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 70)

Label	Polynomial	Discriminant	Galois group	Class group
16.2.117614702500000000.1	x^16 + 3x^14 - 5x^10 - x^8 - x^6 - 8x^4 - 7x^2 - 1	\( -\,2^{8}\cdot 5^{10}\cdot 19^{6} \)	16T1774	Trivial
16.2.588073512500000000.1	x^16 - 4x^15 + 6x^14 - 8x^13 + 15x^12 - 19x^11 + 22x^10 - 36x^9 + 42x^8 - 36x^7 + 35x^6 - 37x^5 + 34x^4 - 29x^3 + 18x^2 - 6x + 1	\( -\,2^{8}\cdot 5^{11}\cdot 19^{6} \)	16T1774	Trivial
16.0.2234679347500000000.1	x^16 - 2x^10 + 11x^8 - 19x^4 + 19x^2 + 19	\( 2^{8}\cdot 5^{10}\cdot 19^{7} \)	16T1774	Trivial
16.4.2234679347500000000.1	x^16 - 3x^15 + 4x^14 + 5x^13 - 23x^12 + 31x^11 - 17x^10 - 33x^9 + 20x^8 + 9x^7 - 41x^6 + 28x^5 + 4x^4 - 22x^3 + 9x^2 - 1	\( 2^{8}\cdot 5^{10}\cdot 19^{7} \)	16T1774	Trivial
16.0.2234679347500000000.2	x^16 - x^15 + x^14 + 6x^13 - 7x^12 + 9x^11 + 5x^10 - 8x^9 + 26x^8 - 47x^7 + 85x^6 - 98x^5 + 79x^4 - 65x^3 + 45x^2 - 20x + 5	\( 2^{8}\cdot 5^{10}\cdot 19^{7} \)	16T1774	Trivial
16.0.4128508568837890625.1	x^16 - 2x^15 + 7x^14 - 16x^13 + 30x^12 - 37x^11 + 44x^10 - 55x^9 + 77x^8 - 95x^7 + 102x^6 - 91x^5 + 69x^4 - 48x^3 + 31x^2 - 16x + 4	\( 5^{10}\cdot 41^{6}\cdot 89 \)	16T1774	Trivial
16.4.11173396737500000000.1	x^16 - x^15 - 3x^14 + 3x^13 + x^12 + 21x^11 - 53x^10 + 37x^9 - 23x^8 + 72x^7 - 72x^6 - 6x^5 + 15x^4 - x^3 + 11x^2 - 2x + 1	\( 2^{8}\cdot 5^{11}\cdot 19^{7} \)	16T1774	Trivial
16.0.14101871965468750000.1	x^16 - 3x^15 + 3x^14 - 3x^13 + 12x^12 - 13x^11 - 4x^9 + 26x^8 - 13x^7 + 5x^6 - 15x^5 + 13x^4 + 9x^3 - x^2 + 2x + 1	\( 2^{4}\cdot 5^{10}\cdot 19\cdot 41^{6} \)	16T1774	Trivial
16.2.12982767816893310546875.1	x^16 - 3x^15 + 5x^14 - 10x^13 + 20x^12 + 36x^11 - 133x^10 + 30x^9 + 345x^8 - 825x^7 + 1187x^6 - 896x^5 - 10x^4 + 480x^3 - 280x^2 + 63x - 9	\( -\,5^{13}\cdot 41^{6}\cdot 2239 \)	16T1774	Trivial (GRH)
16.6.12982767816893310546875.1	x^16 - 8x^15 + 31x^14 - 77x^13 + 130x^12 - 143x^11 + 58x^10 + 139x^9 - 382x^8 + 551x^7 - 557x^6 + 416x^5 - 221x^4 + 74x^3 - 8x^2 - 4x + 1	\( -\,5^{13}\cdot 41^{6}\cdot 2239 \)	16T1774	Trivial (GRH)
16.2.43047819684062500000000.1	x^16 + 11x^14 + 46x^12 + 71x^10 - 79x^8 - 485x^6 - 770x^4 - 545x^2 - 145	\( -\,2^{8}\cdot 5^{13}\cdot 29\cdot 41^{6} \)	16T1774	Trivial (GRH)
16.6.43047819684062500000000.1	x^16 - 7x^15 + 21x^14 - 6x^13 - 159x^12 + 594x^11 - 1089x^10 + 924x^9 + 576x^8 - 3066x^7 + 4639x^6 - 3757x^5 + 669x^4 + 1941x^3 - 1926x^2 + 745x - 109	\( -\,2^{8}\cdot 5^{13}\cdot 29\cdot 41^{6} \)	16T1774	Trivial (GRH)
