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 all 38 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.28446927251784561.1	x^16 - x^15 + x^14 - x^13 - x^12 + 5x^11 - 5x^10 + 7x^9 - 11x^8 + 3x^7 + 10x^6 - 12x^5 + 10x^4 - 13x^3 + 13x^2 - 6x + 1	\( 3^{12}\cdot 13^{4}\cdot 37^{4} \)	16T1275	Trivial
16.0.69300891562890625.1	x^16 - 2x^15 + 7x^14 - 7x^13 + 14x^12 - 3x^11 + 8x^10 + 12x^9 - x^8 + 12x^7 + 8x^6 - 3x^5 + 14x^4 - 7x^3 + 7x^2 - 2x + 1	\( 5^{8}\cdot 11^{4}\cdot 59^{4} \)	16T1275	Trivial
16.0.896799908823040000.1	x^16 - 2x^14 - 4x^13 + 8x^12 - 4x^11 + 2x^10 - 8x^9 + 20x^8 - 48x^7 + 42x^6 + 32x^5 - 36x^4 + 16x^3 + 14x^2 - 8x + 1	\( 2^{34}\cdot 5^{4}\cdot 17^{4} \)	16T1275	Trivial
16.0.13665147289600000000.1	x^16 - 2x^15 + 2x^14 - 4x^13 + 8x^12 - 6x^11 - 4x^10 + 2x^9 - x^8 + 10x^7 - 4x^6 - 10x^5 + 38x^4 - 44x^3 + 34x^2 - 10x + 1	\( 2^{28}\cdot 5^{8}\cdot 19^{4} \)	16T1275	Trivial
16.4.13665147289600000000.1	x^16 + 2x^14 - 10x^12 - 4x^11 - 6x^10 + 60x^9 + 8x^8 - 64x^7 - 22x^6 + 8x^5 + 30x^4 + 12x^3 - 6x^2 - 12x - 1	\( 2^{28}\cdot 5^{8}\cdot 19^{4} \)	16T1275	Trivial (GRH)
16.4.13665147289600000000.2	x^16 - 2x^15 - 2x^14 + 4x^13 - 4x^12 + 10x^11 - 20x^10 + 34x^9 - 3x^8 - 38x^7 + 12x^6 + 10x^5 - 38x^4 + 20x^3 - 6x^2 + 22x + 19	\( 2^{28}\cdot 5^{8}\cdot 19^{4} \)	16T1275	Trivial (GRH)
16.0.228470091372870762496.1	x^16 - 2x^15 + x^14 - 2x^13 + x^12 + 8x^10 - 24x^9 + 40x^8 - 20x^7 + 16x^6 - 116x^5 + 255x^4 - 266x^3 + 151x^2 - 46x + 7	\( 2^{24}\cdot 17^{4}\cdot 113^{4} \)	16T1275	Trivial
16.4.241236403530422265625.1	x^16 - 3x^15 - 5x^14 + 28x^13 - 21x^12 - 65x^11 + 154x^10 - 76x^9 - 169x^8 + 371x^7 - 358x^6 + 186x^5 - 31x^4 - 28x^3 + 24x^2 - 8x + 1	\( 5^{8}\cdot 11^{4}\cdot 59^{6} \)	16T1275	Trivial
16.0.765499680797350690816.1	x^16 + 4x^14 - 16x^13 + 14x^12 - 28x^11 + 90x^10 - 80x^9 + 50x^8 - 240x^7 + 410x^6 - 368x^5 + 523x^4 - 624x^3 + 370x^2 - 180x + 81	\( 2^{24}\cdot 23^{4}\cdot 113^{4} \)	16T1275	Trivial
16.4.2143437045005000114176.1	x^16 - 3x^14 - 2x^13 - 10x^12 + 44x^11 - 56x^10 + 68x^9 - 31x^8 - 80x^7 + 54x^6 + 56x^5 + 38x^4 - 176x^3 + 116x^2 - 8x - 10	\( 2^{28}\cdot 41^{8} \)	16T1275	Trivial
16.8.4933118171545600000000.1	x^16 - 2x^15 - 4x^14 + 4x^13 - 6x^12 + 52x^11 - 52x^10 - 32x^9 - 18x^8 + 196x^7 - 152x^6 - 112x^5 + 232x^4 - 128x^3 + 8x^2 + 16x - 4	\( 2^{28}\cdot 5^{8}\cdot 19^{6} \)	16T1275	Trivial (GRH)
16.8.4933118171545600000000.2	x^16 - 2x^15 - 2x^13 - 18x^12 + 60x^11 + 16x^10 - 130x^9 + 105x^8 - 72x^7 - 160x^6 + 394x^5 - 14x^4 - 270x^3 + 72x^2 + 12x - 1	\( 2^{28}\cdot 5^{8}\cdot 19^{6} \)	16T1275	Trivial (GRH)
16.0.13348273655014443974656.1	x^16 - 6x^15 + 23x^14 - 62x^13 + 146x^12 - 286x^11 + 539x^10 - 990x^9 + 1759x^8 - 2744x^7 + 3680x^6 - 4360x^5 + 4632x^4 - 4112x^3 + 2776x^2 - 1248x + 288	\( 2^{24}\cdot 47^{4}\cdot 113^{4} \)	16T1275	Trivial
