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 122)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.4146377695556640625.4	x^16 - 6x^15 + 21x^14 - 49x^13 + 82x^12 - 109x^11 + 111x^10 - 92x^9 + 89x^8 + 3x^7 + 108x^6 + 70x^5 + 171x^4 + 60x^3 + 115x^2 + 25x + 25	\( 5^{12}\cdot 19^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2]$
16.0.18446744073709551616.8	x^16 + 12x^12 + 6x^8 + 12x^4 + 1	\( 2^{64} \)	$C_2\wr C_4$ (as 16T172)	Trivial
16.0.73786976294838206464.3	x^16 + 4x^12 - 2x^8 + 4x^4 + 1	\( 2^{66} \)	$C_2\wr C_4$ (as 16T172)	Trivial (GRH)
16.0.35847274805742431640625.3	x^16 - 4x^15 - x^14 + 6x^13 + 50x^12 - 104x^11 + 97x^10 - 202x^9 + 148x^8 - 662x^7 + 2407x^6 - 1898x^5 + 349x^4 - 633x^3 + 1413x^2 - 8613x + 9801	\( 5^{12}\cdot 59^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2]$ (GRH)
16.0.43190748110316471478641.2	x^16 - 5x^15 + 9x^14 - 5x^13 + 7x^11 - 135x^10 + 592x^9 - 1351x^8 + 1596x^7 + 675x^6 - 6573x^5 + 13146x^4 - 15174x^3 + 10350x^2 - 3429x + 423	\( 3^{8}\cdot 37^{12} \)	$C_2\wr C_4$ (as 16T172)	$[2]$ (GRH)
16.0.48736115900396728515625.1	x^16 - x^15 + 13x^14 - 17x^13 + 61x^12 + 14x^11 + 10x^10 + 269x^9 - 141x^8 + 538x^7 + 40x^6 + 112x^5 + 976x^4 - 544x^3 + 832x^2 - 128x + 256	\( 5^{14}\cdot 41^{8} \)	$C_2\wr C_4$ (as 16T172)	$[8]$ (GRH)
16.0.122718822702791268499456.2	x^16 - 8x^14 + 64x^12 - 188x^10 + 833x^8 - 996x^6 + 198x^4 + 8536x^2 + 8836	\( 2^{44}\cdot 17^{8} \)	$C_2\wr C_4$ (as 16T172)	$[4]$ (GRH)
16.0.370387893043593994140625.3	x^16 - 3x^15 - 12x^13 + 95x^12 + 80x^11 - 567x^10 - 1963x^9 + 4237x^8 + 4169x^7 - 6593x^6 - 126x^5 + 6113x^4 + 2400x^3 - 1664x^2 + 512x + 4096	\( 5^{12}\cdot 79^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2]$ (GRH)
16.0.475262857646065983187681.4	x^16 - 4x^15 + 22x^14 - 85x^13 + 275x^12 - 796x^11 + 1976x^10 - 4323x^9 + 8297x^8 - 13610x^7 + 19093x^6 - 22373x^5 + 19712x^4 - 11605x^3 + 4616x^2 - 1740x + 608	\( 13^{8}\cdot 17^{12} \)	$C_2\wr C_4$ (as 16T172)	$[4]$ (GRH)
16.0.1170088580305670166015625.1	x^16 - 6x^15 + 22x^14 - 48x^13 + 115x^12 - 332x^11 + 962x^10 - 2089x^9 + 3716x^8 - 6790x^7 + 13325x^6 - 26650x^5 + 49790x^4 - 87855x^3 + 124730x^2 - 117665x + 59105	\( 5^{14}\cdot 61^{8} \)	$C_2\wr C_4$ (as 16T172)	$[8]$ (GRH)
16.0.1824496001102094673202161.2	x^16 - 3x^15 + 7x^14 + 6x^13 - 3x^12 - 48x^11 + 243x^10 - 156x^9 + 234x^8 + 228x^7 + 663x^6 - 1815x^5 + 2785x^4 - 2103x^3 + 2182x^2 - 897x + 549	\( 13^{12}\cdot 23^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2]$ (GRH)
