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 40 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.2538249124948475904.2	x^16 - 7x^14 + 22x^12 - 39x^10 + 40x^8 - 23x^6 + 9x^4 - 6x^2 + 4	\( 2^{26}\cdot 3^{8}\cdot 7^{8} \)	16T1228	Trivial
16.0.3329778253824000000.1	x^16 - 6x^15 + 14x^14 - 16x^13 + 34x^11 - 46x^10 + 10x^9 + 39x^8 - 26x^7 - 14x^6 + 6x^5 + 38x^4 + 4x^3 - 32x^2 + 6x + 13	\( 2^{28}\cdot 3^{8}\cdot 5^{6}\cdot 11^{2} \)	16T1228	Trivial
16.0.3329778253824000000.2	x^16 - 2x^15 - 6x^14 + 22x^13 - 4x^12 - 68x^11 + 90x^10 + 34x^9 - 161x^8 + 92x^7 + 74x^6 - 110x^5 + 32x^4 + 14x^3 - 8x^2 + 1	\( 2^{28}\cdot 3^{8}\cdot 5^{6}\cdot 11^{2} \)	16T1228	Trivial
16.0.9934297104384000000.1	x^16 - 4x^15 + 2x^14 + 4x^13 + 16x^12 - 28x^11 - 48x^10 + 76x^9 + 74x^8 - 100x^7 - 144x^6 + 232x^5 + 12x^4 - 208x^3 + 144x^2 - 32x + 4	\( 2^{28}\cdot 3^{8}\cdot 5^{6}\cdot 19^{2} \)	16T1228	Trivial
16.0.62086835430400000000.1	x^16 - 6x^15 + 15x^14 - 4x^13 - 56x^12 + 106x^11 + 29x^10 - 262x^9 + 156x^8 + 328x^7 - 281x^6 - 232x^5 + 200x^4 + 82x^3 - 64x^2 - 12x + 9	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 37^{2} \)	16T1228	Trivial
16.0.78002053462779494400.1	x^16 - 6x^15 + 16x^14 - 34x^13 + 74x^12 - 162x^11 + 324x^10 - 550x^9 + 958x^8 - 1706x^7 + 2712x^6 - 3302x^5 + 2954x^4 - 1862x^3 + 804x^2 - 210x + 25	\( 2^{28}\cdot 3^{8}\cdot 5^{2}\cdot 11^{6} \)	16T1228	Trivial
16.4.124124554854400000000.1	x^16 - 4x^15 + 20x^13 - 40x^12 + 12x^11 + 76x^10 - 156x^9 + 117x^8 + 52x^7 - 116x^6 + 116x^5 + 56x^4 - 80x^3 + 60x^2 - 25	\( 2^{40}\cdot 5^{8}\cdot 17^{2} \)	16T1228	Trivial
16.4.124124554854400000000.2	x^16 - 4x^15 + 12x^14 - 32x^13 + 42x^12 - 68x^11 + 72x^10 - 40x^9 + 144x^8 + 44x^7 + 92x^6 + 80x^5 - 30x^4 + 28x^3 + 24x^2 - 8x - 1	\( 2^{40}\cdot 5^{8}\cdot 17^{2} \)	16T1228	Trivial
16.0.52554919692301559136256.3	x^16 - 4x^15 + 12x^14 - 28x^13 - 3x^12 + 116x^11 - 214x^10 + 380x^9 + 230x^8 - 2552x^7 + 2080x^6 - 192x^5 + 6418x^4 - 7392x^3 - 572x^2 - 3112x + 5188	\( 2^{38}\cdot 17^{6}\cdot 89^{2} \)	16T1228	$[2]$
16.0.52554919692301559136256.4	x^16 - 28x^14 - 8x^13 + 339x^12 + 84x^11 - 2112x^10 - 176x^9 + 6994x^8 - 1476x^7 - 8840x^6 + 1652x^5 + 4323x^4 - 688x^3 - 1044x^2 + 1356x + 1289	\( 2^{38}\cdot 17^{6}\cdot 89^{2} \)	16T1228	$[2]$