16.0.27875807780210549456896.1	x^16 + x^14 - 10x^12 - 7x^10 + 81x^8 - 140x^6 + 136x^4 - 64x^2 + 16	\( 2^{20}\cdot 113^{8} \)	16T1275	Trivial (GRH)
16.0.39002837274649600000000.1	x^16 - 5x^14 + 42x^12 - 120x^10 + 423x^8 - 805x^6 + 1667x^4 - 4545x^2 + 10201	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 101^{4} \)	16T1275	Trivial (GRH)
16.8.69513165311816715206656.1	x^16 - 8x^14 - 16x^13 - 11x^12 + 88x^11 + 234x^10 + 220x^9 - 209x^8 - 1120x^7 - 1666x^6 - 1164x^5 + 359x^4 + 1336x^3 + 1126x^2 - 60x - 279	\( 2^{24}\cdot 71^{4}\cdot 113^{4} \)	16T1275	Trivial (GRH)
16.0.77682842831129952649216.1	x^16 - 6x^15 + 31x^14 - 108x^13 + 306x^12 - 706x^11 + 1368x^10 - 2234x^9 + 3105x^8 - 3662x^7 + 3576x^6 - 2614x^5 + 1188x^4 - 292x^3 + 73x^2 - 10x + 7	\( 2^{24}\cdot 73^{4}\cdot 113^{4} \)	16T1275	Trivial (GRH)
16.0.183575008560835685515264.1	x^16 - 8x^13 + 36x^12 - 16x^11 - 96x^10 + 344x^9 - 720x^8 + 768x^7 + 728x^6 - 4152x^5 + 7844x^4 - 9112x^3 + 7112x^2 - 3632x + 953	\( 2^{50}\cdot 113^{4} \)	16T1275	$[2]$ (GRH)
16.8.183575008560835685515264.1	x^16 - 16x^14 - 24x^13 + 44x^12 + 176x^11 + 160x^10 - 272x^9 - 592x^8 - 64x^7 + 464x^6 + 344x^5 - 436x^4 - 1640x^3 - 1440x^2 - 344x - 23	\( 2^{50}\cdot 113^{4} \)	16T1275	Trivial (GRH)
16.0.183575008560835685515264.2	x^16 - 8x^13 - 20x^12 - 16x^11 + 56x^10 + 72x^9 + 144x^8 + 1112x^7 + 3328x^6 + 5680x^5 + 6060x^4 + 4240x^3 + 3224x^2 + 1624x + 953	\( 2^{50}\cdot 113^{4} \)	16T1275	$[2]$ (GRH)
16.0.963642484118737005838336.1	x^16 - 6x^14 - 16x^13 + 8x^12 + 36x^11 + 74x^10 + 174x^9 - 183x^8 + 120x^7 - 144x^6 - 366x^5 + 1501x^4 - 1442x^3 + 317x^2 + 70x + 49	\( 2^{24}\cdot 113^{4}\cdot 137^{4} \)	16T1275	Trivial (GRH)
16.0.482344596142037401600000000.1	x^16 - 2x^15 + 12x^14 + 24x^13 + 2x^12 + 284x^11 + 432x^10 + 632x^9 + 3064x^8 + 3312x^7 + 7688x^6 + 15344x^5 + 4912x^4 + 23904x^3 + 28784x^2 - 16768x + 40624	\( 2^{24}\cdot 5^{8}\cdot 29^{4}\cdot 101^{4} \)	16T1275	$[2, 70]$ (GRH)
16.16.482344596142037401600000000.1	x^16 - 2x^15 - 34x^14 + 32x^13 + 484x^12 + 24x^11 - 3340x^10 - 2802x^9 + 10150x^8 + 15502x^7 - 9102x^6 - 29800x^5 - 10875x^4 + 15732x^3 + 16348x^2 + 5576x + 631	\( 2^{24}\cdot 5^{8}\cdot 29^{4}\cdot 101^{4} \)	16T1275	Trivial (GRH)
16.8.599153284845516154146300625.1	x^16 - 2x^15 + x^14 - 3x^13 - 84x^12 - 103x^11 + 495x^10 + 965x^9 - 540x^8 - 2767x^7 - 1558x^6 + 3032x^5 + 3823x^4 - 1034x^3 - 4423x^2 + 2240x - 80	\( 5^{4}\cdot 97^{4}\cdot 101^{8} \)	16T1275	Trivial (GRH)
16.16.958273018125597330620022784.1	x^16 - 4x^15 - 28x^14 + 112x^13 + 254x^12 - 992x^11 - 1128x^10 + 3736x^9 + 3140x^8 - 6336x^7 - 5236x^6 + 4064x^5 + 3760x^4 - 480x^3 - 704x^2 + 34	\( 2^{46}\cdot 17^{4}\cdot 113^{4} \)	16T1275	Trivial (GRH)
16.0.1237098814777743829444000000.1	x^16 + 22x^14 + 133x^12 + 279x^10 + 302x^8 + 161x^6 + 503x^4 + 843x^2 + 361	\( 2^{8}\cdot 5^{6}\cdot 13^{4}\cdot 101^{8} \)	16T1275	$[2, 2]$ (GRH)
