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 66)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.2565942505126953125.1	x^16 - 7x^15 + 22x^14 - 52x^13 + 113x^12 - 197x^11 + 280x^10 - 375x^9 + 431x^8 - 375x^7 + 280x^6 - 197x^5 + 113x^4 - 52x^3 + 22x^2 - 7x + 1	\( 5^{12}\cdot 101^{5} \)	16T1281	$[2]$
16.0.64148562628173828125.1	x^16 - 5x^15 + 17x^14 - 30x^13 + 23x^12 + 55x^11 - 196x^10 + 315x^9 - 210x^8 - 140x^7 + 559x^6 - 675x^5 + 483x^4 - 185x^3 + 52x^2 - 10x + 1	\( 5^{14}\cdot 101^{5} \)	16T1281	$[2]$
16.0.19677476514830584542781.1	x^16 - 5x^15 + 15x^14 - 38x^13 + 81x^12 - 127x^11 + 122x^10 - 19x^9 - 107x^8 + 129x^7 - 6x^6 - 141x^5 + 178x^4 - 123x^3 + 76x^2 - 36x + 9	\( 13^{12}\cdot 61^{5} \)	16T1281	$[2]$ (GRH)
16.0.26175179494800048828125.1	x^16 - 2x^15 + 15x^14 + 11x^13 - 46x^12 + 326x^11 - 285x^10 + 115x^9 + 1711x^8 - 3640x^7 + 6405x^6 - 7507x^5 + 7181x^4 - 5494x^3 + 3173x^2 - 1329x + 341	\( 5^{12}\cdot 101^{7} \)	16T1281	$[2, 2]$ (GRH)
16.0.26175179494800048828125.2	x^16 - 2x^15 - x^14 + 12x^13 - 36x^12 - 192x^11 + 86x^10 + 594x^9 + 314x^8 + 771x^7 + 4281x^6 + 5990x^5 + 2387x^4 - 71x^3 + 2595x^2 + 3865x + 1681	\( 5^{12}\cdot 101^{7} \)	16T1281	$[2, 2]$ (GRH)
16.0.654379487370001220703125.2	x^16 - 3x^15 + 17x^14 - 69x^13 + 266x^12 - 823x^11 + 2315x^10 - 5577x^9 + 11819x^8 - 21391x^7 + 32530x^6 - 38916x^5 + 34621x^4 - 20657x^3 + 7578x^2 - 1521x + 701	\( 5^{14}\cdot 101^{7} \)	16T1281	$[2, 2]$ (GRH)
16.0.654379487370001220703125.4	x^16 - 5x^15 + 23x^14 - 60x^13 + 148x^12 - 140x^11 - 124x^10 + 1260x^9 - 2160x^8 + 1975x^7 + 2431x^6 - 5905x^5 + 7323x^4 + 640x^3 - 4487x^2 + 5700x + 4061	\( 5^{14}\cdot 101^{7} \)	16T1281	$[2, 4]$ (GRH)
16.0.3325493531006368787729989.1	x^16 - 3x^15 + 11x^14 - 9x^13 + 15x^12 + 15x^11 + 19x^10 + 40x^9 + 57x^8 + 93x^7 + 102x^6 + 120x^5 + 162x^4 + 89x^3 + 67x^2 - 59x + 9	\( 13^{14}\cdot 61^{5} \)	16T1281	$[2]$ (GRH)
16.0.73219890111684605083688101.1	x^16 - 5x^15 + 37x^14 - 137x^13 + 544x^12 - 1369x^11 + 3684x^10 - 6826x^9 + 13921x^8 - 18611x^7 + 29827x^6 - 26637x^5 + 33910x^4 - 16147x^3 + 14196x^2 - 1170x + 81	\( 13^{12}\cdot 61^{7} \)	16T1281	$[2, 2]$ (GRH)
16.0.73219890111684605083688101.2	x^16 - 6x^15 + 8x^14 - 14x^13 + 33x^12 + 173x^11 + 269x^10 + 627x^9 + 1074x^8 + 688x^7 + 980x^6 + 696x^5 + 338x^4 - 58x^3 + 42x^2 - 9x + 81	\( 13^{12}\cdot 61^{7} \)	16T1281	$[2, 2]$ (GRH)