16.0.655344390478233600000000.1	x^16 + 10x^14 - 12x^13 + 72x^12 - 88x^11 + 506x^10 - 1000x^9 + 2779x^8 - 5288x^7 + 11524x^6 - 15508x^5 + 14382x^4 - 8880x^3 + 4956x^2 - 2920x + 850	\( 2^{36}\cdot 3^{8}\cdot 5^{8}\cdot 61^{2} \)	16T1228	$[2]$
16.0.655344390478233600000000.2	x^16 + 2x^14 - 20x^13 - 22x^12 + 192x^11 - 336x^10 + 4x^9 + 1153x^8 - 2616x^7 + 3658x^6 - 3936x^5 + 3858x^4 - 3488x^3 + 2636x^2 - 1320x + 340	\( 2^{36}\cdot 3^{8}\cdot 5^{8}\cdot 61^{2} \)	16T1228	$[2]$ (GRH)
16.12.2786014518176517344722944.1	x^16 - 20x^14 + 106x^12 + 144x^10 - 2225x^8 + 3128x^6 + 2142x^4 - 3468x^2 + 289	\( 2^{44}\cdot 3^{8}\cdot 17^{6} \)	16T1228	Trivial (GRH)
16.8.2786014518176517344722944.1	x^16 - 4x^14 - 46x^12 + 236x^10 + 87x^8 - 1428x^6 + 306x^4 + 2312x^2 + 289	\( 2^{44}\cdot 3^{8}\cdot 17^{6} \)	16T1228	Trivial (GRH)
16.12.2786014518176517344722944.2	x^16 - 12x^14 - 6x^12 + 572x^10 - 2513x^8 + 3804x^6 - 1862x^4 - 272x^2 + 289	\( 2^{44}\cdot 3^{8}\cdot 17^{6} \)	16T1228	Trivial (GRH)
16.8.2786014518176517344722944.2	x^16 + 4x^14 - 46x^12 - 236x^10 + 87x^8 + 1428x^6 + 306x^4 - 2312x^2 + 289	\( 2^{44}\cdot 3^{8}\cdot 17^{6} \)	16T1228	Trivial (GRH)
16.4.2786014518176517344722944.3	x^16 + 20x^14 + 106x^12 - 144x^10 - 2225x^8 - 3128x^6 + 2142x^4 + 3468x^2 + 289	\( 2^{44}\cdot 3^{8}\cdot 17^{6} \)	16T1228	$[2]$
16.4.2786014518176517344722944.4	x^16 + 16x^14 + 26x^12 - 260x^10 - 849x^8 - 36x^6 + 2202x^4 + 1972x^2 + 289	\( 2^{44}\cdot 3^{8}\cdot 17^{6} \)	16T1228	Trivial
16.0.12518258881906239078400000000.1	x^16 + 38x^14 + 589x^12 + 4916x^10 + 24263x^8 + 72420x^6 + 126683x^4 + 116522x^2 + 41209	\( 2^{40}\cdot 5^{8}\cdot 7^{2}\cdot 29^{6} \)	16T1228	$[2, 924]$ (GRH)
16.0.12518258881906239078400000000.2	x^16 + 52x^14 + 1074x^12 + 11194x^10 + 61958x^8 + 177860x^6 + 253143x^4 + 167678x^2 + 41209	\( 2^{40}\cdot 5^{8}\cdot 7^{2}\cdot 29^{6} \)	16T1228	$[2, 972]$ (GRH)
16.8.93432784589729195622400000000.1	x^16 - 4x^15 - 24x^14 - 28x^13 + 242x^12 + 652x^11 + 2560x^10 + 10420x^9 + 5942x^8 - 32036x^7 - 123008x^6 - 429884x^5 - 1023550x^4 - 1464628x^3 - 1259640x^2 - 606364x - 124751	\( 2^{44}\cdot 5^{8}\cdot 17^{2}\cdot 19^{6} \)	16T1228	Trivial (GRH)
16.8.93432784589729195622400000000.2	x^16 - 4x^15 + 4x^14 + 148x^13 - 662x^12 + 380x^11 + 4100x^10 - 14460x^9 - 9170x^8 + 50412x^7 - 44188x^6 - 32524x^5 + 513090x^4 + 737468x^3 + 225604x^2 - 57996x + 81	\( 2^{44}\cdot 5^{8}\cdot 17^{2}\cdot 19^{6} \)	16T1228	Trivial (GRH)
