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 34 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.4080400000000000000.1	x^16 - 4x^15 + 4x^14 + 16x^13 - 59x^12 + 78x^11 + 11x^10 - 212x^9 + 402x^8 - 408x^7 + 231x^6 - 28x^5 - 9x^4 - 66x^3 + 129x^2 - 86x + 31	\( 2^{16}\cdot 5^{14}\cdot 101^{2} \)	16T1392	Trivial (GRH)
16.0.4080400000000000000.2	x^16 - 6x^15 + 9x^14 + 14x^13 - 49x^12 - 8x^11 + 156x^10 - 68x^9 - 288x^8 + 168x^7 + 346x^6 - 212x^5 - 214x^4 + 166x^3 + 39x^2 - 54x + 11	\( 2^{16}\cdot 5^{14}\cdot 101^{2} \)	16T1392	Trivial (GRH)
16.4.88284816000000000000.3	x^16 - 4x^15 + 5x^14 - 14x^13 + 44x^12 - 72x^11 + 91x^10 - 158x^9 + 321x^8 - 516x^7 + 614x^6 - 546x^5 + 364x^4 - 178x^3 + 60x^2 - 12x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 29^{2} \)	16T1392	Trivial (GRH)
16.4.88284816000000000000.4	x^16 - 6x^15 + 19x^14 - 44x^13 + 86x^12 - 128x^11 + 136x^10 - 24x^9 - 294x^8 + 786x^7 - 1295x^6 + 1484x^5 - 1243x^4 + 608x^3 - 110x^2 - 96x + 31	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 29^{2} \)	16T1392	Trivial (GRH)
16.8.290029415062500000000.2	x^16 - 7x^14 + 5x^12 + 38x^10 - 21x^8 - 78x^6 - 30x^4 + 2x^2 + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4} \)	16T1392	Trivial (GRH)
16.8.290029415062500000000.3	x^16 + 2x^14 - 14x^12 - 14x^10 + 39x^8 + 38x^6 - 11x^4 - 11x^2 + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4} \)	16T1392	Trivial (GRH)
16.12.1158738620062500000000.1	x^16 - 5x^14 - 13x^12 + 130x^10 - 311x^8 + 320x^6 - 142x^4 + 20x^2 + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 41^{4} \)	16T1392	Trivial (GRH)
16.4.1158738620062500000000.1	x^16 + 16x^14 + 89x^12 + 222x^10 + 239x^8 + 54x^6 - 49x^4 - 2x^2 + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 41^{4} \)	16T1392	Trivial (GRH)
16.4.2330572176000000000000.2	x^16 - 2x^15 - 2x^14 - 8x^13 + 28x^12 - 32x^11 + 79x^10 + 16x^9 - 262x^8 + 278x^7 - 39x^6 - 160x^5 + 88x^4 + 126x^3 + 57x^2 + 12x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 149^{2} \)	16T1392	Trivial (GRH)
16.4.2330572176000000000000.3	x^16 - 6x^15 + 15x^14 - 30x^13 + 61x^12 - 130x^11 + 264x^10 - 460x^9 + 686x^8 - 860x^7 + 925x^6 - 806x^5 + 601x^4 - 380x^3 + 145x^2 - 80x - 5	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 149^{2} \)	16T1392	Trivial (GRH)
16.12.7250735376562500000000.1	x^16 - 8x^15 + 16x^14 + 23x^13 - 109x^12 + 91x^11 - 26x^10 + 149x^9 - 38x^8 - 691x^7 + 1169x^6 - 654x^5 - 54x^4 + 178x^3 - 44x^2 - 3x + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{14}\cdot 29^{4} \)	16T1392	Trivial (GRH)
16.4.7250735376562500000000.1	x^16 - 40x^12 - 70x^10 + 345x^8 + 1250x^6 + 1425x^4 + 575x^2 + 25	\( 2^{8}\cdot 3^{8}\cdot 5^{14}\cdot 29^{4} \)	16T1392	Trivial (GRH)