16.0.199677172441313720703125.1	x^16 - 4x^15 + 2x^14 + 5x^13 + 14x^12 + 7x^11 - 89x^10 - 129x^9 + 346x^8 - 411x^7 + 1941x^6 - 3183x^5 + 2826x^4 - 2640x^3 + 2840x^2 - 190x + 955	\( 5^{12}\cdot 41^{6}\cdot 172181 \)	16T1774	$[4]$ (GRH)
16.8.199677172441313720703125.1	x^16 - 8x^15 + 23x^14 - 21x^13 - 31x^12 + 95x^11 - 92x^10 + 42x^9 - 13x^8 - 13x^7 + 40x^6 - 24x^5 - 3x^3 - x^2 + 5x + 1	\( 5^{12}\cdot 41^{6}\cdot 172181 \)	16T1774	Trivial (GRH)
16.10.905895972737757998046875.1	x^16 - 2x^15 - 12x^14 + 16x^13 + 23x^12 + 39x^11 - 103x^10 - 67x^9 + 95x^8 + 44x^7 + 68x^6 - 102x^5 - 52x^4 + 73x^3 - 13x^2 - 4x + 1	\( -\,5^{10}\cdot 11^{6}\cdot 31^{6}\cdot 59 \)	16T1774	Trivial (GRH)
16.6.905895972737757998046875.1	x^16 - 4x^15 + 6x^14 - x^13 - 62x^12 + 121x^11 - 95x^10 + 357x^9 + 4x^8 - 541x^7 - 98x^6 - 712x^5 + 386x^4 - 330x^3 - 819x^2 - 703x - 361	\( -\,5^{10}\cdot 11^{6}\cdot 31^{6}\cdot 59 \)	16T1774	Trivial (GRH)
16.10.905895972737757998046875.2	x^16 - 4x^15 + 5x^14 + 15x^13 - 122x^12 + 239x^11 + 155x^10 - 1150x^9 + 1194x^8 + 388x^7 - 1137x^6 + 587x^5 - 634x^4 + 418x^3 + 407x^2 - 484x + 121	\( -\,5^{10}\cdot 11^{6}\cdot 31^{6}\cdot 59 \)	16T1774	Trivial (GRH)
16.6.905895972737757998046875.2	x^16 - 4x^15 + 13x^14 - 46x^13 + 89x^12 - 123x^11 + 45x^10 + 500x^9 - 1359x^8 + 2255x^7 - 2345x^6 - 811x^5 + 4146x^4 - 2040x^3 - 1355x^2 + 1325x - 275	\( -\,5^{10}\cdot 11^{6}\cdot 31^{6}\cdot 59 \)	16T1774	Trivial (GRH)
16.10.3930667271540102500000000.1	x^16 - x^14 - 63x^12 + 68x^10 + 1011x^8 - 1190x^6 - 600x^4 + 1166x^2 - 361	\( -\,2^{8}\cdot 5^{10}\cdot 11^{6}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.2.3930667271540102500000000.1	x^16 + 20x^14 + 140x^12 + 398x^10 + 291x^8 - 600x^6 - 1159x^4 - 661x^2 - 121	\( -\,2^{8}\cdot 5^{10}\cdot 11^{6}\cdot 31^{6} \)	16T1774	$[2, 2]$ (GRH)
16.10.3930667271540102500000000.2	x^16 - 9x^14 - 47x^12 + 305x^10 + 594x^8 - 1521x^6 - 987x^4 + 894x^2 - 121	\( -\,2^{8}\cdot 5^{10}\cdot 11^{6}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.10.3930667271540102500000000.3	x^16 - 20x^14 + 125x^12 - 134x^10 - 1064x^8 + 2350x^6 + 14x^4 - 72x^2 - 1	\( -\,2^{8}\cdot 5^{10}\cdot 11^{6}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.0.8393699763639770751953125.1	x^16 - 4x^15 + 12x^14 - 22x^13 + 57x^12 + x^11 - 258x^10 + 239x^9 - 1260x^8 + 2221x^7 + 3324x^6 - 6012x^5 + 13207x^4 - 26098x^3 + 22252x^2 - 17560x + 16871	\( 5^{12}\cdot 41^{6}\cdot 1279\cdot 5659 \)	16T1774	$[2]$ (GRH)
16.8.8393699763639770751953125.1	x^16 - 8x^15 + 15x^14 + 35x^13 - 136x^12 - 3x^11 + 388x^10 - 125x^9 - 644x^8 + 147x^7 + 753x^6 + 56x^5 - 561x^4 - 246x^3 + 164x^2 + 164x + 41	\( 5^{12}\cdot 41^{6}\cdot 1279\cdot 5659 \)	16T1774	Trivial (GRH)