16.16.11485432797146294675046400000000.1	x^16 - 78x^14 + 2415x^12 - 37818x^10 + 315453x^8 - 1345128x^6 + 2471808x^4 - 968256x^2 + 107584	\( 2^{30}\cdot 5^{8}\cdot 7^{8}\cdot 41^{6} \)	16T1228	Trivial (GRH)
16.8.11485432797146294675046400000000.1	x^16 - 26x^14 - 545x^12 + 15186x^10 - 55187x^8 - 440176x^6 + 1798752x^4 + 1936512x^2 + 107584	\( 2^{30}\cdot 5^{8}\cdot 7^{8}\cdot 41^{6} \)	16T1228	$[2]$ (GRH)
16.8.11485432797146294675046400000000.2	x^16 - 24x^14 - 390x^12 + 7884x^10 + 50733x^8 - 574164x^6 - 1748568x^4 + 484128x^2 + 107584	\( 2^{30}\cdot 5^{8}\cdot 7^{8}\cdot 41^{6} \)	16T1228	Trivial (GRH)
16.8.11485432797146294675046400000000.3	x^16 - 18x^14 - 465x^12 + 7702x^10 + 50653x^8 - 560388x^6 - 2971352x^4 - 2850976x^2 + 107584	\( 2^{30}\cdot 5^{8}\cdot 7^{8}\cdot 41^{6} \)	16T1228	Trivial (GRH)
16.8.11485432797146294675046400000000.4	x^16 + 24x^14 - 390x^12 - 7884x^10 + 50733x^8 + 574164x^6 - 1748568x^4 - 484128x^2 + 107584	\( 2^{30}\cdot 5^{8}\cdot 7^{8}\cdot 41^{6} \)	16T1228	Trivial (GRH)
16.16.183766924754340714800742400000000.1	x^16 - 78x^14 + 2485x^12 - 41778x^10 + 400103x^8 - 2204898x^6 + 6764918x^4 - 10549956x^2 + 6461764	\( 2^{34}\cdot 5^{8}\cdot 7^{8}\cdot 41^{6} \)	16T1228	Trivial (GRH)
16.0.930715663880146904969790025000000.1	x^16 - 6x^15 + 47x^14 - 355x^13 + 3251x^12 - 14666x^11 + 85725x^10 - 296277x^9 + 1374044x^8 - 3916271x^7 + 12754641x^6 - 34075054x^5 + 78845290x^4 - 169349557x^3 + 263496981x^2 - 410243094x + 447723604	\( 2^{6}\cdot 5^{8}\cdot 41^{6}\cdot 97^{8} \)	16T1228	$[29]$ (GRH)
16.0.10922431682739176997092820825145344.1	x^16 - 8x^15 + 20x^14 - 264x^13 + 7974x^12 - 44160x^11 + 80044x^10 - 1036800x^9 + 12590434x^8 - 12843008x^7 + 315562164x^6 + 738308640x^5 + 5621801606x^4 - 13121006632x^3 + 44818888652x^2 + 17297644568x + 272446237993	\( 2^{42}\cdot 3^{8}\cdot 17^{6}\cdot 97^{2}\cdot 1291^{2} \)	16T1228	$[2, 2, 4]$ (GRH)
16.12.2767007058000819292896502809600000000.1	x^16 - 217x^14 + 2326x^12 + 1920664x^10 - 88640101x^8 - 1136668468x^6 + 26685015734x^4 - 102178199739x^2 + 79671272121	\( 2^{16}\cdot 3^{6}\cdot 5^{8}\cdot 7^{6}\cdot 17^{8}\cdot 13441^{2} \)	16T1228	$[2]$ (GRH)
16.12.2767007058000819292896502809600000000.2	x^16 - 148x^14 - 5294x^12 + 1055806x^10 - 16001821x^8 - 451767532x^6 + 8725868189x^4 - 46785043011x^2 + 79671272121	\( 2^{16}\cdot 3^{6}\cdot 5^{8}\cdot 7^{6}\cdot 17^{8}\cdot 13441^{2} \)	16T1228	$[2]$ (GRH)
