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 188)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.299368469619189453125.1	x^16 - 7x^15 + 28x^14 - 77x^13 + 164x^12 - 257x^11 + 277x^10 - 153x^9 - 52x^8 + 177x^7 - 88x^6 - 41x^5 + 55x^4 + 9x^3 - 11x^2 - x + 1	\( 5^{11}\cdot 19^{10} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$
16.0.299368469619189453125.2	x^16 - x^15 + x^14 + 6x^13 + 6x^12 + 2x^11 + 32x^10 - 10x^9 - 85x^8 + 17x^7 + 139x^6 + 18x^5 - 55x^4 - 7x^3 + 17x^2 + 7x + 1	\( 5^{11}\cdot 19^{10} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$
16.0.574987007082761289728.1	x^16 - 9x^14 + 41x^12 - 101x^10 + 164x^8 - 175x^6 + 117x^4 - 51x^2 + 17	\( 2^{24}\cdot 17^{11} \)	$C_4:D_4.D_4$ (as 16T681)	Trivial
16.0.574987007082761289728.2	x^16 + 9x^14 + 41x^12 + 101x^10 + 164x^8 + 175x^6 + 117x^4 + 51x^2 + 17	\( 2^{24}\cdot 17^{11} \)	$C_4:D_4.D_4$ (as 16T681)	Trivial
16.0.10505857648455357927237.1	x^16 - 3x^15 + 3x^14 - x^13 + 2x^12 - 24x^11 + 102x^10 - 221x^9 + 285x^8 - 221x^7 + 102x^6 - 24x^5 + 2x^4 - x^3 + 3x^2 - 3x + 1	\( 3^{10}\cdot 37^{11} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.0.10505857648455357927237.2	x^16 - 2x^15 + 16x^14 - 30x^13 + 116x^12 - 201x^11 + 502x^10 - 776x^9 + 1459x^8 - 1953x^7 + 2738x^6 - 2763x^5 + 2680x^4 - 1796x^3 + 1159x^2 - 432x + 173	\( 3^{10}\cdot 37^{11} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$
16.0.94552718836098221345133.1	x^16 - 6x^15 + 16x^14 - 3x^13 - 56x^12 + 96x^11 - 2x^10 - 120x^9 + 259x^8 - 120x^7 - 2x^6 + 96x^5 - 56x^4 - 3x^3 + 16x^2 - 6x + 1	\( 3^{12}\cdot 37^{11} \)	$C_4:D_4.D_4$ (as 16T681)	$[2, 2]$ (GRH)
16.0.94552718836098221345133.2	x^16 - 6x^15 + 15x^14 - 8x^13 - 54x^12 + 129x^11 + 9x^10 - 453x^9 + 702x^8 - 365x^7 + 264x^6 - 1230x^5 + 2488x^4 - 3006x^3 + 2790x^2 - 2034x + 879	\( 3^{12}\cdot 37^{11} \)	$C_4:D_4.D_4$ (as 16T681)	$[2, 2]$ (GRH)
16.0.108072017532527392578125.1	x^16 - 2x^15 + 18x^14 - 35x^13 + 159x^12 - 254x^11 + 759x^10 - 1053x^9 + 1781x^8 - 2143x^7 + 1609x^6 - 656x^5 - 784x^4 + 775x^3 - 5x^2 - 100x + 25	\( 5^{11}\cdot 19^{12} \)	$C_4:D_4.D_4$ (as 16T681)	$[2, 2]$ (GRH)
16.0.108072017532527392578125.2	x^16 - 2x^15 - 11x^14 - 3x^13 + 76x^12 + 154x^11 - 108x^10 - 804x^9 - 517x^8 + 1814x^7 + 3284x^6 - 318x^5 - 4339x^4 - 1847x^3 + 3224x^2 + 2910x + 1255	\( 5^{11}\cdot 19^{12} \)	$C_4:D_4.D_4$ (as 16T681)	$[2, 2]$ (GRH)
16.4.243680579501983642578125.1	x^16 - 2x^15 + 5x^14 + 10x^13 + 5x^12 + 114x^11 - 83x^10 + 145x^9 + 150x^8 - 1095x^7 + 642x^6 - 614x^5 - 1580x^4 + 1160x^3 + 1405x^2 - 1383x - 419	\( 5^{15}\cdot 41^{8} \)	$C_4:D_4.D_4$ (as 16T681)	Trivial (GRH)
