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 240)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.17247076416015625.1	x^16 - 5x^15 + 13x^14 - 30x^13 + 73x^12 - 160x^11 + 286x^10 - 405x^9 + 455x^8 - 405x^7 + 286x^6 - 160x^5 + 73x^4 - 30x^3 + 13x^2 - 5x + 1	\( 5^{14}\cdot 41^{4} \)	$C_2\wr C_4$ (as 16T158)	Trivial
16.0.25405371337890625.1	x^16 - 4x^15 + 11x^14 - 23x^13 + 47x^12 - 69x^11 + 97x^10 - 108x^9 + 121x^8 - 108x^7 + 97x^6 - 69x^5 + 47x^4 - 23x^3 + 11x^2 - 4x + 1	\( 5^{12}\cdot 101^{4} \)	$C_2\wr C_4$ (as 16T158)	Trivial
16.0.84508306884765625.1	x^16 - 2x^14 - 5x^13 + 3x^12 + 10x^11 + 11x^10 - 5x^9 - 10x^8 - 5x^7 + 11x^6 + 10x^5 + 3x^4 - 5x^3 - 2x^2 + 1	\( 5^{14}\cdot 61^{4} \)	$C_2\wr C_4$ (as 16T158)	Trivial
16.0.1469316970615668736.2	x^16 - 8x^12 + 4x^10 + 49x^8 + 68x^6 + 62x^4 + 8x^2 + 4	\( 2^{44}\cdot 17^{4} \)	$C_2\wr C_4$ (as 16T158)	Trivial
16.0.2386420683693101056.1	x^16 - 5x^15 + 16x^14 - 35x^13 + 57x^12 - 71x^11 + 70x^10 - 57x^9 + 52x^8 - 57x^7 + 70x^6 - 71x^5 + 57x^4 - 35x^3 + 16x^2 - 5x + 1	\( 2^{12}\cdot 17^{12} \)	$C_2\wr C_4$ (as 16T158)	Trivial
16.0.16246753247925108736.2	x^16 - 12x^12 + 12x^10 + 53x^8 - 92x^6 + 2x^4 + 96x^2 + 64	\( 2^{44}\cdot 31^{4} \)	$C_2\wr C_4$ (as 16T158)	Trivial
16.0.16640273717519203921.1	x^16 - 6x^15 + 18x^14 - 37x^13 + 57x^12 - 65x^11 + 74x^10 - 86x^9 + 44x^8 + 3x^7 + 37x^6 - 13x^5 - 41x^4 - 2x^3 + 32x^2 + 32x + 16	\( 13^{4}\cdot 17^{12} \)	$C_2\wr C_4$ (as 16T158)	Trivial
16.8.18446744073709551616.1	x^16 - 12x^12 + 70x^8 - 192x^6 + 308x^4 - 192x^2 + 1	\( 2^{64} \)	$C_2\wr C_4$ (as 16T158)	Trivial (GRH)
16.0.18446744073709551616.9	x^16 - 12x^12 + 70x^8 + 192x^6 + 308x^4 + 192x^2 + 1	\( 2^{64} \)	$C_2\wr C_4$ (as 16T158)	Trivial
16.8.19409669316650390625.2	x^16 - 2x^15 - 7x^14 + 25x^13 - 20x^12 - 53x^11 + 139x^10 - 60x^9 - 186x^8 + 165x^7 + 76x^6 - 71x^5 - 20x^4 + 25x^3 - 13x^2 + x + 1	\( 3^{8}\cdot 5^{12}\cdot 59^{4} \)	$C_2\wr C_4$ (as 16T158)	Trivial
16.8.73786976294838206464.1	x^16 - 12x^12 + 42x^8 - 32x^6 + 28x^4 - 32x^2 + 1	\( 2^{66} \)	$C_2\wr C_4$ (as 16T158)	Trivial (GRH)
16.0.73786976294838206464.7	x^16 - 12x^12 + 42x^8 + 32x^6 + 28x^4 + 32x^2 + 1	\( 2^{66} \)	$C_2\wr C_4$ (as 16T158)	Trivial
16.0.183833097995319003361.2	x^16 - 7x^13 + 13x^11 + 33x^10 - 52x^9 - 65x^8 + 59x^7 + 195x^6 - 221x^5 - 64x^4 + 65x^3 + 247x^2 - 312x + 117	\( 13^{12}\cdot 53^{4} \)	$C_2\wr C_4$ (as 16T158)	$[2]$
16.0.322581582210337451521.1	x^16 - 3x^15 + 9x^14 - 22x^13 + 44x^12 - 30x^11 + 71x^10 + 31x^9 + 28x^8 + 141x^7 + 262x^6 + 407x^5 + 561x^4 + 393x^3 + 191x^2 + 48x + 9	\( 13^{12}\cdot 61^{4} \)	$C_2\wr C_4$ (as 16T158)	Trivial