16.0.1719731248304838654458056435302400000000.1	x^16 - 6x^15 + 11x^14 - 126x^13 + 1443x^12 - 5034x^11 + 7952x^10 - 50506x^9 + 293810x^8 - 416602x^7 - 1018960x^6 + 2788726x^5 + 1860427x^4 - 3908292x^3 + 1805439x^2 + 9719120x + 5685401	\( 2^{26}\cdot 5^{8}\cdot 7^{8}\cdot 241^{8} \)	16T1228	$[4, 60]$ (GRH)
16.0.1719731248304838654458056435302400000000.2	x^16 - 2x^15 - 15x^14 - 316x^13 + 3898x^12 + 364x^11 - 8277x^10 - 735808x^9 + 2943728x^8 + 1110888x^7 + 19937397x^6 - 261805816x^5 + 661014999x^4 - 623815062x^3 + 1769942058x^2 - 5322863812x + 4615706356	\( 2^{26}\cdot 5^{8}\cdot 7^{8}\cdot 241^{8} \)	16T1228	$[4, 60]$ (GRH)
16.4.8840695976077175158703239475879177355264.1	x^16 + 396x^14 + 41118x^12 + 874632x^10 - 38679168x^8 - 902632896x^6 + 7611413040x^4 + 118045509120x^2 + 308531367936	\( 2^{46}\cdot 3^{14}\cdot 11^{14}\cdot 263^{2} \)	16T1228	$[2, 2, 2, 2, 4]$ (GRH)
16.4.8840695976077175158703239475879177355264.2	x^16 + 462x^14 + 54813x^12 + 1686036x^10 - 72314220x^8 - 4620095568x^6 - 28488908646x^4 + 1663873447104x^2 + 21640582979136	\( 2^{46}\cdot 3^{14}\cdot 11^{14}\cdot 263^{2} \)	16T1228	$[2, 2, 2, 2, 4]$ (GRH)
16.8.7044019193056619128660199158998630400000000.1	x^16 - 4x^15 - 90x^14 - 244x^13 + 633x^12 + 28276x^11 + 75894x^10 - 160984x^9 - 2053388x^8 - 7061852x^7 + 21793570x^6 + 119982956x^5 + 209648745x^4 + 263821580x^3 - 837002750x^2 - 1822563328x - 815756591	\( 2^{38}\cdot 5^{8}\cdot 7^{8}\cdot 241^{8} \)	16T1228	$[2, 2, 4]$ (GRH)
16.8.7044019193056619128660199158998630400000000.2	x^16 - 4x^15 + 10x^14 - 564x^13 - 3887x^12 - 10564x^11 - 229166x^10 - 1591384x^9 - 5361528x^8 - 11926252x^7 + 863210x^6 + 101652956x^5 + 248959625x^4 + 212805460x^3 + 32333530x^2 - 22885728x - 3636911	\( 2^{38}\cdot 5^{8}\cdot 7^{8}\cdot 241^{8} \)	16T1228	$[2, 2, 4]$ (GRH)
16.8.428329216131304888705048916200034767627878400000000.1	x^16 - 808x^14 - 110144x^12 + 28031400x^10 + 972187419x^8 - 190660506576x^6 + 2863944241360x^4 + 9042674097920x^2 + 592949281024	\( 2^{32}\cdot 5^{8}\cdot 17^{2}\cdot 19^{10}\cdot 331^{8} \)	16T1228	$[2, 2, 2, 6]$ (GRH)
16.8.428329216131304888705048916200034767627878400000000.2	x^16 - 1224x^14 + 435112x^12 - 30852792x^10 - 3915519483x^8 - 5670878472x^6 + 4340249387320x^4 + 72152735659128x^2 + 286123551244969	\( 2^{32}\cdot 5^{8}\cdot 17^{2}\cdot 19^{10}\cdot 331^{8} \)	16T1228	$[2, 2, 2, 6]$ (GRH)