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 5825)

Label	Polynomial	Discriminant	Galois group	Class group
16.16.5345972853145600000000.1	x^16 - 4x^15 - 20x^14 + 100x^13 + 44x^12 - 624x^11 + 362x^10 + 1370x^9 - 1453x^8 - 936x^7 + 1580x^6 - 82x^5 - 459x^4 + 86x^3 + 41x^2 - 6x - 1	\( 2^{24}\cdot 5^{8}\cdot 13^{8} \)	$Q_8 : C_2$ (as 16T11)	Trivial (GRH)
16.16.6281488174105600000000.1	x^16 - 15x^14 + 88x^12 - 261x^10 + 418x^8 - 354x^6 + 142x^4 - 21x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1340	Trivial (GRH)
16.16.6401786224615359765625.1	x^16 - x^15 - 20x^14 + 8x^13 + 147x^12 + 4x^11 - 483x^10 - 127x^9 + 748x^8 + 266x^7 - 559x^6 - 205x^5 + 188x^4 + 60x^3 - 23x^2 - 4x + 1	\( 5^{8}\cdot 29^{8}\cdot 181^{2} \)	$C_4^2:C_2^2.C_2$ (as 16T406)	Trivial (GRH)
16.16.6710886400000000000000.1	x^16 - 4x^15 - 16x^14 + 76x^13 + 46x^12 - 392x^11 - 24x^10 + 928x^9 - 23x^8 - 1128x^7 - 44x^6 + 672x^5 + 96x^4 - 156x^3 - 36x^2 + 4x + 1	\( 2^{40}\cdot 5^{14} \)	$C_8: C_2$ (as 16T6)	Trivial (GRH)
16.16.6879707136000000000000.1	x^16 - 16x^14 + 105x^12 - 364x^10 + 714x^8 - 784x^6 + 440x^4 - 96x^2 + 1	\( 2^{32}\cdot 3^{8}\cdot 5^{12} \)	$C_4\times C_2^2$ (as 16T2)	Trivial (GRH)
16.16.9573589958277615058944.1	x^16 - 24x^14 - 8x^13 + 200x^12 + 96x^11 - 744x^10 - 360x^9 + 1350x^8 + 544x^7 - 1176x^6 - 312x^5 + 456x^4 + 32x^3 - 72x^2 + 8x + 1	\( 2^{54}\cdot 3^{12} \)	$C_4:C_4$ (as 16T8)	Trivial (GRH)
16.16.11729410522650009765625.1	x^16 - x^15 - 24x^14 + 18x^13 + 216x^12 - 111x^11 - 933x^10 + 284x^9 + 2065x^8 - 233x^7 - 2289x^6 - 145x^5 + 1118x^4 + 225x^3 - 154x^2 - 37x - 1	\( 5^{10}\cdot 7^{4}\cdot 29^{8} \)	$C_4\wr C_2$ (as 16T42)	Trivial (GRH)
16.16.15310680244851363610624.1	x^16 - 15x^14 + 86x^12 - 242x^10 + 360x^8 - 281x^6 + 107x^4 - 18x^2 + 1	\( 2^{16}\cdot 483345053^{2} \)	16T1945	Trivial (GRH)
16.16.16983926204041162848889.1	x^16 - 6x^15 - 3x^14 + 78x^13 - 82x^12 - 345x^11 + 620x^10 + 535x^9 - 1592x^8 + 56x^7 + 1563x^6 - 582x^5 - 517x^4 + 249x^3 + 50x^2 - 27x + 1	\( 11^{6}\cdot 97913143^{2} \)	16T1945	Trivial (GRH)
16.16.17147496360040000913408.1	x^16 - 16x^14 + 94x^12 - 265x^10 + 391x^8 - 308x^6 + 128x^4 - 26x^2 + 2	\( 2^{31}\cdot 41^{8} \)	$C_4.D_4:C_4$ (as 16T289)	Trivial (GRH)