16.0.2643693128974804931640625.19	x^16 - 2x^15 - 23x^13 + 125x^12 - 260x^11 + 963x^10 - 3622x^9 + 8437x^8 - 18634x^7 + 46977x^6 - 86449x^5 + 134228x^4 - 202915x^3 + 242291x^2 - 166837x + 101761	\( 5^{12}\cdot 101^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2, 2]$ (GRH)
16.0.2643693128974804931640625.20	x^16 - 4x^15 + 6x^14 - 16x^13 + 13x^12 + 26x^11 - 41x^10 + 132x^9 + 1248x^8 - 7494x^7 + 16866x^6 - 5228x^5 - 25822x^4 + 52382x^3 - 14591x^2 - 27978x + 119201	\( 5^{12}\cdot 101^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2, 2, 8]$ (GRH)
16.0.17415183620366462784744081.4	x^16 - 5x^15 + 15x^14 - 36x^13 + 41x^12 + 30x^11 - 107x^10 - 187x^9 + 832x^8 - 849x^7 + 1659x^6 - 5520x^5 + 12297x^4 - 17771x^3 + 12337x^2 - 19773x + 28561	\( 3^{8}\cdot 61^{12} \)	$C_2\wr C_4$ (as 16T172)	$[2]$ (GRH)
16.0.137350965859713069141239809.2	x^16 - 4x^15 + 34x^14 - 110x^13 + 379x^12 - 810x^11 + 1524x^10 - 2201x^9 + 2777x^8 - 2900x^7 + 2241x^6 - 978x^5 + 303x^4 - 1031x^3 + 561x^2 + 214x + 16	\( 13^{8}\cdot 17^{14} \)	$C_2\wr C_4$ (as 16T172)	$[4, 8]$ (GRH)
16.0.272312684996154152285848081.5	x^16 + 24x^14 + 294x^12 + 2333x^10 + 13789x^8 + 57967x^6 + 181649x^4 + 363857x^2 + 439569	\( 13^{12}\cdot 43^{8} \)	$C_2\wr C_4$ (as 16T172)	$[8]$ (GRH)
16.0.351205590630400000000000000.1	x^16 - 6x^15 + 42x^14 - 138x^13 + 540x^12 - 1092x^11 + 4022x^10 - 6074x^9 + 15771x^8 - 19660x^7 + 39070x^6 - 37690x^5 + 58760x^4 - 39050x^3 + 50300x^2 - 20300x + 21025	\( 2^{28}\cdot 5^{14}\cdot 11^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2, 2, 2, 24]$ (GRH)
16.16.351205590630400000000000000.1	x^16 - 48x^14 + 598x^12 - 2836x^10 + 5875x^8 - 5516x^6 + 2158x^4 - 228x^2 + 1	\( 2^{28}\cdot 5^{14}\cdot 11^{8} \)	$C_2\wr C_4$ (as 16T172)	Trivial (GRH)
16.8.351205590630400000000000000.1	x^16 - 32x^14 + 118x^12 - 704x^10 + 1535x^8 + 3016x^6 + 3298x^4 - 12992x^2 + 5041	\( 2^{28}\cdot 5^{14}\cdot 11^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2, 2]$ (GRH)
16.8.351205590630400000000000000.2	x^16 - 6x^15 + 12x^14 - 18x^13 - 60x^12 + 888x^11 - 3128x^10 + 5826x^9 - 14349x^8 + 43100x^7 - 76440x^6 + 79670x^5 - 60590x^4 - 1150x^3 + 63600x^2 - 18900x - 12475	\( 2^{28}\cdot 5^{14}\cdot 11^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2]$ (GRH)
16.16.425367234731459587461873664.1	x^16 - 40x^14 - 32x^13 + 556x^12 + 848x^11 - 3008x^10 - 6816x^9 + 4340x^8 + 18800x^7 + 4296x^6 - 18576x^5 - 10752x^4 + 5200x^3 + 4480x^2 + 448x - 2	\( 2^{66}\cdot 7^{8} \)	$C_2\wr C_4$ (as 16T172)	Trivial (GRH)
