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
16.0.2409821569600000000.4	x^16 - x^14 + x^12 - 2x^10 + 6x^8 + 3x^6 + 6x^4 + 4x^2 + 1	\( 2^{12}\cdot 5^{8}\cdot 197^{4} \)	16T1765	Trivial
16.0.2409821569600000000.5	x^16 - 3x^14 + 7x^12 - 9x^10 + 11x^8 - 13x^6 + 11x^4 - 5x^2 + 1	\( 2^{12}\cdot 5^{8}\cdot 197^{4} \)	16T1765	Trivial
16.0.18174874240000000000.1	x^16 - 3x^15 + 4x^14 + x^13 - 5x^12 + 5x^11 - 7x^9 + 4x^8 + 7x^7 - 5x^5 - 5x^4 - x^3 + 4x^2 + 3x + 1	\( 2^{16}\cdot 5^{10}\cdot 73^{4} \)	16T1765	Trivial
16.0.18174874240000000000.2	x^16 - 4x^15 + 12x^14 - 28x^13 + 52x^12 - 96x^11 + 159x^10 - 219x^9 + 269x^8 - 268x^7 + 241x^6 - 173x^5 + 112x^4 - 56x^3 + 23x^2 - 7x + 1	\( 2^{16}\cdot 5^{10}\cdot 73^{4} \)	16T1765	Trivial
16.0.25710774072506781696.2	x^16 - 3x^14 + 7x^12 - 4x^10 + 3x^8 + 16x^6 + 5x^4 + 20x^2 + 16	\( 2^{12}\cdot 3^{8}\cdot 23^{4}\cdot 43^{4} \)	16T1765	Trivial
16.0.25710774072506781696.3	x^16 - 2x^14 - 8x^12 + 32x^8 + 46x^6 + 30x^4 + 9x^2 + 1	\( 2^{12}\cdot 3^{8}\cdot 23^{4}\cdot 43^{4} \)	16T1765	Trivial
16.4.7269949696000000000000.1	x^16 - 4x^15 + 12x^14 - 22x^13 + 43x^12 - 32x^11 + 27x^10 + 64x^9 - 65x^8 + 228x^7 - 42x^6 + 168x^5 + 61x^4 + 8x^3 - 42x^2 - 40x - 4	\( 2^{20}\cdot 5^{12}\cdot 73^{4} \)	16T1765	Trivial (GRH)
16.4.7269949696000000000000.2	x^16 - 4x^15 + 12x^14 - 22x^13 + 13x^12 - 32x^11 + 47x^10 - 16x^9 + 35x^8 - 12x^7 + 8x^6 - 62x^5 + 51x^4 - 2x^3 - 22x^2 + 20x - 4	\( 2^{20}\cdot 5^{12}\cdot 73^{4} \)	16T1765	Trivial (GRH)
16.0.7309866965017600000000.2	x^16 + 7x^14 + 18x^12 + 25x^10 + 27x^8 + 21x^6 + 14x^4 + 7x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 17^{4}\cdot 43^{4} \)	16T1765	$[2, 2]$
16.8.7309866965017600000000.2	x^16 - 7x^14 + 18x^12 - 25x^10 + 27x^8 - 21x^6 + 14x^4 - 7x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 17^{4}\cdot 43^{4} \)	16T1765	Trivial (GRH)
16.8.9870629149081600000000.1	x^16 - 8x^15 + 26x^14 - 42x^13 - 16x^12 + 278x^11 - 798x^10 + 1394x^9 - 1603x^8 + 1106x^7 - 108x^6 - 732x^5 + 922x^4 - 604x^3 + 232x^2 - 48x + 4	\( 2^{24}\cdot 5^{8}\cdot 197^{4} \)	16T1765	Trivial (GRH)
16.8.9870629149081600000000.2	x^16 - 2x^15 - 8x^14 + 8x^13 + 25x^12 + 34x^11 - 128x^10 + 18x^9 + 21x^8 + 102x^7 + 32x^6 - 192x^5 + 87x^4 + 14x^3 - 14x^2 + 4x - 1	\( 2^{24}\cdot 5^{8}\cdot 197^{4} \)	16T1765	Trivial (GRH)
16.0.27865972927434184474624.1	x^16 - 4x^14 - 9x^12 + 31x^10 + 45x^8 - 121x^6 + 157x^4 + 24x^2 + 4	\( 2^{14}\cdot 7^{8}\cdot 11^{4}\cdot 67^{4} \)	16T1765	Trivial
16.0.146334787433680397664256.1	x^16 + 4x^14 + 6x^12 + 8x^10 + 10x^8 + 12x^6 + 18x^4 + 8x^2 + 1	\( 2^{48}\cdot 151^{4} \)	16T1765	$[2]$ (GRH)
