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 241)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.17247076416015625.2	x^16 - x^15 - 5x^14 + 5x^13 + 15x^12 - 13x^11 - 37x^10 + 15x^9 + 65x^8 + 15x^7 - 37x^6 - 13x^5 + 15x^4 + 5x^3 - 5x^2 - x + 1	\( 5^{14}\cdot 41^{4} \)	$C_2\wr C_4$ (as 16T157)	Trivial
16.0.25405371337890625.2	x^16 - x^15 + x^14 + 3x^13 + 7x^12 - x^11 + 7x^10 + 23x^9 + 41x^8 + 23x^7 + 7x^6 - x^5 + 7x^4 + 3x^3 + x^2 - x + 1	\( 5^{12}\cdot 101^{4} \)	$C_2\wr C_4$ (as 16T157)	Trivial
16.0.84508306884765625.2	x^16 + x^14 - 5x^13 - 8x^12 - 5x^11 + 18x^10 + 25x^9 + 10x^8 - 25x^7 - 33x^6 - 15x^5 + 12x^4 + 20x^3 + 14x^2 + 5x + 1	\( 5^{14}\cdot 61^{4} \)	$C_2\wr C_4$ (as 16T157)	Trivial
16.4.1469316970615668736.1	x^16 - 8x^12 - 24x^11 - 44x^10 - 48x^9 - 43x^8 - 48x^7 - 44x^6 - 24x^5 - 8x^4 + 1	\( 2^{44}\cdot 17^{4} \)	$C_2\wr C_4$ (as 16T157)	Trivial
16.0.16246753247925108736.1	x^16 + 8x^14 + 36x^12 - 16x^11 + 80x^10 - 32x^9 + 123x^8 - 104x^7 + 180x^6 - 136x^5 + 144x^4 - 80x^3 + 56x^2 - 16x + 4	\( 2^{44}\cdot 31^{4} \)	$C_2\wr C_4$ (as 16T157)	Trivial
16.4.16640273717519203921.1	x^16 - x^15 + x^13 + 4x^12 - 4x^11 - 9x^10 - 6x^9 - 16x^8 + 27x^7 + 60x^6 + 16x^5 - 47x^4 - 30x^3 + 4x + 1	\( 13^{4}\cdot 17^{12} \)	$C_2\wr C_4$ (as 16T157)	Trivial
16.8.19409669316650390625.1	x^16 - 4x^15 - 3x^14 + 28x^13 - 14x^12 - 66x^11 + 62x^10 + 74x^9 - 123x^8 + 20x^7 + 68x^6 - 63x^5 + 32x^4 - 6x^3 - 11x^2 + 5x + 1	\( 3^{8}\cdot 5^{12}\cdot 59^{4} \)	$C_2\wr C_4$ (as 16T157)	Trivial
16.0.19409669316650390625.3	x^16 - 3x^15 + 7x^14 - 3x^13 - 7x^12 + 27x^11 - 15x^10 - 15x^9 + 41x^8 - 15x^7 - 15x^6 + 27x^5 - 7x^4 - 3x^3 + 7x^2 - 3x + 1	\( 3^{8}\cdot 5^{12}\cdot 59^{4} \)	$C_2\wr C_4$ (as 16T157)	$[2]$
16.8.36982551763916015625.1	x^16 - x^15 + x^14 - 4x^13 - 12x^12 + 14x^11 + 34x^10 + 3x^9 - 72x^8 - 91x^7 + 41x^6 + 173x^5 + 48x^4 - 97x^3 - 26x^2 + 18x + 1	\( 3^{8}\cdot 5^{14}\cdot 31^{4} \)	$C_2\wr C_4$ (as 16T157)	Trivial (GRH)
16.8.73786976294838206464.3	x^16 - 32x^10 - 68x^8 + 256x^4 - 64x^2 + 4	\( 2^{66} \)	$C_2\wr C_4$ (as 16T157)	Trivial (GRH)
16.0.73786976294838206464.10	x^16 + 32x^10 - 68x^8 + 256x^4 + 64x^2 + 4	\( 2^{66} \)	$C_2\wr C_4$ (as 16T157)	Trivial