16.0.425367234731459587461873664.1	x^16 + 8x^14 - 48x^13 + 76x^12 - 304x^11 + 1168x^10 - 1696x^9 + 6292x^8 - 6832x^7 + 23560x^6 - 27312x^5 + 61696x^4 - 56016x^3 + 86336x^2 - 47360x + 49022	\( 2^{66}\cdot 7^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2, 160]$ (GRH)
16.0.1411114225648575427835680561.2	x^16 - 3x^15 + 2x^14 + 8x^13 - 8x^12 - 307x^11 + 1296x^10 - 4138x^9 + 5343x^8 - 142x^7 - 1048x^6 + 35383x^5 + 10082x^4 - 29340x^3 + 15142x^2 - 3535x + 343	\( 11^{8}\cdot 37^{12} \)	$C_2\wr C_4$ (as 16T172)	$[4]$ (GRH)
16.0.1450531566903202684958906641.19	x^16 + 13x^14 - 46x^13 + 221x^12 - 741x^11 + 2178x^10 - 6292x^9 + 21242x^8 - 53150x^7 + 63947x^6 + 11375x^5 - 94847x^4 - 30706x^3 + 295893x^2 - 300456x + 94419	\( 13^{12}\cdot 53^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2, 4]$ (GRH)
16.0.1450531566903202684958906641.25	x^16 - 2x^15 + 37x^14 - 39x^13 + 272x^12 + 125x^11 - 639x^10 - 1340x^9 + 31820x^8 - 78107x^7 + 90672x^6 + 75155x^5 - 226678x^4 + 112359x^3 + 403234x^2 - 649142x + 374959	\( 13^{12}\cdot 53^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2, 2, 16]$ (GRH)
16.0.1969658413423416139858084729.2	x^16 + 8x^14 + 80x^12 + 459x^10 - 684x^8 - 3961x^6 + 29096x^4 + 86536x^2 + 16641	\( 13^{14}\cdot 29^{8} \)	$C_2\wr C_4$ (as 16T172)	$[8]$ (GRH)
16.0.2159514057650567877197265625.2	x^16 - 8x^15 + 60x^14 - 280x^13 + 1125x^12 - 3474x^11 + 8917x^10 - 18460x^9 + 30350x^8 - 39130x^7 + 38607x^6 - 28376x^5 + 27740x^4 - 30880x^3 + 3440x^2 + 10368x + 9216	\( 5^{14}\cdot 29^{12} \)	$C_2\wr C_4$ (as 16T172)	$[4, 24]$ (GRH)
16.0.2832009822518079193000591441.2	x^16 - 4x^15 + 22x^14 - 108x^13 + 375x^12 - 1234x^11 + 3752x^10 - 9327x^9 + 21168x^8 - 49818x^7 + 114701x^6 - 232324x^5 + 382792x^4 - 472479x^3 + 397448x^2 - 200163x + 45487	\( 7^{8}\cdot 53^{12} \)	$C_2\wr C_4$ (as 16T172)	$[10]$ (GRH)
16.0.4466413296812760910104974161.19	x^16 + 33x^14 + 59x^12 - 4986x^10 - 18147x^8 + 129051x^6 + 1022099x^4 + 1939782x^2 + 312481	\( 13^{12}\cdot 61^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2, 2]$ (GRH)
16.0.4466413296812760910104974161.22	x^16 - 6x^15 + 9x^14 - 7x^13 + 4x^12 + 471x^11 - 1537x^10 + 590x^9 + 1306x^8 - 15861x^7 + 89768x^6 - 152713x^5 + 77250x^4 - 2739x^3 + 33908x^2 - 222270x + 508743	\( 13^{12}\cdot 61^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2, 2, 40]$ (GRH)
16.0.13872985106194361214049869121.9	x^16 - 4x^15 - 34x^14 + 162x^13 + 381x^12 - 2516x^11 - 825x^10 + 18420x^9 - 13366x^8 - 51128x^7 + 48569x^6 + 37860x^5 + 299347x^4 - 1154488x^3 + 1466315x^2 - 814322x + 168437	\( 17^{12}\cdot 47^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2, 4]$ (GRH)