16.8.1496842348095947265625.1	x^16 - 5x^14 - 24x^12 + 115x^10 - 169x^8 + 60x^6 + 46x^4 - 20x^2 + 1	\( 5^{12}\cdot 19^{10} \)	$C_2\wr C_4$ (as 16T158)	Trivial (GRH)
16.0.1496842348095947265625.2	x^16 - 5x^15 + 4x^14 - 6x^13 + 29x^12 - 13x^11 + 54x^10 + 156x^9 + 416x^8 + 581x^7 + 646x^6 + 516x^5 + 271x^4 + 81x^3 + 21x^2 + 2x + 1	\( 5^{12}\cdot 19^{10} \)	$C_2\wr C_4$ (as 16T158)	$[2, 2]$
16.8.1719192030488525390625.1	x^16 - 5x^15 - 7x^14 + 60x^13 - 20x^12 - 250x^11 + 303x^10 + 445x^9 - 756x^8 - 35x^7 + 672x^6 - 445x^5 - 95x^4 + 225x^3 - 43x^2 - 20x + 1	\( 3^{8}\cdot 5^{12}\cdot 181^{4} \)	$C_2\wr C_4$ (as 16T158)	Trivial (GRH)
16.8.1719192030488525390625.2	x^16 - 2x^15 + 5x^14 + 5x^13 - 59x^12 + 125x^11 - 244x^10 - 70x^9 + 851x^8 - 925x^7 + 455x^6 - 128x^5 - 399x^4 + 645x^3 - 265x^2 - 25x + 25	\( 3^{8}\cdot 5^{12}\cdot 181^{4} \)	$C_2\wr C_4$ (as 16T158)	Trivial (GRH)
16.0.2784831507453778823209.2	x^16 - 5x^15 + 12x^14 - 17x^13 - 11x^12 + 103x^11 - 223x^10 + 231x^9 + 94x^8 - 709x^7 + 1357x^6 - 1500x^5 + 1150x^4 - 756x^3 + 313x^2 - 36x + 9	\( 13^{14}\cdot 29^{4} \)	$C_2\wr C_4$ (as 16T158)	Trivial
16.0.2843010661187557386241.2	x^16 - 4x^15 + 6x^14 - 7x^13 + 22x^12 - 28x^11 + 19x^10 - 135x^9 + 326x^8 - 159x^7 - 59x^6 - 131x^5 + 134x^4 + 58x^3 + 58x^2 + 55x + 13	\( 17^{12}\cdot 47^{4} \)	$C_2\wr C_4$ (as 16T158)	Trivial
16.0.4809039104363049933169.3	x^16 - 4x^14 + 24x^12 - 24x^10 + 168x^8 - 125x^6 + 316x^4 - 16x^2 + 256	\( 13^{4}\cdot 17^{14} \)	$C_2\wr C_4$ (as 16T158)	$[4]$
16.0.11740491199707618712081.2	x^16 - 2x^15 + 4x^14 - 8x^13 + 15x^12 - 56x^11 + 140x^10 - 137x^9 - 105x^8 + 160x^7 + 971x^6 - 270x^5 - 1605x^4 + 1109x^3 + 955x^2 - 692x + 404	\( 17^{12}\cdot 67^{4} \)	$C_2\wr C_4$ (as 16T158)	Trivial (GRH)
16.0.24073289246567116570624.1	x^16 + 24x^14 + 208x^12 + 792x^10 + 1346x^8 + 1080x^6 + 400x^4 + 56x^2 + 1	\( 2^{58}\cdot 17^{4} \)	$C_2\wr C_4$ (as 16T158)	$[2, 2]$
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)
16.0.36555024820228837034401.1	x^16 - 4x^15 + 10x^14 - 30x^13 + 76x^12 - 162x^11 + 348x^10 - 608x^9 + 1010x^8 - 1482x^7 + 2036x^6 - 2054x^5 + 1515x^4 - 940x^3 + 428x^2 - 96x + 16	\( 17^{12}\cdot 89^{4} \)	$C_2\wr C_4$ (as 16T158)	$[7]$ (GRH)
16.0.48736115900396728515625.4	x^16 - 7x^15 + 13x^14 + 51x^13 - 325x^12 + 616x^11 + 458x^10 - 4847x^9 + 10281x^8 - 7000x^7 - 8180x^6 + 12050x^5 + 19365x^4 - 58345x^3 + 56890x^2 - 25615x + 5555	\( 5^{14}\cdot 41^{8} \)	$C_2\wr C_4$ (as 16T158)	$[2, 2]$ (GRH)