16.16.18780357640955901417873.1	x^16 - x^15 - 16x^14 + 16x^13 + 103x^12 - 103x^11 - 339x^10 + 339x^9 + 596x^8 - 596x^7 - 526x^6 + 526x^5 + 188x^4 - 188x^3 - 16x^2 + 16x + 1	\( 3^{8}\cdot 17^{15} \)	$C_{16}$ (as 16T1)	Trivial (GRH)
16.16.24073289246567116570624.1	x^16 - 24x^14 - 16x^13 + 208x^12 + 248x^11 - 728x^10 - 1200x^9 + 826x^8 + 1968x^7 - 200x^6 - 1232x^5 - 4x^4 + 304x^3 - 24x^2 - 16x + 2	\( 2^{58}\cdot 17^{4} \)	$C_2\wr C_4$ (as 16T158)	Trivial (GRH)
16.16.29948379136000000000000.1	x^16 - 8x^15 + 8x^14 + 84x^13 - 222x^12 - 124x^11 + 908x^10 - 448x^9 - 1280x^8 + 1296x^7 + 442x^6 - 956x^5 + 231x^4 + 116x^3 - 48x^2 + 1	\( 2^{32}\cdot 5^{12}\cdot 13^{4} \)	$C_4 \times D_4$ (as 16T19)	Trivial (GRH)
16.16.31130283153817600000000.1	x^16 - 4x^15 - 16x^14 + 56x^13 + 112x^12 - 260x^11 - 406x^10 + 478x^9 + 665x^8 - 412x^7 - 508x^6 + 174x^5 + 177x^4 - 34x^3 - 25x^2 + 2x + 1	\( 2^{24}\cdot 5^{8}\cdot 41^{6} \)	$C_2\times C_4\wr C_2$ (as 16T111)	Trivial (GRH)
16.16.33251650373060437890625.1	x^16 - 8x^15 + 2x^14 + 126x^13 - 251x^12 - 496x^11 + 1829x^10 - 642x^9 - 3338x^8 + 4884x^7 - 2263x^6 - 320x^5 + 672x^4 - 208x^3 + 4x^2 + 8x - 1	\( 5^{8}\cdot 19^{4}\cdot 29^{4}\cdot 31^{4} \)	$D_4^2.C_2$ (as 16T388)	Trivial (GRH)
16.16.34820097123453788749824.1	x^16 - 4x^15 - 12x^14 + 56x^13 + 50x^12 - 292x^11 - 88x^10 + 716x^9 + 72x^8 - 884x^7 - 40x^6 + 560x^5 + 22x^4 - 172x^3 - 8x^2 + 20x + 1	\( 2^{40}\cdot 3^{8}\cdot 13^{6} \)	$C_2\times C_4\wr C_2$ (as 16T111)	Trivial (GRH)
16.16.40354076112897600000000.1	x^16 - 16x^14 + 98x^12 - 299x^10 + 488x^8 - 418x^6 + 167x^4 - 23x^2 + 1	\( 2^{12}\cdot 3^{12}\cdot 5^{8}\cdot 83^{4} \)	$C_2^3:S_4.C_2$ (as 16T763)	Trivial (GRH)
16.16.42329869320217600000000.1	x^16 - 16x^14 + 96x^12 - 280x^10 + 425x^8 - 330x^6 + 121x^4 - 19x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{2}\cdot 29^{4}\cdot 139^{2} \)	16T1340	Trivial (GRH)
16.16.43627449983512312890625.1	x^16 - 2x^15 - 23x^14 + 35x^13 + 192x^12 - 209x^11 - 721x^10 + 498x^9 + 1262x^8 - 473x^7 - 1028x^6 + 181x^5 + 384x^4 - 13x^3 - 55x^2 - 5x + 1	\( 5^{8}\cdot 101^{4}\cdot 181^{4} \)	$D_4^2.C_2$ (as 16T388)	Trivial (GRH)
16.16.44463896402329600000000.1	x^16 - 6x^15 - 11x^14 + 102x^13 + 39x^12 - 690x^11 - 114x^10 + 2372x^9 + 633x^8 - 4202x^7 - 1898x^6 + 3364x^5 + 1990x^4 - 1060x^3 - 754x^2 + 84x + 79	\( 2^{24}\cdot 5^{8}\cdot 7^{4}\cdot 41^{4} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial (GRH)