16.0.7758791056000000000000.1	x^16 - 6x^15 + 12x^14 + 18x^13 - 175x^12 + 494x^11 - 632x^10 - 438x^9 + 4080x^8 - 10482x^7 + 17604x^6 - 21072x^5 + 19534x^4 - 13606x^3 + 9306x^2 - 5188x + 2861	\( 2^{16}\cdot 5^{12}\cdot 19^{4}\cdot 61^{2} \)	16T1392	$[2]$ (GRH)
16.0.78345418253203369140625.1	x^16 - 4x^15 + 28x^14 - 88x^13 + 302x^12 - 682x^11 + 1537x^10 - 2539x^9 + 3950x^8 - 4498x^7 + 4616x^6 - 3328x^5 + 2263x^4 - 967x^3 + 530x^2 - 131x + 61	\( 5^{12}\cdot 41^{2}\cdot 661^{4} \)	16T1392	$[3]$ (GRH)
16.0.998848331776000000000000.1	x^16 + 20x^14 - 12x^13 + 140x^12 - 120x^11 + 484x^10 - 540x^9 + 995x^8 - 1248x^7 + 1240x^6 - 1260x^5 + 1116x^4 - 480x^3 + 60x^2 + 25	\( 2^{40}\cdot 5^{12}\cdot 61^{2} \)	16T1392	$[2]$ (GRH)
16.8.998848331776000000000000.1	x^16 - 16x^14 - 12x^13 + 50x^12 + 64x^11 - 40x^10 - 252x^9 + 22x^8 + 768x^7 + 328x^6 - 1180x^5 - 586x^4 + 736x^3 + 208x^2 - 172x - 19	\( 2^{40}\cdot 5^{12}\cdot 61^{2} \)	16T1392	Trivial (GRH)
16.0.998848331776000000000000.2	x^16 - 4x^13 - 30x^12 + 80x^11 - 104x^10 - 60x^9 + 1430x^8 - 64x^7 + 840x^6 - 100x^5 - 794x^4 - 2320x^3 + 2400x^2 + 500x + 125	\( 2^{40}\cdot 5^{12}\cdot 61^{2} \)	16T1392	$[6]$ (GRH)
16.8.998848331776000000000000.2	x^16 - 4x^14 - 4x^13 - 100x^12 - 88x^11 + 140x^10 + 156x^9 + 827x^8 + 224x^7 - 1688x^6 - 140x^5 + 1604x^4 - 32x^3 - 1228x^2 - 264x + 121	\( 2^{40}\cdot 5^{12}\cdot 61^{2} \)	16T1392	Trivial (GRH)
16.12.28379910764965177995302489030656.1	x^16 - 40x^14 + 324x^12 + 5160x^10 - 90786x^8 + 394376x^6 - 153564x^4 - 1126216x^2 + 693889	\( 2^{66}\cdot 17^{2}\cdot 191^{4} \)	16T1392	Trivial (GRH)
16.4.8201794211074936440642419329859584.1	x^16 + 40x^14 - 876x^12 - 57096x^10 - 728694x^8 - 523736x^6 + 32570300x^4 + 94604728x^2 + 24137569	\( 2^{66}\cdot 17^{4}\cdot 191^{4} \)	16T1392	$[2, 2, 4]$ (GRH)
16.4.8201794211074936440642419329859584.2	x^16 + 16x^14 - 1200x^12 - 22000x^10 + 295164x^8 + 7447904x^6 + 33838432x^4 + 7389152x^2 + 334084	\( 2^{66}\cdot 17^{4}\cdot 191^{4} \)	16T1392	$[2, 2, 4]$ (GRH)
16.8.91603437103816431399094670113021609.1	x^16 - 4x^14 - 530x^12 + 1604x^10 + 17321x^8 - 37320x^6 - 92560x^4 + 111488x^2 + 43264	\( 13^{6}\cdot 17^{12}\cdot 2389^{4} \)	16T1392	Trivial (GRH)
16.8.91603437103816431399094670113021609.2	x^16 - 2x^15 - 3x^14 - 1011x^12 + 2505x^11 + 9904x^10 - 29093x^9 + 73976x^8 - 68697x^7 - 369711x^6 + 643684x^5 + 394497x^4 - 1077988x^3 - 230331x^2 + 199950x - 181612	\( 13^{6}\cdot 17^{12}\cdot 2389^{4} \)	16T1392	Trivial (GRH)
16.12.2370318527000656631345659186329419776.1	x^16 - 112x^14 - 192x^13 - 780x^12 + 6448x^11 + 281136x^10 + 751200x^9 - 4977480x^8 - 35641232x^7 - 58032376x^6 + 286004864x^5 + 1391830936x^4 + 2111300176x^3 + 1233840416x^2 + 144814432x - 61147198	\( 2^{66}\cdot 17^{6}\cdot 191^{4} \)	16T1392	$[2, 2]$ (GRH)