16.0.63949946033164306640625.2	x^16 - 8x^15 + 29x^14 - 43x^13 + 2x^12 + 98x^11 - 6x^10 - 669x^9 + 1759x^8 - 2091x^7 + 297x^6 + 2105x^5 - 1969x^4 + 425x^3 + 455x^2 - 635x + 295	\( 3^{12}\cdot 5^{12}\cdot 149^{4} \)	$C_2\wr C_4$ (as 16T158)	$[2]$ (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)
16.8.388716732992848243307769.1	x^16 - 5x^15 + 17x^14 - 52x^13 + 10x^12 + 612x^11 - 2101x^10 + 3008x^9 - 1304x^8 - 2405x^7 + 4628x^6 - 4065x^5 + 2020x^4 - 194x^3 - 142x^2 + 8x + 1	\( 3^{10}\cdot 37^{12} \)	$C_2\wr C_4$ (as 16T158)	Trivial (GRH)
16.0.388716732992848243307769.5	x^16 + 7x^14 + 24x^12 + 103x^10 + 283x^8 + 516x^6 + 1278x^4 + 3888x^2 + 6561	\( 3^{10}\cdot 37^{12} \)	$C_2\wr C_4$ (as 16T158)	$[2, 2]$ (GRH)
16.0.475262857646065983187681.3	x^16 - 5x^15 + 10x^14 - 8x^13 + 114x^12 - 77x^11 + 150x^10 - 214x^9 + 458x^8 + 1359x^7 + 2458x^6 + 2604x^5 + 2213x^4 + 1370x^3 + 632x^2 + 152x + 16	\( 13^{8}\cdot 17^{12} \)	$C_2\wr C_4$ (as 16T158)	$[2, 2]$ (GRH)
16.0.821630081083204084623649.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 155x^12 - 566x^11 + 1303x^10 - 1708x^9 + 851x^8 + 1190x^7 - 2465x^6 + 1700x^5 + 102x^4 - 1054x^3 + 527x^2 + 68	\( 17^{14}\cdot 47^{4} \)	$C_2\wr C_4$ (as 16T158)	$[2]$ (GRH)
16.0.1170088580305670166015625.3	x^16 + 23x^14 + 158x^12 + 556x^10 + 4575x^8 + 32801x^6 + 98463x^4 + 132118x^2 + 116281	\( 5^{14}\cdot 61^{8} \)	$C_2\wr C_4$ (as 16T158)	$[2, 2]$ (GRH)
16.0.2392244374201127641154089.2	x^16 + 33x^14 + 435x^12 + 3033x^10 + 12382x^8 + 30432x^6 + 43773x^4 + 33300x^2 + 10000	\( 13^{14}\cdot 157^{4} \)	$C_2\wr C_4$ (as 16T158)	Trivial (GRH)
16.0.2643693128974804931640625.17	x^16 - x^15 - 4x^14 + 13x^13 + 7x^12 - 331x^11 + 547x^10 + 1543x^9 - 2989x^8 - 17x^7 + 7937x^6 - 34826x^5 + 68112x^4 - 59067x^3 + 37016x^2 - 24321x + 14641	\( 5^{12}\cdot 101^{8} \)	$C_2\wr C_4$ (as 16T158)	$[2, 2, 4]$ (GRH)
16.0.3393001956715501807791409.1	x^16 - 8x^14 + 96x^12 - 5x^10 + 104x^8 - 5x^6 + 96x^4 - 8x^2 + 1	\( 17^{14}\cdot 67^{4} \)	$C_2\wr C_4$ (as 16T158)	$[2, 4]$ (GRH)
16.0.6314189689144773879093121.2	x^16 - 2x^15 + 5x^14 + 18x^13 + 102x^12 + 280x^11 + 478x^10 + 1148x^9 + 2713x^8 + 3734x^7 + 3576x^6 + 3336x^5 + 2992x^4 + 1694x^3 + 577x^2 - 200x + 25	\( 23^{4}\cdot 41^{12} \)	$C_2\wr C_4$ (as 16T158)	$[3]$ (GRH)
16.0.10564402173046133902941889.3	x^16 + 18x^14 + 231x^12 + 1728x^10 + 8753x^8 + 28944x^6 + 63519x^4 + 63882x^2 + 28561	\( 17^{14}\cdot 89^{4} \)	$C_2\wr C_4$ (as 16T158)	$[28]$ (GRH)
16.0.14030845564476355702701601.3	x^16 - 4x^15 + 10x^14 + 13x^13 - 97x^12 + 245x^11 - 45x^10 - 1233x^9 + 4913x^8 - 11494x^7 + 19783x^6 - 23713x^5 + 19273x^4 - 6361x^3 + 637x^2 + 2236x + 2197	\( 13^{4}\cdot 53^{12} \)	$C_2\wr C_4$ (as 16T158)	$[4]$ (GRH)