16.8.146334787433680397664256.1	x^16 - 4x^14 + 6x^12 - 8x^10 + 10x^8 - 12x^6 + 18x^4 - 8x^2 + 1	\( 2^{48}\cdot 151^{4} \)	16T1765	Trivial (GRH)
16.0.445855566838946951593984.1	x^16 - 7x^12 + 5x^10 + 25x^8 - 49x^6 + 43x^4 - 18x^2 + 4	\( 2^{18}\cdot 7^{8}\cdot 11^{4}\cdot 67^{4} \)	16T1765	Trivial (GRH)
16.4.1116252260817973811347456.1	x^16 + 8x^14 - 16x^13 + 48x^12 - 160x^11 + 248x^10 - 640x^9 + 1004x^8 - 1888x^7 + 2576x^6 - 3040x^5 + 3024x^4 - 1280x^3 - 464x^2 + 1440x - 292	\( 2^{50}\cdot 23^{2}\cdot 37^{4} \)	16T1765	Trivial (GRH)
16.4.1116252260817973811347456.2	x^16 - 16x^14 - 16x^13 + 108x^12 + 256x^11 - 152x^10 - 1264x^9 - 1454x^8 + 1248x^7 + 5152x^6 + 5520x^5 + 1764x^4 - 1376x^3 - 1352x^2 - 304x + 41	\( 2^{50}\cdot 23^{2}\cdot 37^{4} \)	16T1765	$[2]$ (GRH)
16.0.2306630648330891196104704.1	x^16 - 6x^14 + 23x^12 - 44x^10 + 40x^8 - 44x^6 + 132x^4 - 8x^2 + 4	\( 2^{42}\cdot 23^{4}\cdot 37^{4} \)	16T1765	$[2]$ (GRH)
16.0.2306630648330891196104704.2	x^16 + 6x^14 + 23x^12 + 44x^10 + 40x^8 + 44x^6 + 132x^4 + 8x^2 + 4	\( 2^{42}\cdot 23^{4}\cdot 37^{4} \)	16T1765	$[2]$ (GRH)
16.4.11779494096708097600000000.1	x^16 + 12x^14 + 50x^12 + 78x^10 - 105x^6 - 62x^4 + 9x^2 + 1	\( 2^{12}\cdot 5^{8}\cdot 59^{4}\cdot 157^{4} \)	16T1765	$[2]$ (GRH)
16.0.13860617012386201600000000.1	x^16 - 6x^15 + 12x^14 - 6x^13 - 15x^12 + 44x^11 + 178x^10 - 1574x^9 + 3753x^8 - 4722x^7 + 5984x^6 - 4808x^5 - 1960x^4 + 5140x^3 + 256x^2 - 2184x + 676	\( 2^{24}\cdot 5^{8}\cdot 59^{2}\cdot 157^{4} \)	16T1765	Trivial (GRH)
16.4.86436844905535897600000000.5	x^16 - 10x^14 - 35x^12 + 474x^10 - 343x^8 - 2370x^6 - 671x^4 + 8784x^2 + 3721	\( 2^{32}\cdot 5^{8}\cdot 61^{6} \)	16T1765	Trivial (GRH)
16.4.86436844905535897600000000.6	x^16 + 38x^14 + 582x^12 + 4518x^10 + 17967x^8 + 29750x^6 - 4270x^4 - 37576x^2 + 3721	\( 2^{32}\cdot 5^{8}\cdot 61^{6} \)	16T1765	Trivial (GRH)
16.12.188471905547329561600000000.1	x^16 - 12x^14 + 50x^12 - 78x^10 + 105x^6 - 62x^4 - 9x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 59^{4}\cdot 157^{4} \)	16T1765	Trivial (GRH)
16.4.188471905547329561600000000.1	x^16 + 8x^14 - 5x^12 - 148x^10 - 180x^8 + 415x^6 + 588x^4 + 101x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 59^{4}\cdot 157^{4} \)	16T1765	$[2]$ (GRH)
16.0.221769872198179225600000000.1	x^16 - 8x^15 + 32x^14 - 68x^13 + 44x^12 + 184x^11 - 744x^10 + 1392x^9 - 472x^8 - 4416x^7 + 8384x^6 + 2784x^5 - 24352x^4 + 18432x^3 + 30016x^2 - 64256x + 37696	\( 2^{28}\cdot 5^{8}\cdot 59^{2}\cdot 157^{4} \)	16T1765	$[4]$ (GRH)
