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 177)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.5605632412826517.1	x^16 - 4x^15 + 11x^14 - 24x^13 + 46x^12 - 75x^11 + 104x^10 - 121x^9 + 121x^8 - 107x^7 + 86x^6 - 63x^5 + 43x^4 - 27x^3 + 14x^2 - 5x + 1	\( 3^{10}\cdot 37^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial
16.0.65015202266328125.1	x^16 - 5x^15 + 8x^14 + x^13 - 15x^12 + x^11 + 44x^10 - 58x^9 + x^8 + 68x^7 - 66x^6 + 4x^5 + 45x^4 - 46x^3 + 24x^2 - 7x + 1	\( 5^{7}\cdot 7^{2}\cdot 19^{8} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial
16.0.185575821724204029.1	x^16 - 4x^15 + 7x^14 - 8x^13 + 14x^12 - 32x^11 + 60x^10 - 76x^9 + 63x^8 - 31x^7 + 15x^6 - 11x^5 + 9x^4 - 5x^3 + 5x^2 - x + 1	\( 3^{10}\cdot 61^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial
16.0.478989551390703125.1	x^16 - 2x^15 + 3x^14 - 4x^13 + 14x^12 - 20x^11 + 10x^10 + 22x^8 - 47x^7 + 23x^6 - 12x^5 + 49x^4 - 62x^3 + 34x^2 - 9x + 1	\( 5^{7}\cdot 19^{10} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial
16.0.7674110773159501773.1	x^16 - 7x^15 + 25x^14 - 62x^13 + 113x^12 - 113x^11 + 24x^10 - 52x^9 + 243x^8 - 232x^7 + 78x^6 - 56x^5 + 36x^4 - 8x^3 + 11x^2 - x + 1	\( 3^{10}\cdot 37^{9} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[2]$
16.0.7674110773159501773.2	x^16 - x^15 + 6x^14 - 8x^13 + 23x^12 - 43x^11 + 85x^10 - 143x^9 + 232x^8 - 264x^7 + 399x^6 - 283x^5 + 366x^4 - 196x^3 + 136x^2 - 88x + 19	\( 3^{10}\cdot 37^{9} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial
16.0.11974738784767578125.1	x^16 - x^15 + x^13 + 12x^12 - x^11 + 29x^10 - 2x^9 + 44x^8 - 54x^7 + 86x^6 - 31x^5 + 31x^4 + 12x^3 + 3x^2 + 1	\( 5^{9}\cdot 19^{10} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial
16.0.11974738784767578125.2	x^16 - 6x^15 + 24x^14 - 72x^13 + 178x^12 - 383x^11 + 724x^10 - 1221x^9 + 1831x^8 - 2411x^7 + 2771x^6 - 2724x^5 + 2238x^4 - 1497x^3 + 765x^2 - 266x + 49	\( 5^{9}\cdot 19^{10} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[2]$
16.0.299368469619189453125.3	x^16 - 5x^15 + 20x^14 - 63x^13 + 160x^12 - 308x^11 + 516x^10 - 757x^9 + 983x^8 - 1145x^7 + 1379x^6 - 1639x^5 + 1733x^4 - 1519x^3 + 1056x^2 - 496x + 119	\( 5^{11}\cdot 19^{10} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[2]$
16.0.331826821728530394413.1	x^16 - 3x^15 - 18x^13 + 42x^12 + 27x^11 + 16x^10 + 49x^9 - 5x^8 - 49x^7 + 16x^6 - 27x^5 + 42x^4 + 18x^3 + 3x + 1	\( 7^{10}\cdot 53^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial
16.0.690527632635763191909.1	x^16 - x^15 - 9x^14 + 5x^13 + 72x^12 + 20x^11 - 213x^10 + 28x^9 + 715x^8 + 251x^7 - 1152x^6 - 933x^5 + 885x^4 + 1749x^3 + 1129x^2 + 357x + 49	\( 3^{10}\cdot 61^{9} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[2]$
16.0.690527632635763191909.2	x^16 - 5x^15 + 23x^14 - 86x^13 + 242x^12 - 580x^11 + 1214x^10 - 2157x^9 + 3306x^8 - 4469x^7 + 5367x^6 - 5584x^5 + 5158x^4 - 4036x^3 + 2806x^2 - 1518x + 541	\( 3^{10}\cdot 61^{9} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial
16.0.2462288405368583548933.2	x^16 - 3x^15 - 4x^14 + 10x^13 + 47x^12 - 109x^11 + 67x^10 - 338x^9 + 1024x^8 - 914x^7 + 327x^6 - 1110x^5 + 1585x^4 - 88x^3 - 484x^2 - 407x + 407	\( 11^{10}\cdot 37^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial
