^{4} \)	16T1887	Trivial
16.2.5761803985554132434944.2	x^16 + 16x^12 + 14x^10 + 49x^8 + 102x^6 - 57x^4 - 110x^2 - 1	\( -\,2^{34}\cdot 761^{4} \)	16T1887	Trivial
16.6.5761803985554132434944.2	x^16 + 16x^12 - 14x^10 + 49x^8 - 102x^6 - 57x^4 + 110x^2 - 1	\( -\,2^{34}\cdot 761^{4} \)	16T1887	Trivial
16.0.25218049053069374652416.1	x^16 - 4x^15 + 14x^14 - 40x^13 + 113x^12 - 288x^11 + 622x^10 - 1056x^9 + 1388x^8 - 1404x^7 + 1128x^6 - 724x^5 + 366x^4 - 144x^3 + 42x^2 - 8x + 1	\( 2^{32}\cdot 7\cdot 19^{4}\cdot 23^{5} \)	16T1887	Trivial
16.0.25218049053069374652416.2	x^16 - 12x^13 - 13x^12 + 4x^11 + 58x^10 + 24x^9 - 39x^8 + 104x^7 + 166x^6 + 184x^5 + 179x^4 + 68x^3 + 40x^2 + 4x + 1	\( 2^{32}\cdot 7\cdot 19^{4}\cdot 23^{5} \)	16T1887	Trivial
16.8.55677842407053355078125.1	x^16 - 3x^15 - 9x^14 + 29x^13 + 24x^12 - 89x^11 - 44x^10 + 214x^9 - 142x^8 - 325x^7 + 930x^6 - 806x^5 + 233x^4 - 62x^3 + 75x^2 - 18x - 4	\( 3^{4}\cdot 5^{8}\cdot 29\cdot 2791^{4} \)	16T1887	Trivial (GRH)
16.8.55677842407053355078125.2	x^16 - 4x^15 + 25x^13 - 57x^12 + 49x^11 + 36x^10 - 190x^9 + 400x^8 - 569x^7 + 475x^6 - 146x^5 - 89x^4 + 34x^3 + 49x^2 + 6x - 1	\( 3^{4}\cdot 5^{8}\cdot 29\cdot 2791^{4} \)	16T1887	Trivial (GRH)
16.10.59517693607539793359375.1	x^16 - 4x^15 + 2x^14 + 18x^13 - 56x^12 + 50x^11 + 78x^10 - 191x^9 + 176x^8 - 212x^7 + 148x^6 + 184x^5 - 300x^4 + 70x^3 + 67x^2 - 34x + 4	\( -\,3^{4}\cdot 5^{8}\cdot 31\cdot 2791^{4} \)	16T1887	Trivial (GRH)
16.6.59517693607539793359375.1	x^16 + 4x^14 - 26x^12 - 131x^10 - 113x^8 + 128x^6 + 159x^4 - 7x^2 - 31	\( -\,3^{4}\cdot 5^{8}\cdot 31\cdot 2791^{4} \)	16T1887	Trivial
16.6.113275610414349929296875.1	x^16 - 2x^15 - 3x^14 + 14x^13 - 48x^11 + 61x^10 + 92x^9 - 231x^8 - 35x^7 + 257x^6 - 9x^5 - 122x^4 - 14x^3 + 42x^2 - 3x - 1	\( -\,3^{4}\cdot 5^{8}\cdot 59\cdot 2791^{4} \)	16T1887	Trivial
16.10.136314717617268558984375.1	x^16 - x^15 - 13x^14 + 11x^13 + 69x^12 - 50x^11 - 225x^10 + 90x^9 + 602x^8 + 248x^7 - 1029x^6 - 1404x^5 + 200x^4 + 1461x^3 + 869x^2 + 101x - 19	\( -\,3^{4}\cdot 5^{8}\cdot 71\cdot 2791^{4} \)	16T1887	Trivial (GRH)
16.10.136314717617268558984375.2	x^16 - x^15 - 11x^14 + 24x^13 + 30x^12 - 208x^11 + 49x^10 + 905x^9 - 313x^8 - 2256x^7 + 261x^6 + 3397x^5 + 435x^4 - 2898x^3 - 751x^2 + 971x + 349	\( -\,3^{4}\cdot 5^{8}\cdot 71\cdot 2791^{4} \)	16T1887	Trivial (GRH)
16.10.151674122419214312109375.1	x^16 - 3x^15 - 13x^14 + 37x^13 + 33x^12 - 120x^11 + 154x^10 + 28x^9 - 470x^8 + 443x^7 - 25x^6 - 228x^5 + 260x^4 - 323x^3 + 291x^2 + 95x - 151	\( -\,3^{4}\cdot 5^{8}\cdot 79\cdot 2791^{4} \)	16T1887	Trivial (GRH)