16.16.45086848686489600000000.1	x^16 - 24x^14 + 198x^12 - 684x^10 + 1043x^8 - 756x^6 + 258x^4 - 36x^2 + 1	\( 2^{44}\cdot 3^{8}\cdot 5^{8} \)	$Q_8 : C_2$ (as 16T11)	Trivial (GRH)
16.16.53139778627174400000000.1	x^16 - 6x^15 - 3x^14 + 86x^13 - 129x^12 - 320x^11 + 950x^10 - 74x^9 - 1982x^8 + 1736x^7 + 934x^6 - 1920x^5 + 620x^4 + 280x^3 - 211x^2 + 38x - 1	\( 2^{24}\cdot 5^{8}\cdot 7^{6}\cdot 41^{3} \)	16T1202	Trivial (GRH)
16.16.54419558400000000000000.1	x^16 - 4x^15 - 30x^14 + 170x^13 - 30x^12 - 1002x^11 + 1038x^10 + 1840x^9 - 2280x^8 - 1770x^7 + 1908x^6 + 1068x^5 - 655x^4 - 350x^3 + 60x^2 + 36x + 1	\( 2^{24}\cdot 3^{12}\cdot 5^{14} \)	$C_8: C_2$ (as 16T6)	Trivial (GRH)
16.16.63949946033164306640625.1	x^16 - 3x^15 - 23x^14 + 74x^13 + 118x^12 - 474x^11 - 161x^10 + 1227x^9 - 122x^8 - 1436x^7 + 376x^6 + 728x^5 - 187x^4 - 142x^3 + 13x^2 + 11x + 1	\( 3^{12}\cdot 5^{12}\cdot 149^{4} \)	$C_2\wr C_4$ (as 16T157)	Trivial (GRH)
16.16.63949946033164306640625.2	x^16 - 2x^15 - 28x^14 + 47x^13 + 317x^12 - 415x^11 - 1887x^10 + 1761x^9 + 6355x^8 - 3786x^7 - 12117x^6 + 4010x^5 + 12527x^4 - 1882x^3 - 6358x^2 + 307x + 1231	\( 3^{12}\cdot 5^{12}\cdot 149^{4} \)	$C_2\wr C_4$ (as 16T158)	Trivial (GRH)
16.16.65772588499765987890625.1	x^16 - x^15 - 22x^14 + 17x^13 + 172x^12 - 92x^11 - 601x^10 + 196x^9 + 1014x^8 - 189x^7 - 844x^6 + 74x^5 + 325x^4 - 46x^2 - 4x + 1	\( 5^{8}\cdot 17^{14} \)	$C_8\times C_2$ (as 16T5)	Trivial (GRH)
16.16.66874197993062400000000.1	x^16 - 24x^14 - 6x^13 + 180x^12 + 78x^11 - 527x^10 - 210x^9 + 741x^8 + 210x^7 - 527x^6 - 78x^5 + 180x^4 + 6x^3 - 24x^2 + 1	\( 2^{24}\cdot 3^{6}\cdot 5^{8}\cdot 241^{3} \)	$C_2.D_4^2.C_2$ (as 16T660)	Trivial (GRH)
16.16.67791400715173078515625.1	x^16 - 2x^15 - 27x^14 + 64x^13 + 219x^12 - 584x^11 - 680x^10 + 2121x^9 + 789x^8 - 3351x^7 - 148x^6 + 2148x^5 - 53x^4 - 471x^3 - 42x^2 + 14x + 1	\( 5^{8}\cdot 19^{2}\cdot 29^{8}\cdot 31^{2} \)	$D_4^2.C_2$ (as 16T396)	Trivial (GRH)
16.16.68719476736000000000000.1	x^16 - 16x^14 + 104x^12 - 352x^10 + 659x^8 - 664x^6 + 316x^4 - 48x^2 + 1	\( 2^{48}\cdot 5^{12} \)	$C_4^2$ (as 16T4)	Trivial (GRH)