16.0.72646052899365103388916015625.1	x^16 - 5x^15 + 23x^14 - 20x^13 - 130x^12 + 205x^11 - 312x^10 + 1220x^9 + 7554x^8 + 9955x^7 + 30272x^6 + 24430x^5 + 43715x^4 + 17365x^3 + 10717x^2 + 1890x + 576	\( 5^{12}\cdot 29^{14} \)	$C_2\wr C_4$ (as 16T172)	$[4, 24]$ (GRH)
16.0.105305708997757955232277716721.2	x^16 - 2x^15 + 17x^14 - 66x^13 + 116x^12 - 590x^11 + 1237x^10 - 1558x^9 + 3661x^8 + 4376x^7 - 7623x^6 + 78685x^5 + 37741x^4 - 51675x^3 + 572377x^2 - 340957x + 293423	\( 11^{8}\cdot 53^{12} \)	$C_2\wr C_4$ (as 16T172)	$[2]$ (GRH)
16.0.236584058764743389289008392801.17	x^16 - 2x^15 - 13x^14 + 9x^13 + 80x^12 + 161x^11 + 11x^10 - 3190x^9 - 16594x^8 - 42411x^7 + 240659x^6 + 552678x^5 + 578774x^4 + 1788879x^3 + 5390198x^2 + 7334272x + 4079744	\( 17^{12}\cdot 67^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2, 40]$ (GRH)
16.0.400734980167009195224860426161.17	x^16 - 3x^15 + 9x^14 - 37x^13 - 39x^12 - 480x^11 + 2336x^10 + 1863x^9 - 10939x^8 + 9223x^7 + 79x^6 - 42762x^5 + 189151x^4 - 192733x^3 + 221734x^2 - 97055x + 41111	\( 13^{8}\cdot 53^{12} \)	$C_2\wr C_4$ (as 16T172)	$[2, 8]$ (GRH)
16.0.400734980167009195224860426161.27	x^16 + 38x^14 + 461x^12 + 1758x^10 + 1624x^8 + 8226x^6 + 120945x^4 + 391522x^2 + 829921	\( 13^{8}\cdot 53^{12} \)	$C_2\wr C_4$ (as 16T172)	$[2, 2, 2, 32]$ (GRH)
16.0.440166027395300672133281640625.2	x^16 - x^15 - 12x^14 + 9x^13 + 180x^12 - 93x^11 - 2514x^10 + 4185x^9 + 12140x^8 - 38510x^7 + 7604x^6 + 88051x^5 - 85833x^4 - 79769x^3 + 138810x^2 - 21672x + 1849	\( 5^{8}\cdot 101^{12} \)	$C_2\wr C_4$ (as 16T172)	$[10, 10]$ (GRH)
16.0.440166027395300672133281640625.5	x^16 - 4x^15 + 30x^14 - 166x^13 + 867x^12 - 3169x^11 + 8916x^10 - 20367x^9 + 37640x^8 - 60065x^7 + 86087x^6 - 103912x^5 + 102866x^4 - 87122x^3 + 59273x^2 - 25915x + 5041	\( 5^{8}\cdot 101^{12} \)	$C_2\wr C_4$ (as 16T172)	$[4, 80]$ (GRH)
16.0.1766969156799962667099298073761.7	x^16 - 4x^15 - 38x^14 + 130x^13 + 681x^12 - 1744x^11 - 6837x^10 + 11648x^9 + 37978x^8 - 46316x^7 - 95415x^6 + 148276x^5 + 128687x^4 - 395560x^3 + 136103x^2 + 136510x + 133225	\( 23^{8}\cdot 41^{12} \)	$C_2\wr C_4$ (as 16T172)	$[2, 24]$ (GRH)
16.0.2165234002589380425486809479441.10	x^16 - 2x^15 + 33x^14 - 128x^13 + 689x^12 - 2213x^11 + 9153x^10 - 26156x^9 + 80234x^8 - 171376x^7 + 381852x^6 - 583197x^5 + 840967x^4 - 873606x^3 + 787813x^2 - 389678x + 171239	\( 13^{8}\cdot 61^{12} \)	$C_2\wr C_4$ (as 16T172)	$[4, 144]$ (GRH)
16.0.2165234002589380425486809479441.24	x^16 - 7x^15 + 25x^14 + 64x^13 - 685x^12 + 2062x^11 + 3636x^10 - 40745x^9 + 104734x^8 + 64942x^7 - 1090436x^6 + 2368569x^5 + 34363x^4 - 10187697x^3 + 16326193x^2 - 3402607x + 7078513	\( 13^{8}\cdot 61^{12} \)	$C_2\wr C_4$ (as 16T172)	$[2, 18]$ (GRH)