16.0.2599452143140344908533.1	x^16 - 2x^15 + 5x^14 + 6x^13 + 15x^12 - 21x^11 + 127x^10 - 82x^9 + 154x^8 - 106x^7 + 140x^6 - 193x^5 + 139x^4 - 17x^3 + 2x^2 - 12x + 8	\( 13^{7}\cdot 23^{10} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[3]$
16.8.3947017030826272489472.1	x^16 - 4x^15 + 28x^13 - 28x^12 - 116x^11 + 116x^10 + 330x^9 - 309x^8 - 444x^7 + 422x^6 + 214x^5 - 119x^4 - 190x^3 + 79x^2 + 38x - 17	\( 2^{24}\cdot 113^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial
16.0.10505857648455357927237.3	x^16 - 21x^14 - 18x^13 + 198x^12 + 307x^11 - 827x^10 - 1987x^9 + 1141x^8 + 5673x^7 + 2326x^6 - 5323x^5 - 7132x^4 - 8046x^3 - 1212x^2 + 14440x + 15613	\( 3^{10}\cdot 37^{11} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[2]$ (GRH)
16.0.30468981617476954930037.1	x^16 - 2x^14 - 4x^13 + 15x^12 + 40x^11 - 16x^10 - 152x^9 + 311x^8 - 660x^7 + 680x^6 - 489x^5 + 545x^4 - 355x^3 + 182x^2 - 66x + 45	\( 11^{10}\cdot 53^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial (GRH)
16.0.39930996351612609453125.1	x^16 - 2x^15 + 2x^14 - x^13 - 12x^12 - 18x^11 + 113x^10 - 178x^9 + 279x^8 - 90x^7 - 190x^6 - 289x^5 + 578x^4 - 457x^3 + 606x^2 - 396x + 81	\( 5^{7}\cdot 59^{10} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[3]$ (GRH)
16.8.63152272493220359831552.1	x^16 - 6x^15 + 19x^14 - 28x^13 - 64x^12 + 266x^11 - 76x^10 - 622x^9 + 499x^8 + 642x^7 - 712x^6 - 106x^5 + 122x^4 - 128x^3 + 493x^2 - 390x + 89	\( 2^{28}\cdot 113^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial
16.8.63152272493220359831552.2	x^16 - 2x^15 - 5x^14 + 17x^12 + 16x^11 - 87x^10 + 44x^9 + 114x^8 + 124x^7 + 47x^6 - 1152x^5 + 401x^4 + 1606x^3 - 838x^2 - 572x + 263	\( 2^{28}\cdot 113^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial (GRH)
16.0.166104174696434739378521.1	x^16 - x^15 - 52x^13 + 112x^12 - 13x^11 + 241x^10 - 773x^9 + 500x^8 + 22x^7 + 12x^6 + 9x^5 - 59x^4 - 22x^3 + 24x^2 - x + 1	\( 31^{8}\cdot 41^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[3]$ (GRH)
16.0.439307412190718289542077.1	x^16 - x^15 + 8x^14 - 12x^13 + 4x^12 - 111x^11 + 358x^10 - 633x^9 + 1822x^8 - 1822x^7 + 36x^6 - 2559x^5 + 7799x^4 - 7710x^3 + 3540x^2 - 768x + 64	\( 13^{9}\cdot 23^{10} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[3]$ (GRH)
16.0.439307412190718289542077.2	x^16 - 7x^15 + 22x^14 - 44x^13 + 46x^12 + 111x^11 - 561x^10 + 941x^9 - 744x^8 - 773x^7 + 4887x^6 - 6458x^5 - 1846x^4 + 8553x^3 - 1956x^2 - 4770x + 2887	\( 13^{9}\cdot 23^{10} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[6]$ (GRH)
16.0.739709068955222437578125.1	x^16 - 6x^15 + 16x^14 - 21x^13 + 19x^12 - 62x^11 + 161x^10 - 64x^9 - 192x^8 - 49x^7 + 755x^6 - 558x^5 + 100x^4 - 704x^3 + 704x^2 + 1024	\( 5^{7}\cdot 79^{10} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[5]$ (GRH)
16.0.932101542235441877906117.1	x^16 - 2x^15 + 7x^14 + 19x^13 - 27x^12 + 63x^11 + 295x^10 - 745x^9 + 1373x^8 + 543x^7 - 4113x^6 + 7541x^5 - 3395x^4 - 5465x^3 + 12023x^2 - 10140x + 3319	\( 7^{10}\cdot 53^{9} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial (GRH)