16.2.19653336357700512500000000.1	x^16 + 27x^14 + 263x^12 + 1142x^10 + 2081x^8 + 220x^6 - 3850x^4 - 3630x^2 - 605	\( -\,2^{8}\cdot 5^{11}\cdot 11^{6}\cdot 31^{6} \)	16T1774	$[2]$ (GRH)
16.6.19653336357700512500000000.1	x^16 + 11x^14 - 43x^12 - 381x^10 + 956x^8 + 2625x^6 - 3655x^4 - 7090x^2 - 605	\( -\,2^{8}\cdot 5^{11}\cdot 11^{6}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.6.19653336357700512500000000.2	x^16 - 2x^15 - 16x^14 - 6x^13 + 72x^12 + 133x^11 - 2x^10 - 361x^9 - 529x^8 + 61x^7 + 738x^6 + 417x^5 + 52x^4 + 281x^3 - 16x^2 - 13x + 1	\( -\,2^{8}\cdot 5^{11}\cdot 11^{6}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.10.43237339986941127500000000.1	x^16 - 19x^14 + 80x^12 - 25x^10 - 291x^8 + 243x^6 + 218x^4 - 191x^2 - 11	\( -\,2^{8}\cdot 5^{10}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.14.43237339986941127500000000.1	x^16 - 18x^14 + 77x^12 + 180x^10 - 1551x^8 + 2568x^6 - 1493x^4 + 252x^2 - 11	\( -\,2^{8}\cdot 5^{10}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.6.43237339986941127500000000.1	x^16 - 2x^15 - 14x^14 + 44x^13 + 20x^12 - 478x^11 + 140x^10 + 3164x^9 + 1005x^8 - 9516x^7 - 9256x^6 + 6376x^5 + 10019x^4 + 2034x^3 + 2273x^2 + 2268x - 379	\( -\,2^{8}\cdot 5^{10}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.14.43237339986941127500000000.2	x^16 - 18x^14 + 105x^12 - 190x^10 - 136x^8 + 606x^6 - 448x^4 + 122x^2 - 11	\( -\,2^{8}\cdot 5^{10}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.12.43237339986941127500000000.1	x^16 - 14x^14 - 17x^12 + 620x^10 - 1009x^8 - 290x^6 + 1157x^4 - 448x^2 + 11	\( 2^{8}\cdot 5^{10}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.4.43237339986941127500000000.1	x^16 + 19x^14 + 97x^12 + 22x^10 - 785x^8 - 1302x^6 - 148x^4 + 166x^2 + 11	\( 2^{8}\cdot 5^{10}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.8.43237339986941127500000000.1	x^16 + 7x^14 - 44x^12 - 283x^10 - 51x^8 + 1347x^6 + 1356x^4 - 273x^2 + 11	\( 2^{8}\cdot 5^{10}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.12.43237339986941127500000000.2	x^16 - 12x^14 + 3x^12 + 370x^10 - 1324x^8 + 1650x^6 - 627x^4 - 88x^2 + 11	\( 2^{8}\cdot 5^{10}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.4.43237339986941127500000000.2	x^16 + 10x^14 - x^12 - 245x^10 - 664x^8 - 275x^6 + 539x^4 + 385x^2 + 11	\( 2^{8}\cdot 5^{10}\cdot 11^{7}\cdot 31^{6} \)	16T1774	$[4]$ (GRH)