16.16.69876989027353600000000.1	x^16 - 15x^14 + 87x^12 - 251x^10 + 384x^8 - 306x^6 + 117x^4 - 19x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 1652141^{2} \)	16T1868	Trivial (GRH)
16.16.73870292887944560640000.1	x^16 - 24x^14 + 212x^12 - 872x^10 + 1728x^8 - 1568x^6 + 552x^4 - 80x^2 + 4	\( 2^{54}\cdot 3^{8}\cdot 5^{4} \)	$C_4 \times D_4$ (as 16T19)	Trivial (GRH)
16.16.74247530256000000000000.1	x^16 - 22x^14 + 165x^12 - 517x^10 + 774x^8 - 583x^6 + 215x^4 - 33x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4} \)	$C_2 \times (C_2^2:C_4)$ (as 16T21)	Trivial (GRH)
16.16.78172909329970208715008.1	x^16 - 7x^15 + 5x^14 + 62x^13 - 114x^12 - 187x^11 + 510x^10 + 209x^9 - 990x^8 - 20x^7 + 938x^6 - 107x^5 - 416x^4 + 60x^3 + 69x^2 - 10x - 1	\( 2^{8}\cdot 43^{2}\cdot 2777^{5} \)	16T1764	Trivial (GRH)
16.16.81753664774171848863873.1	x^16 - 3x^15 - 25x^14 + 92x^13 + 98x^12 - 583x^11 + 49x^10 + 1383x^9 - 647x^8 - 1357x^7 + 807x^6 + 520x^5 - 251x^4 - 114x^3 + 19x^2 + 11x + 1	\( 13^{4}\cdot 17^{15} \)	$C_{16} : C_2$ (as 16T22)	Trivial (GRH)
16.16.83564717538041455968256.1	x^16 - 4x^15 - 18x^14 + 52x^13 + 115x^12 - 252x^11 - 316x^10 + 612x^9 + 372x^8 - 780x^7 - 106x^6 + 472x^5 - 92x^4 - 92x^3 + 36x^2 - 1	\( 2^{44}\cdot 41^{6} \)	$C_4\wr C_2$ (as 16T28)	Trivial (GRH)
16.16.83564717538041455968256.2	x^16 - 20x^14 + 150x^12 - 544x^10 + 1044x^8 - 1088x^6 + 600x^4 - 160x^2 + 16	\( 2^{44}\cdot 41^{6} \)	$(C_2\times C_4).D_4$ (as 16T121)	Trivial (GRH)
16.16.85297744596832966672384.1	x^16 - 24x^14 - 16x^13 + 180x^12 + 176x^11 - 560x^10 - 608x^9 + 842x^8 + 864x^7 - 696x^6 - 512x^5 + 340x^4 + 80x^3 - 80x^2 + 16x - 1	\( 2^{68}\cdot 17^{2} \)	$C_2^5.C_2.C_2$ (as 16T258)	Trivial (GRH)
16.16.91782565332490799087616.1	x^16 - 15x^14 + 89x^12 - 267x^10 + 428x^8 - 356x^6 + 139x^4 - 21x^2 + 1	\( 2^{16}\cdot 3^{2}\cdot 19^{4}\cdot 103^{6} \)	16T1664	Trivial (GRH)
16.16.93492089436304834560000.1	x^16 - 24x^14 - 16x^13 + 176x^12 + 168x^11 - 516x^10 - 600x^9 + 582x^8 + 848x^7 - 192x^6 - 504x^5 - 48x^4 + 112x^3 + 24x^2 - 8x - 2	\( 2^{48}\cdot 3^{12}\cdot 5^{4} \)	$(C_2^2\times C_4):C_2$ (as 16T54)	Trivial (GRH)
16.16.96293156986268466282496.1	x^16 - 24x^14 - 8x^13 + 208x^12 + 144x^11 - 800x^10 - 808x^9 + 1298x^8 + 1744x^7 - 576x^6 - 1288x^5 - 128x^4 + 240x^3 + 40x^2 - 8x - 1	\( 2^{60}\cdot 17^{4} \)	$C_2\wr C_4$ (as 16T157)	Trivial (GRH)