16.8.221769872198179225600000000.2	x^16 - 2x^15 - 4x^14 + 42x^13 - 50x^12 - 506x^11 - 808x^10 - 138x^9 + 2834x^8 + 3614x^7 - 1932x^6 - 2278x^5 - 4234x^4 - 2786x^3 + 8360x^2 - 1986x - 171	\( 2^{28}\cdot 5^{8}\cdot 59^{2}\cdot 157^{4} \)	16T1765	Trivial (GRH)
16.12.954139021833355905600000000.1	x^16 - x^14 - 101x^12 + 187x^10 + 467x^8 - 1509x^6 + 1431x^4 - 567x^2 + 81	\( 2^{12}\cdot 3^{4}\cdot 5^{8}\cdot 59^{4}\cdot 157^{4} \)	16T1765	Trivial (GRH)
16.8.8866688212183945757826482176.1	x^16 - 24x^14 + 4x^12 + 2568x^10 - 2762x^8 - 83240x^6 - 137884x^4 - 13640x^2 + 47089	\( 2^{44}\cdot 23^{4}\cdot 31^{2}\cdot 37^{4} \)	16T1765	Trivial (GRH)
16.0.16107537565044937378584592384.1	x^16 - 36x^14 + 592x^12 - 5428x^10 + 30016x^8 - 102064x^6 + 198244x^4 - 183816x^2 + 103684	\( 2^{44}\cdot 23^{2}\cdot 31^{4}\cdot 37^{4} \)	16T1765	$[2, 2]$ (GRH)
16.8.90939508218265868697600000000.1	x^16 - 4x^15 - 22x^14 + 138x^13 - 96x^12 - 1370x^11 + 5206x^10 - 1564x^9 - 35133x^8 + 88226x^7 + 6130x^6 - 378620x^5 + 458022x^4 + 336786x^3 - 547964x^2 - 148970x + 5959	\( 2^{24}\cdot 3^{8}\cdot 5^{8}\cdot 59^{2}\cdot 157^{4} \)	16T1765	Trivial (GRH)
16.8.141867011394943132125223714816.1	x^16 - 8x^14 - 94x^12 + 752x^10 + 614x^8 - 6376x^6 - 9100x^4 - 992x^2 + 961	\( 2^{48}\cdot 23^{4}\cdot 31^{2}\cdot 37^{4} \)	16T1765	Trivial (GRH)
16.0.257720601040718998057353478144.1	x^16 - 32x^14 + 360x^12 - 160x^10 - 3696x^8 + 1344x^6 + 11360x^4 + 11776x^2 + 33856	\( 2^{48}\cdot 23^{2}\cdot 31^{4}\cdot 37^{4} \)	16T1765	$[2, 2]$ (GRH)
16.16.56439717689818399417250046546018304.1	x^16 - 196x^14 + 12770x^12 - 397676x^10 + 6623154x^8 - 60058004x^6 + 281455796x^4 - 584478276x^2 + 382319809	\( 2^{48}\cdot 23^{4}\cdot 37^{4}\cdot 19553^{2} \)	16T1765	Trivial (GRH)
16.16.56439717689818399417250046546018304.2	x^16 - 212x^14 + 14804x^12 - 458572x^10 + 7109906x^8 - 57369148x^6 + 241684994x^4 - 495473020x^2 + 382319809	\( 2^{48}\cdot 23^{4}\cdot 37^{4}\cdot 19553^{2} \)	16T1765	Trivial (GRH)
16.0.40198805069552937123844028608838939705344.1	x^16 + 1320x^14 + 695390x^12 + 188299712x^10 + 28176729004x^8 + 2334616894288x^6 + 100031244818584x^4 + 1742607190434464x^2 + 1089218734982596	\( 2^{48}\cdot 23^{4}\cdot 37^{4}\cdot 601^{2}\cdot 27457^{2} \)	16T1765	$[2, 2, 2, 135809000]$ (GRH)
16.0.46871787785697452696878168826792882590449664.1	x^16 + 1712x^14 + 1233350x^12 + 488006872x^10 + 115758148212x^8 + 16792514721616x^6 + 1446242915789840x^4 + 67056318133293792x^2 + 1270028532190841476	\( 2^{48}\cdot 23^{6}\cdot 37^{4}\cdot 24499031^{2} \)	16T1765	$[2, 2, 2, 2723433000]$ (GRH)