16.4.243680579501983642578125.2	x^16 - 2x^15 + 5x^14 + 25x^13 - 95x^12 + 239x^11 - 138x^10 - 620x^9 + 2315x^8 - 4725x^7 + 5682x^6 - 6234x^5 + 3345x^4 - 2260x^3 - 1570x^2 + 882x - 239	\( 5^{15}\cdot 41^{8} \)	$C_4:D_4.D_4$ (as 16T681)	Trivial (GRH)
16.4.243680579501983642578125.3	x^16 - 4x^15 + 5x^14 + 5x^13 - 25x^12 + 8x^11 + 68x^10 - 35x^9 - 240x^8 + 530x^7 - 462x^6 + 163x^5 - 110x^4 + 125x^3 - 25x^2 + 6x - 9	\( 5^{15}\cdot 41^{8} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.4.243680579501983642578125.4	x^16 - 7x^15 + 25x^14 - 50x^13 + 20x^12 + 119x^11 - 143x^10 - 275x^9 + 690x^8 - 20x^7 - 1558x^6 + 2321x^5 - 1585x^4 + 525x^3 - 55x^2 - 8x + 1	\( 5^{15}\cdot 41^{8} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.0.2569453321037674837093389.1	x^16 + 6x^14 - 19x^13 + 35x^12 - 96x^11 + 225x^10 - 335x^9 + 630x^8 - 921x^7 + 1137x^6 - 1314x^5 + 1356x^4 - 1038x^3 + 618x^2 - 249x + 45	\( 3^{10}\cdot 61^{11} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.0.2569453321037674837093389.2	x^16 - 7x^15 + 13x^14 + 29x^13 - 174x^12 + 272x^11 + 183x^10 - 1799x^9 + 4977x^8 - 9822x^7 + 15537x^6 - 19626x^5 + 19275x^4 - 14214x^3 + 7503x^2 - 2562x + 441	\( 3^{10}\cdot 61^{11} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.4.5850442901528350830078125.1	x^16 - 6x^15 + 20x^14 - 15x^13 - 115x^12 + 467x^11 - 672x^10 - 630x^9 + 4100x^8 - 7225x^7 + 3503x^6 + 8017x^5 - 21485x^4 + 23860x^3 - 16600x^2 + 4824x - 464	\( 5^{15}\cdot 61^{8} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.4.5850442901528350830078125.2	x^16 - 5x^14 - 5x^13 + 5x^12 - 55x^11 - 105x^10 - 80x^9 + 60x^8 + 100x^7 - 925x^6 + 1300x^5 - 1275x^4 + 425x^3 - 325x^2 + 75x + 25	\( 5^{15}\cdot 61^{8} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.4.5850442901528350830078125.3	x^16 - 2x^15 + 10x^14 - 25x^13 + 120x^12 - 436x^11 + 1032x^10 - 2185x^9 + 2470x^8 - 2690x^7 - 903x^6 + 3671x^5 - 9185x^4 + 7995x^3 - 7935x^2 + 2282x + 196	\( 5^{15}\cdot 61^{8} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.4.5850442901528350830078125.4	x^16 - 4x^15 + 5x^14 - 15x^13 + 35x^12 - 2x^11 + 43x^10 + 15x^9 - 255x^8 - 445x^7 - 302x^6 - 287x^5 - 1205x^4 - 1125x^3 - 435x^2 + 111x + 341	\( 5^{15}\cdot 61^{8} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.0.23125079889339073533840501.1	x^16 - 6x^15 + 32x^14 - 84x^13 + 255x^12 - 375x^11 + 1004x^10 - 690x^9 + 2887x^8 + 375x^7 + 4701x^6 + 2052x^5 + 3192x^4 + 1053x^3 + 369x^2 + 9	\( 3^{12}\cdot 61^{11} \)	$C_4:D_4.D_4$ (as 16T681)	$[2, 2]$ (GRH)