16.8.14978832121137903853657515625.1	x^16 - 7x^15 - 4x^14 + 150x^13 - 318x^12 - 412x^11 + 2021x^10 - 3094x^9 + 2474x^8 + 7452x^7 - 21650x^6 + 13516x^5 + 8155x^4 - 11401x^3 + 2457x^2 + 1032x - 359	\( 5^{6}\cdot 97^{4}\cdot 101^{8} \)	16T1275	$[2]$ (GRH)
16.0.14978832121137903853657515625.3	x^16 + 22x^14 - 11x^13 + 79x^12 + 228x^11 + 299x^10 - 550x^9 + 1639x^8 + 3343x^7 - 913x^6 - 1102x^5 + 15452x^4 + 8281x^3 - 3747x^2 + 17411x + 21793	\( 5^{6}\cdot 97^{4}\cdot 101^{8} \)	16T1275	$[12]$ (GRH)
16.0.125015544363803099161600000000.1	x^16 + 87x^14 + 3102x^12 + 58812x^10 + 639588x^8 + 3982276x^6 + 13169203x^4 + 18412939x^2 + 2627641	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 1621^{4} \)	16T1275	$[11400]$ (GRH)
16.4.277280164669720467865600000000.1	x^16 - 6x^15 + 24x^14 - 70x^13 + 146x^12 - 140x^11 - 2134x^10 - 978x^9 + 43507x^8 - 174208x^7 + 219686x^6 + 251926x^5 - 29840x^4 + 333106x^3 + 252166x^2 - 77336x - 43021	\( 2^{28}\cdot 5^{8}\cdot 71^{4}\cdot 101^{4} \)	16T1275	Trivial (GRH)
16.4.277280164669720467865600000000.2	x^16 - 2x^15 - 8x^14 + 88x^13 - 100x^12 - 44x^11 + 2124x^10 - 52x^9 - 7660x^8 - 45012x^7 - 118016x^6 - 230312x^5 - 340336x^4 - 367600x^3 - 284600x^2 - 175000x - 2500	\( 2^{28}\cdot 5^{8}\cdot 71^{4}\cdot 101^{4} \)	16T1275	$[2]$ (GRH)
16.0.374470803028447596341437890625.1	x^16 - x^15 - 4x^14 + 93x^13 - 135x^12 - 275x^11 + 2603x^10 - 4305x^9 - 2715x^8 + 365x^7 + 10445x^6 - 7300x^5 + 17200x^4 - 7575x^3 + 5200x^2 - 1375x + 125	\( 5^{8}\cdot 97^{4}\cdot 101^{8} \)	16T1275	$[8]$ (GRH)
16.8.35332779248867141512750084000000.1	x^16 - 21x^14 - 309x^12 + 181x^10 + 6970x^8 - 6973x^6 + 5145x^4 - 2950x^2 + 625	\( 2^{8}\cdot 5^{6}\cdot 13^{8}\cdot 101^{8} \)	16T1275	$[2, 2]$ (GRH)
16.8.35332779248867141512750084000000.2	x^16 + 6x^14 + 127x^12 - 5144x^10 + 23711x^8 + 16878x^6 - 8239x^4 - 21340x^2 + 400	\( 2^{8}\cdot 5^{6}\cdot 13^{8}\cdot 101^{8} \)	16T1275	$[2, 2]$ (GRH)
16.0.695053442111154907045733771247616.1	x^16 - 14x^14 + 137x^12 + 960x^10 - 2750x^8 - 17708x^6 + 228546x^4 + 569536x^2 + 512656	\( 2^{48}\cdot 7^{8}\cdot 809^{4} \)	16T1275	$[22]$ (GRH)
16.0.2780213768444619628182935084990464.1	x^16 + 4x^14 + 38x^12 - 280x^10 - 3280x^8 + 124320x^6 + 2021424x^4 + 11560000x^2 + 25000000	\( 2^{50}\cdot 7^{8}\cdot 809^{4} \)	16T1275	$[44]$ (GRH)
16.8.337465832223268533088336601531023360000.1	x^16 + 32x^14 - 5684x^12 + 43670x^10 + 1997738x^8 - 3137136x^6 - 116614611x^4 + 76117990x^2 + 1243225	\( 2^{24}\cdot 5^{4}\cdot 13^{4}\cdot 101^{12} \)	16T1275	$[2, 2]$ (GRH)
16.8.337465832223268533088336601531023360000.2	x^16 - 28x^14 - 4140x^12 + 16396x^10 + 2770854x^8 - 4903364x^6 - 421149516x^4 + 2290997460x^2 + 162435025	\( 2^{24}\cdot 5^{4}\cdot 13^{4}\cdot 101^{12} \)	16T1275	$[2, 2]$ (GRH)