16.0.2293544177031779368362112832641.4	x^16 + 44x^14 - 34x^13 + 812x^12 - 1564x^11 + 8536x^10 - 28424x^9 + 78408x^8 - 318070x^7 + 874948x^6 - 2782084x^5 + 7955375x^4 - 12899464x^3 + 26393084x^2 - 19477920x + 35320816	\( 17^{12}\cdot 89^{8} \)	$C_2\wr C_4$ (as 16T172)	$[28]$ (GRH)
16.0.4009292695690170390860412175969.2	x^16 + 64x^14 + 1452x^12 + 16534x^10 + 111076x^8 + 454948x^6 + 1048825x^4 + 1032972x^2 + 256	\( 17^{14}\cdot 47^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2, 4, 4]$ (GRH)
16.0.19244198650569257148820544058721.18	x^16 - 2x^15 - 27x^14 - 71x^13 + 80x^12 + 3369x^11 + 7028x^10 + 5649x^9 + 39799x^8 - 160713x^7 + 1470441x^6 - 4148370x^5 + 14735693x^4 - 14162372x^3 + 39990424x^2 - 12569079x + 26924347	\( 31^{8}\cdot 41^{12} \)	$C_2\wr C_4$ (as 16T172)	$[2, 2, 16]$ (GRH)
16.0.45080303137796743213973710214161.1	x^16 - x^15 + 39x^14 + 3x^13 + 541x^12 + 731x^11 + 2681x^10 + 10249x^9 + 3655x^8 + 12964x^7 - 18882x^6 - 111968x^5 - 53641x^4 + 8619x^3 + 158589x^2 + 98172x + 35559	\( 19^{8}\cdot 61^{12} \)	$C_2\wr C_4$ (as 16T172)	$[4]$ (GRH)
16.0.52944586525988002867127761920001.6	x^16 - 8x^15 - 18x^14 + 266x^13 - 315x^12 - 1932x^11 + 6445x^10 - 7222x^9 + 10054x^8 - 30720x^7 + 164141x^6 - 380752x^5 + 580060x^4 - 564240x^3 + 28144x^2 + 196096x + 1002752	\( 11^{8}\cdot 89^{12} \)	$C_2\wr C_4$ (as 16T172)	$[2, 4]$ (GRH)
16.0.68372792983010839504523425519489.2	x^16 + 36x^14 + 142x^12 - 626x^10 + 1073x^8 + 23406x^6 + 23041x^4 + 30139x^2 + 13924	\( 17^{14}\cdot 67^{8} \)	$C_2\wr C_4$ (as 16T172)	$[2, 2, 2, 4, 40]$ (GRH)
16.0.79253796088782001552124351073601.6	x^16 - 8x^15 - 8x^14 + 196x^13 + 178x^12 - 3980x^11 - 3526x^10 + 59738x^9 + 67167x^8 - 680600x^7 - 511450x^6 + 4221358x^5 - 1294141x^4 - 5387882x^3 + 12528339x^2 - 8995382x + 114193360	\( 37^{8}\cdot 41^{12} \)	$C_2\wr C_4$ (as 16T172)	$[2, 48]$ (GRH)
16.0.143672747301451241912563249451281.5	x^16 - 4x^15 - 57x^14 + 197x^13 + 1379x^12 - 4365x^11 - 16438x^10 + 63465x^9 + 104169x^8 - 680824x^7 - 678604x^6 + 4806966x^5 + 7124578x^4 - 17591757x^3 - 36133339x^2 + 65807565x + 165230275	\( 29^{12}\cdot 67^{8} \)	$C_2\wr C_4$ (as 16T172)	$[4]$ (GRH)
16.0.228477145661885006672293047985201.3	x^16 - 5x^15 - 57x^14 + 440x^13 + 361x^12 - 11388x^11 + 33304x^10 + 39299x^9 - 604110x^8 + 2056869x^7 - 1227572x^6 - 15542808x^5 + 64709569x^4 - 130400988x^3 + 154253711x^2 - 103177579x + 30084761	\( 29^{12}\cdot 71^{8} \)	$C_2\wr C_4$ (as 16T172)	$[14]$ (GRH)