16.0.183833097995319003361.1	x^16 - 4x^15 + 10x^14 - 19x^13 + 27x^12 - 31x^11 + 56x^10 - 52x^9 + 10x^8 + 117x^7 - 92x^6 - 177x^5 + 152x^4 + 213x^3 - 198x^2 - 81x + 81	\( 13^{12}\cdot 53^{4} \)	$C_2\wr C_4$ (as 16T157)	Trivial
16.0.295147905179352825856.1	x^16 + 8x^14 + 44x^12 + 152x^10 + 290x^8 + 296x^6 + 148x^4 + 24x^2 + 1	\( 2^{68} \)	$C_2\wr C_4$ (as 16T157)	Trivial
16.8.295147905179352825856.2	x^16 - 8x^14 + 44x^12 - 152x^10 + 290x^8 - 296x^6 + 148x^4 - 24x^2 + 1	\( 2^{68} \)	$C_2\wr C_4$ (as 16T157)	Trivial (GRH)
16.0.322581582210337451521.3	x^16 - 4x^15 + 10x^14 - 13x^13 + 9x^12 + 5x^11 - 25x^10 + 77x^9 + x^8 + 108x^7 + 172x^6 + 174x^5 + 302x^4 + 195x^3 + 153x^2 + 81x + 81	\( 13^{12}\cdot 61^{4} \)	$C_2\wr C_4$ (as 16T157)	Trivial
16.0.1719192030488525390625.1	x^16 - 3x^15 + 9x^14 - 9x^13 + 17x^12 - 3x^11 + 63x^10 + 21x^9 + 81x^8 - 21x^7 + 63x^6 + 3x^5 + 17x^4 + 9x^3 + 9x^2 + 3x + 1	\( 3^{8}\cdot 5^{12}\cdot 181^{4} \)	$C_2\wr C_4$ (as 16T157)	$[6]$
16.0.1719192030488525390625.2	x^16 - x^15 + 3x^14 - 9x^13 + 53x^12 + 9x^11 + 35x^10 + 5x^9 + 111x^8 - 5x^7 + 35x^6 - 9x^5 + 53x^4 + 9x^3 + 3x^2 + x + 1	\( 3^{8}\cdot 5^{12}\cdot 181^{4} \)	$C_2\wr C_4$ (as 16T157)	$[6]$
16.0.2784831507453778823209.1	x^16 - x^15 + 8x^14 - 5x^13 + 11x^12 + 21x^11 - 51x^10 + 135x^9 - 134x^8 + 55x^7 + 173x^6 - 376x^5 + 462x^4 - 360x^3 + 187x^2 - 54x + 9	\( 13^{14}\cdot 29^{4} \)	$C_2\wr C_4$ (as 16T157)	Trivial
16.0.2843010661187557386241.1	x^16 - x^15 + 10x^14 - 24x^13 + 76x^12 - 141x^11 + 277x^10 - 337x^9 + 458x^8 - 403x^7 + 369x^6 - 224x^5 + 144x^4 - 57x^3 + 24x^2 - 4x + 1	\( 17^{12}\cdot 47^{4} \)	$C_2\wr C_4$ (as 16T157)	Trivial
16.4.4809039104363049933169.2	x^16 - x^15 + x^14 + 16x^13 + 18x^12 - 35x^11 + 188x^10 + 84x^9 + 171x^8 - 188x^7 - 356x^6 - 239x^5 - 152x^4 - 86x^3 - 33x^2 - x + 1	\( 13^{4}\cdot 17^{14} \)	$C_2\wr C_4$ (as 16T157)	$[2]$ (GRH)
16.0.11740491199707618712081.1	x^16 - 2x^15 + 15x^14 - 35x^13 + 113x^12 - 221x^11 + 535x^10 - 943x^9 + 1741x^8 - 2527x^7 + 3341x^6 - 3537x^5 + 3093x^4 - 2129x^3 + 1061x^2 - 332x + 47	\( 17^{12}\cdot 67^{4} \)	$C_2\wr C_4$ (as 16T157)	Trivial (GRH)