16.8.43237339986941127500000000.2	x^16 - 2x^14 - 98x^12 - 90x^10 + 1001x^8 + 550x^6 - 2992x^4 - 176x^2 + 1331	\( 2^{8}\cdot 5^{10}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.12.43237339986941127500000000.3	x^16 - 20x^14 + 112x^12 - 82x^10 - 356x^8 + 268x^6 + 269x^4 - 148x^2 + 11	\( 2^{8}\cdot 5^{10}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.4.43237339986941127500000000.3	x^16 + 33x^14 + 381x^12 + 2043x^10 + 5294x^8 + 5683x^6 + 881x^4 - 247x^2 + 11	\( 2^{8}\cdot 5^{10}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.8.43237339986941127500000000.3	x^16 + x^14 - 133x^12 - 122x^10 + 865x^8 - 148x^6 - 708x^4 + 174x^2 + 11	\( 2^{8}\cdot 5^{10}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.12.43237339986941127500000000.4	x^16 - 31x^14 + 272x^12 - 600x^10 + 61x^8 + 440x^6 - 198x^4 - 11x^2 + 11	\( 2^{8}\cdot 5^{10}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.8.43237339986941127500000000.4	x^16 + 6x^14 - 51x^12 - 36x^10 + 384x^8 - 44x^6 - 616x^4 + 264x^2 + 11	\( 2^{8}\cdot 5^{10}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.6.98266681788502562500000000.1	x^16 + 9x^14 - 59x^12 - 476x^10 + 1121x^8 + 5440x^6 - 1070x^4 - 14300x^2 - 9025	\( -\,2^{8}\cdot 5^{12}\cdot 11^{6}\cdot 31^{6} \)	16T1774	$[2]$ (GRH)
16.0.216186699934705637500000000.1	x^16 - 5x^15 + 9x^14 + 36x^13 - 177x^12 + 376x^11 + 193x^10 - 2511x^9 + 4915x^8 - 6071x^7 + 12392x^6 - 15904x^5 + 21541x^4 - 22264x^3 + 15345x^2 - 8866x + 2981	\( 2^{8}\cdot 5^{11}\cdot 11^{7}\cdot 31^{6} \)	16T1774	$[2, 18]$ (GRH)
16.8.216186699934705637500000000.1	x^16 - 4x^15 - 17x^14 + 71x^13 + 129x^12 - 455x^11 - 647x^10 + 1258x^9 + 1858x^8 - 1784x^7 - 2993x^6 + 1984x^5 + 3809x^4 - 1413x^3 - 3769x^2 - 713x + 589	\( 2^{8}\cdot 5^{11}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.0.216186699934705637500000000.2	x^16 + 38x^14 + 530x^12 + 3356x^10 + 9879x^8 + 13470x^6 + 7705x^4 + 1225x^2 + 55	\( 2^{8}\cdot 5^{11}\cdot 11^{7}\cdot 31^{6} \)	16T1774	$[2, 18]$ (GRH)
16.8.216186699934705637500000000.2	x^16 - 3x^15 - 7x^14 + 5x^13 + 10x^12 + 123x^11 + 170x^10 + 131x^9 - 369x^8 - 3300x^7 - 5575x^6 - 3768x^5 + 511x^4 + 4229x^3 + 2980x^2 + 176x - 209	\( 2^{8}\cdot 5^{11}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.8.216186699934705637500000000.3	x^16 + 9x^14 - 100x^12 - 318x^10 + 1534x^8 + 1755x^6 - 530x^4 - 310x^2 + 55	\( 2^{8}\cdot 5^{11}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.8.216186699934705637500000000.4	x^16 - 10x^14 - 4x^12 + 180x^10 + 19x^8 - 870x^6 - 585x^4 + 175x^2 + 55	\( 2^{8}\cdot 5^{11}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)
16.8.216186699934705637500000000.5	x^16 - 20x^14 + 19x^12 + 1030x^10 - 11x^8 - 13540x^6 - 18895x^4 - 5190x^2 + 55	\( 2^{8}\cdot 5^{11}\cdot 11^{7}\cdot 31^{6} \)	16T1774	Trivial (GRH)