16.6.151674122419214312109375.1	x^16 - 6x^15 + 10x^14 + 13x^13 - 91x^12 + 162x^11 - 99x^10 + 69x^9 - 622x^8 + 1570x^7 - 1221x^6 - 320x^5 + 691x^4 + 129x^3 - 291x^2 - 117x - 9	\( -\,3^{4}\cdot 5^{8}\cdot 79\cdot 2791^{4} \)	16T1887	Trivial (GRH)
16.8.161330511595515708178432.1	x^16 - 6x^15 + 13x^14 - 10x^13 - 33x^12 + 184x^11 - 384x^10 + 340x^9 + 75x^8 - 1010x^7 + 2571x^6 - 3234x^5 + 1502x^4 + 834x^3 - 1193x^2 + 134x + 233	\( 2^{36}\cdot 7\cdot 761^{4} \)	16T1887	Trivial
16.12.193912485624565133203125.1	x^16 - 2x^15 - 15x^14 + 37x^13 + 25x^12 - 92x^11 + 21x^10 + 62x^9 - 152x^8 + 71x^7 + 214x^6 - 79x^5 - 140x^4 + x^3 + 35x^2 + 11x + 1	\( 3^{4}\cdot 5^{8}\cdot 101\cdot 2791^{4} \)	16T1887	Trivial (GRH)
16.4.193912485624565133203125.1	x^16 - 8x^15 + 29x^14 - 63x^13 + 66x^12 + 59x^11 - 368x^10 + 751x^9 - 817x^8 + 269x^7 + 822x^6 - 1785x^5 + 2029x^4 - 1503x^3 + 742x^2 - 224x + 31	\( 3^{4}\cdot 5^{8}\cdot 101\cdot 2791^{4} \)	16T1887	Trivial
16.4.209271890426510886328125.1	x^16 - 5x^15 + 2x^14 + 16x^13 - 23x^12 - 3x^11 + 17x^10 + 19x^9 - 49x^8 + 19x^7 + 17x^6 - 3x^5 - 23x^4 + 16x^3 + 2x^2 - 5x + 1	\( 3^{4}\cdot 5^{8}\cdot 109\cdot 2791^{4} \)	16T1887	Trivial
16.8.209271890426510886328125.1	x^16 - x^15 + 3x^13 + 7x^12 + x^11 - 65x^10 + 90x^9 + 30x^8 - 231x^7 + 16x^6 + 102x^5 + 173x^4 - 106x^3 - 11x^2 + 11x - 1	\( 3^{4}\cdot 5^{8}\cdot 109\cdot 2791^{4} \)	16T1887	Trivial (GRH)
16.4.286068914436239651953125.1	x^16 - 4x^15 + 11x^14 - 21x^13 - 2x^12 + 116x^11 - 416x^10 + 822x^9 - 973x^8 + 903x^7 - 720x^6 + 388x^5 + 104x^4 - 205x^3 - 40x^2 + 46x + 19	\( 3^{4}\cdot 5^{8}\cdot 149\cdot 2791^{4} \)	16T1887	Trivial
16.8.286068914436239651953125.1	x^16 - 8x^15 + 29x^14 - 63x^13 + 48x^12 + 167x^11 - 566x^10 + 751x^9 - 169x^8 - 1135x^7 + 1976x^6 - 1521x^5 + 156x^4 + 759x^3 - 689x^2 + 264x - 16	\( 3^{4}\cdot 5^{8}\cdot 149\cdot 2791^{4} \)	16T1887	Trivial (GRH)
16.12.347506533644022664453125.1	x^16 - 6x^15 - x^14 + 70x^13 - 124x^12 - 121x^11 + 588x^10 - 649x^9 + 21x^8 + 1013x^7 - 1882x^6 + 1968x^5 - 1420x^4 + 792x^3 - 302x^2 + 54x - 1	\( 3^{4}\cdot 5^{8}\cdot 181\cdot 2791^{4} \)	16T1887	Trivial (GRH)
16.4.347506533644022664453125.1	x^16 - 5x^15 + 9x^14 - 8x^13 + 13x^12 - 107x^11 + 330x^10 - 507x^9 + 429x^8 - 189x^7 + 250x^6 - 657x^5 + 649x^4 - 234x^3 + 301x^2 - 173x - 181	\( 3^{4}\cdot 5^{8}\cdot 181\cdot 2791^{4} \)	16T1887	Trivial