16.4.36555024820228837034401.1	x^16 - 7x^15 + 25x^14 - 58x^13 + 74x^12 + 30x^11 - 432x^10 + 1288x^9 - 2608x^8 + 4186x^7 - 5678x^6 + 6826x^5 - 7289x^4 + 6535x^3 - 4385x^2 + 1912x - 404	\( 17^{12}\cdot 89^{4} \)	$C_2\wr C_4$ (as 16T157)	Trivial (GRH)
16.0.48736115900396728515625.5	x^16 - 7x^15 + 21x^14 - 13x^13 - 214x^12 + 919x^11 - 841x^10 - 3714x^9 + 11282x^8 - 6054x^7 - 23126x^6 + 47194x^5 - 21139x^4 - 39468x^3 + 66681x^2 - 41202x + 9801	\( 5^{14}\cdot 41^{8} \)	$C_2\wr C_4$ (as 16T157)	$[2, 2]$ (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)
16.0.63949946033164306640625.1	x^16 - 6x^15 + 16x^14 - 21x^13 - 4x^12 + 75x^11 - 140x^10 + 45x^9 + 340x^8 - 900x^7 + 1550x^6 - 2325x^5 + 2900x^4 - 3000x^3 + 2750x^2 - 1875x + 625	\( 3^{12}\cdot 5^{12}\cdot 149^{4} \)	$C_2\wr C_4$ (as 16T157)	$[2]$ (GRH)
16.0.96293156986268466282496.1	x^16 + 24x^14 + 216x^12 + 928x^10 + 1996x^8 + 2064x^6 + 880x^4 + 128x^2 + 4	\( 2^{60}\cdot 17^{4} \)	$C_2\wr C_4$ (as 16T157)	$[2, 2]$
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)
16.4.475262857646065983187681.1	x^16 - 6x^15 + 8x^14 + 32x^13 - 163x^12 + 432x^11 - 1068x^10 + 2529x^9 - 4576x^8 + 5366x^7 - 3627x^6 + 1492x^5 - 1128x^4 + 991x^3 + 4x^2 - 455x + 169	\( 13^{8}\cdot 17^{12} \)	$C_2\wr C_4$ (as 16T157)	$[2]$ (GRH)
16.8.540360087662636962890625.1	x^16 - 4x^15 - 11x^14 + 56x^13 + 25x^12 - 304x^11 + 147x^10 + 708x^9 - 782x^8 - 492x^7 + 1097x^6 - 303x^5 - 326x^4 + 232x^3 - 12x^2 - 28x + 1	\( 5^{12}\cdot 19^{12} \)	$C_2\wr C_4$ (as 16T157)	Trivial (GRH)
16.0.540360087662636962890625.4	x^16 - 7x^15 + 21x^14 - 26x^13 - 24x^12 + 199x^11 - 594x^10 + 1124x^9 - 449x^8 - 5566x^7 + 22924x^6 - 52632x^5 + 82214x^4 - 89994x^3 + 67089x^2 - 31190x + 7031	\( 5^{12}\cdot 19^{12} \)	$C_2\wr C_4$ (as 16T157)	$[2, 2]$ (GRH)
16.0.821630081083204084623649.3	x^16 + x^14 + 10x^12 - 34x^11 + 11x^10 - 34x^9 + 117x^8 - 68x^7 + 44x^6 - 272x^5 + 160x^4 + 64x^2 + 256	\( 17^{14}\cdot 47^{4} \)	$C_2\wr C_4$ (as 16T157)	$[2]$ (GRH)
16.0.1170088580305670166015625.4	x^16 + 26x^14 - 5x^13 + 342x^12 - 250x^11 + 3133x^10 - 3595x^9 + 17940x^8 - 17865x^7 + 46967x^6 - 2305x^5 + 8932x^4 + 143460x^3 - 66026x^2 - 2395x + 226391	\( 5^{14}\cdot 61^{8} \)	$C_2\wr C_4$ (as 16T157)	$[2, 2]$ (GRH)