16.0.23125079889339073533840501.2	x^16 - 7x^15 + 22x^14 - 47x^13 + 74x^12 - 104x^11 + 174x^10 - 207x^9 - 60x^8 + 1000x^7 - 1411x^6 + 73x^5 + 3643x^4 - 7450x^3 + 12877x^2 - 18348x + 10755	\( 3^{12}\cdot 61^{11} \)	$C_4:D_4.D_4$ (as 16T681)	$[2, 2]$ (GRH)
16.0.24956872719757880908203125.1	x^16 - 16x^14 - 18x^13 + 123x^12 + 223x^11 - 384x^10 - 1290x^9 + 311x^8 + 3086x^7 + 1379x^6 - 3451x^5 - 595x^4 + 2746x^3 - 185x^2 - 1384x + 659	\( 5^{11}\cdot 59^{10} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.0.24956872719757880908203125.2	x^16 - 2x^15 + 14x^14 - 2x^13 + 36x^12 + 121x^11 + 141x^10 + 134x^9 + 2063x^8 - 1599x^7 + 7588x^6 - 2708x^5 + 10677x^4 - 911x^3 + 17043x^2 - 20x + 2549	\( 5^{11}\cdot 59^{10} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.4.7561037361641682928770951437.3	x^16 - 4x^15 + 18x^14 - 67x^13 + 60x^12 - 183x^11 - 143x^10 + 885x^9 - 512x^8 + 1416x^7 - 9099x^6 + 10697x^5 + 2848x^4 - 3553x^3 + 6671x^2 - 17745x - 13221	\( 13^{8}\cdot 53^{11} \)	$C_4:D_4.D_4$ (as 16T681)	Trivial (GRH)
16.4.7561037361641682928770951437.5	x^16 - 5x^15 - 3x^14 - 8x^13 + 101x^12 - 93x^11 - 301x^10 - 602x^9 + 553x^8 - 2507x^7 - 16420x^6 - 28693x^5 - 23578x^4 + 13430x^3 + 15342x^2 + 14843x - 8047	\( 13^{8}\cdot 53^{11} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.4.7561037361641682928770951437.10	x^16 - 6x^15 + 31x^14 - 117x^13 + 337x^12 - 879x^11 + 1709x^10 - 3363x^9 + 5157x^8 - 8466x^7 + 11329x^6 - 12344x^5 + 8549x^4 + 2635x^3 - 6187x^2 + 3144x - 211	\( 13^{8}\cdot 53^{11} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.4.7561037361641682928770951437.11	x^16 + 21x^14 - 149x^12 - 912x^10 - 53x^8 + 20512x^6 + 1203x^4 + 1113x^2 + 53	\( 13^{8}\cdot 53^{11} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.4.7561037361641682928770951437.13	x^16 - 3x^15 - 18x^13 + 110x^12 - 174x^11 - 532x^10 + 2830x^9 - 5446x^8 + 8838x^7 - 15512x^6 + 22642x^5 - 26571x^4 + 13468x^3 + 3874x^2 + 507x + 169	\( 13^{8}\cdot 53^{11} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.4.7561037361641682928770951437.14	x^16 - x^15 + 9x^14 - 38x^13 + 46x^12 + 90x^11 - 414x^10 - 1054x^9 - 3197x^8 + 3656x^7 + 16722x^6 + 15527x^5 - 1681x^4 - 7475x^3 - 1443x^2 + 1690x + 169	\( 13^{8}\cdot 53^{11} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.4.7561037361641682928770951437.15	x^16 - 3x^15 - 11x^14 + 3x^13 - 61x^12 - 6x^11 + 1089x^10 + 3823x^9 + 9018x^8 + 11451x^7 + 12158x^6 + 20640x^5 + 25240x^4 + 24216x^3 + 15859x^2 + 3807x + 1899	\( 13^{8}\cdot 53^{11} \)	$C_4:D_4.D_4$ (as 16T681)	Trivial (GRH)