16.6.382065194448400608984375.1	x^16 - 4x^15 + 16x^14 - 36x^13 + 18x^12 + 196x^11 - 856x^10 + 1707x^9 - 1796x^8 + 24x^7 + 2602x^6 - 3114x^5 + 882x^4 + 1044x^3 - 1007x^2 + 303x - 29	\( -\,3^{4}\cdot 5^{8}\cdot 199\cdot 2791^{4} \)	16T1887	Trivial (GRH)
16.12.1349250316018193600000000.1	x^16 - 2x^15 - 6x^14 - 5x^13 + 65x^12 - 14x^11 - 369x^10 + 638x^9 + 339x^8 - 1497x^7 + 517x^6 + 927x^5 - 661x^4 - 66x^3 + 168x^2 - 48x + 4	\( 2^{12}\cdot 5^{8}\cdot 11^{5}\cdot 269^{4} \)	16T1887	Trivial (GRH)
16.12.1349250316018193600000000.2	x^16 - 18x^14 - 18x^13 + 116x^12 + 198x^11 - 334x^10 - 458x^9 + 19x^8 - 114x^7 + 1238x^6 + 1238x^5 - 1462x^4 - 986x^3 + 404x^2 + 104x - 29	\( 2^{12}\cdot 5^{8}\cdot 11^{5}\cdot 269^{4} \)	16T1887	Trivial (GRH)
16.14.1962545914208281600000000.1	x^16 - 15x^14 + 50x^12 + 57x^10 - 436x^8 + 575x^6 - 254x^4 + 39x^2 - 1	\( -\,2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 269^{4} \)	16T1887	Trivial (GRH)
16.2.1962545914208281600000000.1	x^16 + 18x^14 + 114x^12 + 246x^10 - 304x^8 - 2018x^6 - 2570x^4 - 1062x^2 - 121	\( -\,2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 269^{4} \)	16T1887	$[2, 2]$
16.8.6268842736282896089219072.1	x^16 - 16x^14 + 106x^12 - 382x^10 + 821x^8 - 1078x^6 + 851x^4 - 380x^2 + 68	\( 2^{40}\cdot 17\cdot 761^{4} \)	16T1887	Trivial
16.14.6625987515152409600000000.1	x^16 - 21x^14 + 119x^12 - 14x^10 - 1514x^8 + 3538x^6 - 2411x^4 + 367x^2 - 1	\( -\,2^{16}\cdot 3^{4}\cdot 5^{8}\cdot 7^{4}\cdot 191^{4} \)	16T1887	Trivial (GRH)
16.2.6625987515152409600000000.1	x^16 + 18x^14 + 113x^12 + 304x^10 + 304x^8 - 68x^6 - 272x^4 - 128x^2 - 16	\( -\,2^{16}\cdot 3^{4}\cdot 5^{8}\cdot 7^{4}\cdot 191^{4} \)	16T1887	Trivial
16.0.79443753352820378013007872.1	x^16 - 6x^15 + 37x^14 - 102x^13 + 317x^12 - 448x^11 + 1072x^10 - 1332x^9 + 4065x^8 - 2894x^7 + 7545x^6 - 1626x^5 + 15476x^4 + 998x^3 + 29185x^2 + 14710x + 37289	\( 2^{36}\cdot 3^{2}\cdot 383\cdot 761^{4} \)	16T1887	$[2]$ (GRH)
16.0.86934098534040750178435072.1	x^16 + 24x^14 + 246x^12 + 1398x^10 + 4771x^8 + 9842x^6 + 11581x^4 + 6530x^2 + 943	\( 2^{38}\cdot 23\cdot 41\cdot 761^{4} \)	16T1887	$[2, 4]$ (GRH)
16.16.20249017846305763737600000000.1	x^16 - 48x^14 + 800x^12 - 5980x^10 + 20187x^8 - 26126x^6 + 12988x^4 - 2674x^2 + 191	\( 2^{20}\cdot 3^{4}\cdot 5^{8}\cdot 7^{4}\cdot 191^{5} \)	16T1887	Trivial (GRH)
16.8.20249017846305763737600000000.1	x^16 - 20x^14 - 50x^12 + 2164x^10 - 1673x^8 - 57570x^6 + 65814x^4 + 54064x^2 + 191	\( 2^{20}\cdot 3^{4}\cdot 5^{8}\cdot 7^{4}\cdot 191^{5} \)	16T1887	Trivial (GRH)