16.0.2392244374201127641154089.1	x^16 - 4x^15 - 3x^14 + 15x^13 + 111x^12 - 385x^11 + 329x^10 - 9x^9 + 1261x^8 - 2917x^7 + 2161x^6 - 987x^5 + 4987x^4 - 1275x^3 + 5463x^2 - 486x + 2349	\( 13^{14}\cdot 157^{4} \)	$C_2\wr C_4$ (as 16T157)	Trivial (GRH)
16.0.2643693128974804931640625.13	x^16 - 4x^15 - 8x^14 + 11x^13 + 53x^12 + 276x^11 + 161x^10 - 4162x^9 + 8038x^8 - 17579x^7 + 69244x^6 - 165310x^5 + 224283x^4 - 187268x^3 + 99078x^2 - 31174x + 4481	\( 5^{12}\cdot 101^{8} \)	$C_2\wr C_4$ (as 16T157)	$[2, 4]$ (GRH)
16.0.3393001956715501807791409.2	x^16 + 9x^14 + 62x^12 - 204x^11 + 369x^10 - 510x^9 + 563x^8 - 510x^7 + 369x^6 - 204x^5 + 62x^4 + 9x^2 + 1	\( 17^{14}\cdot 67^{4} \)	$C_2\wr C_4$ (as 16T157)	$[2, 4]$ (GRH)
16.8.3498450596935634189769921.1	x^16 - 8x^15 + 28x^14 - 56x^13 - 66x^12 + 760x^11 - 2567x^10 + 5487x^9 - 6647x^8 + 2598x^7 + 4184x^6 - 7542x^5 + 5897x^4 - 2695x^3 + 737x^2 - 111x + 7	\( 3^{12}\cdot 37^{12} \)	$C_2\wr C_4$ (as 16T157)	Trivial (GRH)
16.0.3498450596935634189769921.3	x^16 - 3x^15 + 5x^14 + 3x^13 - 21x^12 + 33x^11 + 17x^10 - 105x^9 + 301x^8 - 315x^7 + 153x^6 + 891x^5 - 1701x^4 + 729x^3 + 3645x^2 - 6561x + 6561	\( 3^{12}\cdot 37^{12} \)	$C_2\wr C_4$ (as 16T157)	$[2, 2]$ (GRH)
16.0.6314189689144773879093121.1	x^16 - 92x^12 + 410x^10 + 140x^8 - 2788x^6 + 2213x^4 + 2132x^2 + 16	\( 23^{4}\cdot 41^{12} \)	$C_2\wr C_4$ (as 16T157)	Trivial (GRH)
16.4.10564402173046133902941889.3	x^16 - 2x^15 + 3x^14 + 15x^13 + 2x^12 + 33x^11 + 158x^10 - 181x^9 - 1056x^8 - 2395x^7 - 3509x^6 - 6081x^5 - 13898x^4 - 15926x^3 - 4804x^2 + 9849x + 6799	\( 17^{14}\cdot 89^{4} \)	$C_2\wr C_4$ (as 16T157)	$[2]$ (GRH)
16.0.14030845564476355702701601.1	x^16 + 19x^14 + 82x^12 - 52x^10 + 465x^8 - 704x^6 + 430x^4 - 313x^2 + 169	\( 13^{4}\cdot 53^{12} \)	$C_2\wr C_4$ (as 16T157)	Trivial (GRH)
16.8.20837857125684480535711201.2	x^16 - 5x^15 + 10x^14 - 50x^13 + 106x^12 + 15x^11 - 5x^10 - 20x^9 - 240x^8 + 20x^7 - 5x^6 - 15x^5 + 106x^4 + 50x^3 + 10x^2 + 5x + 1	\( 31^{4}\cdot 41^{12} \)	$C_2\wr C_4$ (as 16T157)	Trivial (GRH)