16.0.932101542235441877906117.2	x^16 - 5x^15 + 19x^14 - 38x^13 + 56x^12 - 25x^11 - 55x^10 + 214x^9 - 245x^8 - 699x^7 + 5212x^6 - 15859x^5 + 32970x^4 - 45841x^3 + 47262x^2 - 28339x + 12604	\( 7^{10}\cdot 53^{9} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[2]$ (GRH)
16.0.998274908790315236328125.1	x^16 - 4x^15 + 5x^14 + 18x^13 - 56x^12 + 49x^11 + 115x^10 - 244x^9 + 184x^8 + 310x^7 - 456x^6 + 226x^5 + 1071x^4 - 1725x^3 + 1625x^2 - 425x + 35	\( 5^{9}\cdot 59^{10} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[6]$ (GRH)
16.0.998274908790315236328125.2	x^16 - 6x^15 + 20x^14 - 24x^13 - 62x^12 + 175x^11 + 24x^10 - 309x^9 - 248x^8 + 773x^7 + 777x^6 - 1295x^5 + 96x^4 + 990x^3 + 590x^2 + 200x + 35	\( 5^{9}\cdot 59^{10} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[3]$ (GRH)
16.8.1010436359891525757304832.1	x^16 + 6x^14 - 4x^13 - 21x^12 - 24x^11 - 224x^10 - 76x^9 + 612x^8 + 496x^7 - 94x^6 + 420x^5 + 1155x^4 + 776x^3 + 88x^2 - 84x - 23	\( 2^{32}\cdot 113^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial (GRH)
16.4.1010436359891525757304832.1	x^16 - 4x^15 - 2x^14 + 6x^13 - 2x^12 + 44x^11 + 115x^10 - 142x^9 - 606x^8 - 584x^7 + 554x^6 + 1734x^5 + 1410x^4 + 232x^3 - 331x^2 - 22x + 121	\( 2^{32}\cdot 113^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial (GRH)
16.4.1010436359891525757304832.2	x^16 - 4x^15 - 2x^14 + 22x^13 + 4x^12 - 156x^11 + 267x^10 + 346x^9 - 1660x^8 - 80x^7 + 6578x^6 - 4746x^5 - 12492x^4 + 18840x^3 - 8219x^2 + 2866x - 1081	\( 2^{32}\cdot 113^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial (GRH)
16.12.1010436359891525757304832.3	x^16 - 4x^15 - 8x^14 + 22x^13 - 46x^12 + 252x^11 + 233x^10 - 1318x^9 - 297x^8 + 1288x^7 + 636x^6 + 1024x^5 - 728x^4 - 1392x^3 - 236x^2 + 40x + 4	\( 2^{32}\cdot 113^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial (GRH)
16.12.1010436359891525757304832.4	x^16 - 6x^15 + 3x^14 + 8x^13 + 56x^12 + 66x^11 - 610x^10 + 34x^9 + 1829x^8 - 682x^7 - 2484x^6 + 1006x^5 + 1750x^4 - 500x^3 - 607x^2 + 66x + 71	\( 2^{32}\cdot 113^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial (GRH)
16.0.1356088465330316024208733.1	x^16 - 6x^15 + 6x^14 + 18x^13 + 33x^12 - 328x^11 + 488x^10 + 8x^9 + 19x^8 - 1864x^7 + 3382x^6 - 2283x^5 + 851x^4 - 497x^3 + 238x^2 + 6x + 9	\( 13^{7}\cdot 43^{10} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial (GRH)
16.0.2569453321037674837093389.3	x^16 - 4x^15 + 38x^14 - 130x^13 + 641x^12 - 1757x^11 + 5897x^10 - 12483x^9 + 31044x^8 - 47785x^7 + 91545x^6 - 91886x^5 + 136834x^4 - 79970x^3 + 96634x^2 - 49215x + 85039	\( 3^{10}\cdot 61^{11} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[2]$ (GRH)
16.0.3370872826949590878489277.4	x^16 - 5x^15 + 31x^14 - 79x^13 + 191x^12 - 166x^11 + 3x^10 + 442x^9 - 845x^8 + 945x^7 - 901x^6 + 110x^5 + 850x^4 - 1692x^3 + 1815x^2 - 1050x + 625	\( 11^{10}\cdot 37^{9} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[2, 2]$ (GRH)
16.0.3370872826949590878489277.7	x^16 - 2x^15 - 14x^14 + 4x^13 + 103x^12 + 163x^11 - 445x^10 - 992x^9 + 867x^8 + 2277x^7 + 2523x^6 - 11477x^5 + 10500x^4 - 12097x^3 + 24231x^2 - 25348x + 9959	\( 11^{10}\cdot 37^{9} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial (GRH)