16.4.7561037361641682928770951437.19	x^16 - 3x^15 + 4x^14 + 45x^13 - 42x^12 - 256x^11 + 161x^10 + 541x^9 - 2932x^8 - 3270x^7 + 8161x^6 + 18493x^5 + 6552x^4 + 2957x^3 - 4011x^2 - 10083x + 10331	\( 13^{8}\cdot 53^{11} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.4.25605559374504409818155101477.1	x^16 - 6x^15 + 25x^14 - 21x^13 - 117x^12 + 338x^11 - 442x^10 - 234x^9 + 2288x^8 - 7059x^7 + 16666x^6 - 26065x^5 + 35204x^4 - 33490x^3 + 15261x^2 - 10242x + 1836	\( 13^{15}\cdot 29^{8} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.4.25605559374504409818155101477.2	x^16 - 4x^15 + 14x^14 - 25x^13 + 26x^12 + 91x^11 - 949x^10 + 4121x^9 - 15002x^8 + 32487x^7 - 58240x^6 + 43277x^5 - 2275x^4 - 37086x^3 + 113400x^2 + 186813x + 65367	\( 13^{15}\cdot 29^{8} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.4.25605559374504409818155101477.3	x^16 - 2x^15 + 10x^14 - 8x^13 - 117x^12 + 910x^11 - 3367x^10 + 6214x^9 - 7904x^8 + 5460x^7 + 9139x^6 - 47580x^5 + 61763x^4 + 8718x^3 - 71685x^2 + 8478x + 74439	\( 13^{15}\cdot 29^{8} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.4.25605559374504409818155101477.4	x^16 - 3x^15 + 16x^14 - 66x^13 - 39x^12 + 156x^11 - 715x^10 + 5148x^9 + 1677x^8 + 4836x^7 - 254072x^6 + 561171x^5 + 298753x^4 - 2798238x^3 + 5367456x^2 - 4861080x + 1688688	\( 13^{15}\cdot 29^{8} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.0.86874873937477183441455078125.1	x^16 - 2x^15 - 20x^14 + 4x^13 + 168x^12 + 325x^11 - 953x^10 - 2716x^9 + 7890x^8 + 19766x^7 - 48x^6 - 99480x^5 + 13538x^4 + 378341x^3 - 102285x^2 - 751719x + 789479	\( 5^{11}\cdot 59^{12} \)	$C_4:D_4.D_4$ (as 16T681)	$[2, 2]$ (GRH)
16.0.86874873937477183441455078125.2	x^16 - 4x^15 + 44x^14 - 172x^13 + 932x^12 - 3398x^11 + 10869x^10 - 35165x^9 + 86380x^8 - 191415x^7 + 450586x^6 - 758009x^5 + 1116794x^4 - 1838647x^3 + 2021597x^2 - 1197593x + 1133189	\( 5^{11}\cdot 59^{12} \)	$C_4:D_4.D_4$ (as 16T681)	$[2, 2]$ (GRH)
16.4.108951986979034819834970703125.2	x^16 - x^15 - 43x^14 + 85x^13 + 677x^12 - 2060x^11 - 3805x^10 + 20100x^9 - 6635x^8 - 68780x^7 + 113935x^6 - 45115x^5 - 96760x^4 + 362275x^3 - 641275x^2 + 532775x - 165475	\( 5^{10}\cdot 101^{11} \)	$C_4:D_4.D_4$ (as 16T681)	Trivial (GRH)
16.4.108951986979034819834970703125.6	x^16 - 4x^15 - 4x^14 - 8x^13 - 393x^12 - 960x^11 - 2981x^10 - 12543x^9 - 27936x^8 - 56316x^7 - 101273x^6 - 130450x^5 - 142974x^4 - 147768x^3 - 110558x^2 - 45677x - 7633	\( 5^{10}\cdot 101^{11} \)	$C_4:D_4.D_4$ (as 16T681)	Trivial (GRH)