16.4.42287613544824591671753041.1	x^16 - 8x^15 + 32x^14 - 84x^13 + 130x^12 - 52x^11 - 32x^10 - 412x^9 + 677x^8 + 908x^7 - 7256x^6 + 15648x^5 - 14480x^4 + 5376x^3 + 21952x^2 - 22400x + 5888	\( 37^{4}\cdot 41^{12} \)	$C_2\wr C_4$ (as 16T157)	Trivial (GRH)
16.0.75810861054913358267806081.1	x^16 - 8x^15 + 24x^14 - 28x^13 + 86x^12 - 516x^11 + 1834x^10 - 4154x^9 + 6510x^8 - 7364x^7 + 6269x^6 - 4185x^5 + 6786x^4 - 10033x^3 + 7675x^2 - 2897x + 449	\( 13^{4}\cdot 61^{12} \)	$C_2\wr C_4$ (as 16T157)	Trivial (GRH)
16.4.137350965859713069141239809.7	x^16 - 2x^15 - 4x^14 - 11x^13 + 73x^12 - 488x^11 - 657x^10 - 380x^9 + 3173x^8 + 3943x^7 - 1680x^6 - 2993x^5 - 6922x^4 + 1815x^3 + 7743x^2 - 8131x + 2209	\( 13^{8}\cdot 17^{14} \)	$C_2\wr C_4$ (as 16T157)	$[2, 2]$ (GRH)
16.0.273409957389535508936652241.1	x^16 - 2x^15 + 6x^14 - 22x^13 + 88x^12 - 84x^11 + 331x^10 - 1008x^9 + 2263x^8 - 1530x^7 + 11303x^6 - 10210x^5 + 6167x^4 - 1606x^3 + 760x^2 - 160x + 16	\( 41^{12}\cdot 59^{4} \)	$C_2\wr C_4$ (as 16T157)	Trivial (GRH)
16.0.704265643832481075413250625.1	x^16 - x^15 + x^14 - 9x^13 - 89x^12 + 75x^11 + 37x^10 + 333x^9 + 2727x^8 - 333x^7 + 37x^6 - 75x^5 - 89x^4 + 9x^3 + x^2 + x + 1	\( 5^{4}\cdot 101^{12} \)	$C_2\wr C_4$ (as 16T157)	$[5]$ (GRH)
16.0.1070825365555164876577830001.1	x^16 - 8x^15 + 46x^14 - 182x^13 + 602x^12 - 1610x^11 + 3843x^10 - 7841x^9 + 14530x^8 - 23064x^7 + 33239x^6 - 40203x^5 + 38147x^4 - 26348x^3 + 12040x^2 - 3192x + 368	\( 41^{12}\cdot 83^{4} \)	$C_2\wr C_4$ (as 16T157)	Trivial (GRH)
16.8.1410629873249683485564270561.1	x^16 - 8x^15 + 26x^14 - 42x^13 - 31x^12 + 368x^11 - 1157x^10 + 2364x^9 - 2597x^8 + 252x^7 + 4549x^6 - 8630x^5 + 8420x^4 - 4878x^3 + 575x^2 + 788x - 149	\( 3^{12}\cdot 61^{12} \)	$C_2\wr C_4$ (as 16T157)	Trivial (GRH)
16.0.1410629873249683485564270561.1	x^16 - 8x^15 + 44x^14 - 168x^13 + 412x^12 - 652x^11 + 952x^10 - 1834x^9 + 3838x^8 - 6372x^7 + 7169x^6 - 5123x^5 + 1999x^4 - 93x^3 + 585x^2 - 750x + 375	\( 3^{12}\cdot 61^{12} \)	$C_2\wr C_4$ (as 16T157)	$[2, 2]$ (GRH)
16.0.1450531566903202684958906641.15	x^16 - 7x^15 + 2x^14 + 31x^13 + 210x^12 - 398x^11 - 309x^10 - 1536x^9 + 7236x^8 + 2786x^7 + 13896x^6 - 31552x^5 + 21560x^4 + 19678x^3 + 150733x^2 + 90297x + 44001	\( 13^{12}\cdot 53^{8} \)	$C_2\wr C_4$ (as 16T157)	$[4, 4]$ (GRH)