16.0.4041745439566103029219328.1	x^16 - 4x^15 + 12x^14 - 22x^13 + 57x^12 - 88x^11 + 263x^10 - 380x^9 + 770x^8 - 776x^7 + 1571x^6 - 596x^5 + 1869x^4 + 956x^3 + 249x^2 - 218x + 223	\( 2^{34}\cdot 113^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[3, 6]$ (GRH)
16.16.4041745439566103029219328.1	x^16 - 28x^14 + 324x^12 - 2008x^10 + 7201x^8 - 14964x^6 + 16790x^4 - 8136x^2 + 452	\( 2^{34}\cdot 113^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial (GRH)
16.0.18492726723880560939453125.1	x^16 - 4x^15 + 21x^14 - 64x^13 + 182x^12 - 221x^11 + 381x^10 - 37x^9 - 1405x^8 + 302x^7 + 4446x^6 - 4001x^5 + 8032x^4 - 9331x^3 + 5710x^2 - 1172x + 104	\( 5^{9}\cdot 79^{10} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[10]$ (GRH)
16.0.18492726723880560939453125.2	x^16 - 4x^15 + 11x^14 - 49x^13 + 138x^12 - 90x^11 + 918x^10 + 557x^9 + 3240x^8 + 3840x^7 + 7041x^6 + 8581x^5 + 9376x^4 + 9059x^3 + 5682x^2 + 3502x + 1289	\( 5^{9}\cdot 79^{10} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[5]$ (GRH)
16.0.19268364558874174255049821.2	x^16 - 3x^15 + 13x^14 - 35x^13 + 12x^12 + 32x^11 + 55x^10 - 80x^9 - 63x^8 - 746x^7 + 964x^6 + 332x^5 + 2625x^4 + 1654x^3 + 1504x^2 + 1117x + 311	\( 19^{10}\cdot 61^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial (GRH)
16.0.24956872719757880908203125.3	x^16 - 4x^15 - 8x^14 + 11x^13 + 120x^12 + 81x^11 + 14x^10 - 3929x^9 + 3056x^8 + 2795x^7 + 14235x^6 - 10587x^5 + 19309x^4 - 19510x^3 + 2730x^2 - 5850x + 8275	\( 5^{11}\cdot 59^{10} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[6]$ (GRH)
16.16.57089654333871205287723008.1	x^16 - 21x^14 + 162x^12 - 593x^10 + 1108x^8 - 1027x^6 + 409x^4 - 54x^2 + 2	\( 2^{31}\cdot 113^{8} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial (GRH)
16.0.64667927033057648467509248.1	x^16 + 28x^14 + 324x^12 + 2008x^10 + 7201x^8 + 14964x^6 + 16790x^4 + 8136x^2 + 452	\( 2^{38}\cdot 113^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[2, 34]$ (GRH)
16.0.74242952660231390932611013.1	x^16 - 4x^15 + 13x^14 - 52x^13 + 266x^12 - 755x^11 + 2077x^10 - 6041x^9 + 21381x^8 - 37708x^7 + 65162x^6 - 116589x^5 + 176926x^4 - 195871x^3 + 161590x^2 - 93028x + 26728	\( 13^{11}\cdot 23^{10} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[6]$ (GRH)
16.0.85587369363492766398473933.1	x^16 - 26x^13 + 40x^12 + 254x^11 - 894x^10 - 99x^9 + 7137x^8 - 14827x^7 + 12815x^6 - 2812x^5 - 4216x^4 - 11799x^3 + 23559x^2 - 215x + 12511	\( 11^{10}\cdot 53^{9} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial (GRH)
16.0.85587369363492766398473933.2	x^16 - 6x^15 + 2x^14 + 17x^13 + 26x^12 + 54x^11 + 149x^10 - 205x^9 - 2463x^8 - 3539x^7 + 3093x^6 + 8765x^5 + 16697x^4 + 35362x^3 + 40434x^2 + 26465x + 21101	\( 11^{10}\cdot 53^{9} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	$[2]$ (GRH)
16.0.138816876576378001590580409.1	x^16 - 3x^15 + 2x^14 - 17x^13 + 91x^12 - 134x^11 + 359x^10 - 597x^9 + 1446x^8 - 4703x^7 + 4549x^6 - 4130x^5 + 15976x^4 - 21928x^3 + 12448x^2 + 9120x + 5184	\( 11^{12}\cdot 89^{7} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial (GRH)
16.0.229178950640823408091275877.1	x^16 - 2x^15 - 2x^14 + 51x^13 - 61x^12 - 440x^11 + 1587x^10 - 2663x^9 + 2743x^8 - 942x^7 - 1863x^6 + 2939x^5 - 1219x^4 - 928x^3 + 1089x^2 - 290x + 31	\( 13^{9}\cdot 43^{10} \)	$(C_2^3\times C_4).D_4$ (as 16T675)	Trivial (GRH)