16.4.108951986979034819834970703125.9	x^16 - x^15 - 32x^14 + 116x^13 - 88x^12 + 40x^11 - 1315x^10 + 5455x^9 - 11480x^8 + 15975x^7 - 16120x^6 + 12185x^5 - 6960x^4 + 2975x^3 - 925x^2 + 200x - 25	\( 5^{10}\cdot 101^{11} \)	$C_4:D_4.D_4$ (as 16T681)	Trivial (GRH)
16.4.108951986979034819834970703125.13	x^16 - x^15 - 29x^14 + 63x^13 + 506x^12 + 635x^11 + 2254x^10 + 4744x^9 - 10132x^8 - 14206x^7 + 2145x^6 - 10483x^5 - 377x^4 + 12557x^3 + 1253x^2 + 33522x + 15353	\( 5^{10}\cdot 101^{11} \)	$C_4:D_4.D_4$ (as 16T681)	Trivial (GRH)
16.0.240414920542051180813313277797.1	x^16 - 8x^15 + 27x^14 - 49x^13 + 53x^12 - 45x^11 - 33x^10 + 363x^9 - 484x^8 - 451x^7 + 1815x^6 - 2129x^5 + 5031x^4 - 7873x^3 - 2049x^2 + 5831x + 2107	\( 11^{10}\cdot 53^{11} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.0.240414920542051180813313277797.2	x^16 - x^15 + 4x^14 - 10x^12 + 250x^11 - 784x^10 + 347x^9 + 3305x^8 + 2519x^7 + 13315x^6 - 40402x^5 + 127119x^4 - 96554x^3 + 14387x^2 + 40872x + 10161	\( 11^{10}\cdot 53^{11} \)	$C_4:D_4.D_4$ (as 16T681)	$[2]$ (GRH)
16.4.313426397802392026311505288813.2	x^16 - 5x^15 + 23x^14 - 92x^13 + 5x^12 + 373x^11 - 2967x^10 + 3754x^9 + 14359x^8 + 20408x^7 + 75241x^6 + 28094x^5 - 81462x^4 - 129250x^3 - 391063x^2 - 386833x - 77607	\( 13^{11}\cdot 53^{10} \)	$C_4:D_4.D_4$ (as 16T681)	Trivial (GRH)
16.4.313426397802392026311505288813.8	x^16 - 6x^15 - 11x^14 + 118x^13 - 19x^12 - 987x^11 + 1667x^10 + 774x^9 - 3520x^8 + 643x^7 + 1339x^6 + 237x^5 - 3444x^4 + 6137x^3 - 3038x^2 - 981x + 909	\( 13^{11}\cdot 53^{10} \)	$C_4:D_4.D_4$ (as 16T681)	Trivial (GRH)
16.4.313426397802392026311505288813.11	x^16 - 4x^15 - 15x^14 + 109x^13 - 17x^12 - 1210x^11 + 1387x^10 + 13691x^9 - 64519x^8 + 140155x^7 - 185880x^6 + 127518x^5 + 85563x^4 - 185692x^3 + 26000x^2 + 153283x + 29237	\( 13^{11}\cdot 53^{10} \)	$C_4:D_4.D_4$ (as 16T681)	Trivial (GRH)
16.4.313426397802392026311505288813.17	x^16 - 40x^14 - 78x^13 + 297x^12 + 1653x^11 + 3949x^10 - 4977x^9 - 68979x^8 - 172465x^7 - 36282x^6 + 713049x^5 + 1896839x^4 + 2609981x^3 + 2177663x^2 + 1056685x + 234563	\( 13^{11}\cdot 53^{10} \)	$C_4:D_4.D_4$ (as 16T681)	Trivial (GRH)
16.0.594882994674022504125031032809.2	x^16 - 2x^15 + 17x^14 - 94x^13 + 95x^12 + 550x^11 + 472x^10 - 6950x^9 + 5408x^8 + 16546x^7 + 4628x^6 - 39502x^5 - 16769x^4 + 27680x^3 + 57639x^2 + 30868x + 11461	\( 11^{8}\cdot 89^{11} \)	$C_4:D_4.D_4$ (as 16T681)	Trivial (GRH)
16.0.594882994674022504125031032809.3	x^16 - x^15 + 23x^13 + 35x^12 - 130x^11 - 105x^10 + 7317x^9 + 45676x^8 + 141137x^7 + 287185x^6 + 441734x^5 + 548736x^4 + 544952x^3 + 402960x^2 + 196032x + 47872	\( 11^{8}\cdot 89^{11} \)	$C_4:D_4.D_4$ (as 16T681)	Trivial (GRH)