16.16.103849422541860250845184.1	x^16 - 24x^14 + 204x^12 - 792x^10 + 1544x^8 - 1536x^6 + 744x^4 - 144x^2 + 4	\( 2^{54}\cdot 7^{8} \)	$C_2^2 : C_4$ (as 16T10)	Trivial (GRH)
16.16.105264012958105600000000.1	x^16 - 22x^14 + 178x^12 - 666x^10 + 1243x^8 - 1182x^6 + 542x^4 - 96x^2 + 1	\( 2^{32}\cdot 5^{8}\cdot 89^{4} \)	$C_2\wr C_2^2$ (as 16T149)	Trivial (GRH)
16.16.108398345460121600000000.1	x^16 - 26x^14 - 8x^13 + 234x^12 + 116x^11 - 952x^10 - 562x^9 + 1899x^8 + 1160x^7 - 1844x^6 - 1010x^5 + 805x^4 + 282x^3 - 133x^2 + 6x + 1	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 761^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial (GRH)
16.16.108398345460121600000000.2	x^16 - 2x^15 - 25x^14 + 30x^13 + 172x^12 - 152x^11 - 513x^10 + 368x^9 + 753x^8 - 456x^7 - 547x^6 + 276x^5 + 182x^4 - 70x^3 - 25x^2 + 6x + 1	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 761^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial (GRH)
16.16.113799786888217600000000.1	x^16 - 16x^14 + 96x^12 - 282x^10 + 441x^8 - 367x^6 + 151x^4 - 26x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 2108389^{2} \)	16T1868	Trivial (GRH)
16.16.115302930002001431363584.1	x^16 - 19x^14 + 129x^12 - 390x^10 + 567x^8 - 409x^6 + 144x^4 - 22x^2 + 1	\( 2^{20}\cdot 43^{2}\cdot 2777^{4} \)	16T1664	Trivial (GRH)
16.16.119590095763705692160000.1	x^16 - 2x^15 - 21x^14 + 38x^13 + 146x^12 - 260x^11 - 425x^10 + 748x^9 + 609x^8 - 1016x^7 - 447x^6 + 644x^5 + 154x^4 - 162x^3 - 19x^2 + 10x + 1	\( 2^{24}\cdot 5^{4}\cdot 7^{4}\cdot 41^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	Trivial (GRH)
16.16.121029087867608368152576.1	x^16 - 16x^14 + 104x^12 - 352x^10 + 660x^8 - 672x^6 + 336x^4 - 64x^2 + 1	\( 2^{64}\cdot 3^{8} \)	$C_8\times C_2$ (as 16T5)	Trivial (GRH)
16.16.132892327936000000000000.1	x^16 - 4x^15 - 18x^14 + 104x^13 - 34x^12 - 520x^11 + 738x^10 + 500x^9 - 1538x^8 + 500x^7 + 738x^6 - 520x^5 - 34x^4 + 104x^3 - 18x^2 - 4x + 1	\( 2^{36}\cdot 5^{12}\cdot 89^{2} \)	$C_2^4.C_2^3$ (as 16T208)	Trivial (GRH)
16.16.135218704423321600000000.1	x^16 - 6x^15 - 6x^14 + 88x^13 - 62x^12 - 402x^11 + 520x^10 + 612x^9 - 1025x^8 - 394x^7 + 818x^6 + 140x^5 - 288x^4 - 36x^3 + 38x^2 + 4x - 1	\( 2^{24}\cdot 5^{8}\cdot 379^{4} \)	16T1291	Trivial (GRH)