16.8.13895289211961074442017936000000000000.1	x^16 - 4x^14 - 1122x^12 + 3380x^10 + 219641x^8 - 444920x^6 - 2111568x^4 + 2334592x^2 + 952576	\( 2^{16}\cdot 5^{12}\cdot 61^{2}\cdot 123601^{4} \)	16T1392	Trivial (GRH)
16.12.16657103355112538759522949529600000000.1	x^16 - 59x^14 + 788x^12 + 6978x^10 - 196420x^8 + 771016x^6 + 3790960x^4 - 18249536x^2 + 1893376	\( 2^{24}\cdot 5^{8}\cdot 17^{12}\cdot 257^{4} \)	16T1392	$[2, 2]$ (GRH)
16.12.31049437544654067124090386841600000000.1	x^16 - 119x^14 + 2448x^12 + 59126x^10 - 1956632x^8 + 9645664x^6 + 24747648x^4 - 152702976x^2 + 75759616	\( 2^{22}\cdot 5^{8}\cdot 17^{14}\cdot 103^{4} \)	16T1392	$[4]$ (GRH)
16.8.467063129754478147962797661051173208064.1	x^16 - 48x^14 - 64x^13 - 3408x^12 + 7200x^11 + 53536x^10 - 108272x^9 + 3455620x^8 - 2300608x^7 + 4685344x^6 + 24897568x^5 - 434348320x^4 - 451978368x^3 - 1755236576x^2 - 1566486560x + 11378288956	\( 2^{62}\cdot 17^{6}\cdot 127^{6} \)	16T1392	$[2]$ (GRH)
16.8.467063129754478147962797661051173208064.2	x^16 - 8x^15 + 40x^14 + 1160x^13 - 5160x^12 - 73240x^11 + 54016x^10 + 1888200x^9 - 345306x^8 - 42616648x^7 - 94591600x^6 + 214400888x^5 + 1048954592x^4 + 880219560x^3 - 1527001640x^2 - 3117641336x - 1528687073	\( 2^{62}\cdot 17^{6}\cdot 127^{6} \)	16T1392	$[2]$ (GRH)
16.0.1662738954297838893504019372193112653824.1	x^16 - 100x^14 + 4502x^12 - 118900x^10 + 2946513x^8 - 69044400x^6 + 980020000x^4 - 6596000000x^2 + 28900000000	\( 2^{48}\cdot 17^{2}\cdot 103^{4}\cdot 3671^{4} \)	16T1392	$[3, 19596]$ (GRH)
16.8.2145154971555059070700713179815969030144.1	x^16 - 4x^14 - 1930x^12 + 5804x^10 + 456561x^8 - 922800x^6 - 55520x^4 + 517888x^2 + 73984	\( 2^{48}\cdot 17^{2}\cdot 271^{4}\cdot 1487^{4} \)	16T1392	$[2]$ (GRH)
16.16.1747511875136079735717765427007261010558976.1	x^16 - 492x^14 - 344x^13 + 62812x^12 + 56712x^11 - 3180476x^10 - 3553552x^9 + 71711252x^8 + 76869440x^7 - 755140300x^6 - 581322312x^5 + 3594006416x^4 + 935572536x^3 - 6503647516x^2 + 1636792368x + 726055567	\( 2^{48}\cdot 17^{2}\cdot 16673^{6} \)	16T1392	Trivial (GRH)
16.0.1922126231168301760890646394255238227820544.1	x^16 - 148x^14 - 200x^13 + 22422x^12 + 46936x^11 - 1108984x^10 - 2576672x^9 + 59042839x^8 + 33297712x^7 - 2203368876x^6 - 1557349288x^5 + 56424774224x^4 - 35048106120x^3 - 1157432693384x^2 + 1851433282320x + 13920305159422	\( 2^{50}\cdot 17^{4}\cdot 103^{4}\cdot 3671^{4} \)	16T1392	$[2, 6, 19596]$ (GRH)
16.16.2020123727657308174489736833620393728206176256.1	x^16 - 1236x^14 - 136x^13 + 568104x^12 + 111336x^11 - 124399308x^10 - 46989984x^9 + 14186331356x^8 + 8204441920x^7 - 844541825988x^6 - 576556296440x^5 + 24403328720004x^4 + 13466549733144x^3 - 298573308211004x^2 - 106821264489440x + 1048645407290447	\( 2^{50}\cdot 17^{4}\cdot 16673^{6} \)	16T1392	$[2]$ (GRH)