16.8.20837857125684480535711201.1	x^16 - 6x^15 + 76x^13 - 177x^12 + 44x^11 + 260x^10 - 2455x^9 + 7638x^8 + 2662x^7 - 21047x^6 - 3190x^5 + 9198x^4 + 7377x^3 + 766x^2 - 1889x - 529	\( 31^{4}\cdot 41^{12} \)	$C_2\wr C_4$ (as 16T158)	$[2]$ (GRH)
16.0.42287613544824591671753041.1	x^16 - 2x^15 + 20x^14 - 5x^13 + 99x^12 + 115x^11 + 221x^10 + 268x^9 - 469x^8 - 772x^7 - 2082x^6 - 2549x^5 + 6725x^4 + 2675x^3 + 1273x^2 + 270x + 100	\( 37^{4}\cdot 41^{12} \)	$C_2\wr C_4$ (as 16T158)	$[12]$ (GRH)
16.0.75810861054913358267806081.2	x^16 + 3x^14 + 36x^12 + 321x^10 + 2567x^8 + 1137x^6 + 46836x^4 + 110175x^2 + 105625	\( 13^{4}\cdot 61^{12} \)	$C_2\wr C_4$ (as 16T158)	$[9]$ (GRH)
16.8.124784363598789404541015625.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 215x^12 + 744x^11 + 398x^10 - 7523x^9 + 4391x^8 + 33470x^7 - 27190x^6 - 72935x^5 + 57685x^4 + 63150x^3 - 50900x^2 - 1100x + 25775	\( 5^{12}\cdot 59^{10} \)	$C_2\wr C_4$ (as 16T158)	Trivial (GRH)
16.0.124784363598789404541015625.1	x^16 - x^14 - 34x^12 + 4x^10 - 1139x^8 + 10345x^6 - 7975x^4 + 6125x^2 + 625	\( 5^{12}\cdot 59^{10} \)	$C_2\wr C_4$ (as 16T158)	$[2, 2]$ (GRH)
16.0.137350965859713069141239809.10	x^16 - 6x^15 + 20x^14 + 4x^13 - 76x^12 + 559x^11 - 709x^10 + 1501x^9 + 951x^8 + 34x^7 + 17731x^6 - 55794x^5 + 100861x^4 - 114223x^3 + 61982x^2 - 22763x + 10183	\( 13^{8}\cdot 17^{14} \)	$C_2\wr C_4$ (as 16T158)	$[2, 2, 4]$ (GRH)
16.8.156736652583298165062696729.1	x^16 - 5x^15 - x^14 + 68x^13 - 275x^12 + 369x^11 + 971x^10 - 4951x^9 + 9016x^8 - 7859x^7 - 5134x^6 + 5910x^5 + 21463x^4 + 9142x^3 - 19936x^2 - 4321x + 4861	\( 3^{10}\cdot 61^{12} \)	$C_2\wr C_4$ (as 16T158)	Trivial (GRH)
16.0.156736652583298165062696729.4	x^16 + 23x^14 + 146x^12 + 80x^10 - 2011x^8 - 3823x^6 + 15709x^4 + 59625x^2 + 50625	\( 3^{10}\cdot 61^{12} \)	$C_2\wr C_4$ (as 16T158)	$[2, 2]$ (GRH)
16.0.273409957389535508936652241.2	x^16 - 2x^15 + 2x^14 - 37x^13 + 42x^12 + 163x^11 + 172x^10 - 924x^9 + 587x^8 + 4824x^7 + 26536x^6 + 36664x^5 + 34784x^4 + 13280x^3 + 5120x^2 - 2304x + 256	\( 41^{12}\cdot 59^{4} \)	$C_2\wr C_4$ (as 16T158)	Trivial (GRH)
16.0.704265643832481075413250625.2	x^16 - x^15 + 25x^14 - 120x^13 + 368x^12 - 910x^11 + 2354x^10 - 4094x^9 + 7600x^8 - 10795x^7 + 14067x^6 - 15199x^5 + 14342x^4 - 10867x^3 + 6833x^2 - 3160x + 925	\( 5^{4}\cdot 101^{12} \)	$C_2\wr C_4$ (as 16T158)	$[5, 5]$ (GRH)
16.8.965158384583008082123943169.1	x^16 - 31x^14 + 111x^12 + 814x^10 - 1937x^8 + 1162x^6 - 318x^4 + 44x^2 + 1	\( 13^{12}\cdot 23^{10} \)	$C_2\wr C_4$ (as 16T158)	Trivial (GRH)