16.12.76466165698099148448858112.3	x^16 - 4x^15 - 10x^14 + 32x^13 + 225x^12 - 528x^11 - 1266x^10 + 2652x^9 + 2996x^8 - 3932x^7 - 3674x^6 + 1248x^5 + 1153x^4 - 112x^3 - 82x^2 + 4x + 1	\( 2^{44}\cdot 337^{5} \)	16T1281	$[2]$ (GRH)
16.4.76466165698099148448858112.3	x^16 - 8x^15 + 48x^14 - 172x^13 + 460x^12 - 792x^11 + 570x^10 + 1384x^9 - 5916x^8 + 11100x^7 - 11948x^6 + 6016x^5 + 4351x^4 - 12208x^3 + 11212x^2 - 4528x + 446	\( 2^{44}\cdot 337^{5} \)	16T1281	$[2, 4]$ (GRH)
16.0.182400992338192624135120813.4	x^16 - 8x^15 + 2x^14 + 104x^13 - 102x^12 - 605x^11 + 814x^10 + 1632x^9 - 3178x^8 - 1387x^7 + 6695x^6 - 1880x^5 - 6521x^4 + 5025x^3 + 1980x^2 - 3456x + 1053	\( 13^{5}\cdot 53^{12} \)	16T1281	$[2]$ (GRH)
16.0.267013006026455298095703125.1	x^16 - 7x^15 + 29x^14 - 51x^13 - 226x^12 + 2110x^11 - 9063x^10 + 24548x^9 - 27087x^8 - 78822x^7 + 678517x^6 - 2495735x^5 + 6626619x^4 - 12197136x^3 + 15383004x^2 - 10598192x + 8249296	\( 5^{12}\cdot 101^{9} \)	16T1281	$[2, 2, 2]$ (GRH)
16.12.1223458651169586375181729792.1	x^16 - 20x^14 - 56x^13 - 62x^12 + 688x^11 + 3184x^10 + 2928x^9 - 7019x^8 - 25568x^7 - 36964x^6 - 20712x^5 + 1736x^4 + 5232x^3 + 1480x^2 + 144x + 4	\( 2^{48}\cdot 337^{5} \)	16T1281	$[2]$ (GRH)
16.4.1223458651169586375181729792.1	x^16 + 12x^14 - 24x^13 - 46x^12 - 440x^11 - 1156x^10 - 1888x^9 - 2469x^8 + 4224x^7 + 18996x^6 + 50736x^5 + 84782x^4 + 101944x^3 + 82772x^2 + 44504x + 8738	\( 2^{48}\cdot 337^{5} \)	16T1281	$[4]$ (GRH)
16.0.6675325150661382452392578125.2	x^16 - 5x^15 + 52x^14 - 245x^13 + 1643x^12 - 6870x^11 + 30524x^10 - 94175x^9 + 289810x^8 - 654640x^7 + 1511429x^6 - 2584630x^5 + 4545883x^4 - 5708255x^3 + 6879627x^2 - 6443580x + 3798311	\( 5^{14}\cdot 101^{9} \)	16T1281	$[2, 2, 4]$ (GRH)
16.0.12374161428874698259143289069.2	x^16 - x^15 + 20x^14 - 74x^13 + 330x^12 - 1073x^11 + 3633x^10 - 9143x^9 + 24026x^8 - 48033x^7 + 71872x^6 - 42540x^5 - 25968x^4 + 40321x^3 + 100470x^2 + 39825x + 68877	\( 13^{14}\cdot 61^{7} \)	16T1281	$[2, 4]$ (GRH)
16.0.12374161428874698259143289069.6	x^16 - 19x^14 + 149x^12 - 130x^11 - 945x^10 + 1547x^9 + 7351x^8 - 3809x^7 - 19423x^6 + 43589x^5 + 106758x^4 - 154765x^3 - 194447x^2 + 770640x + 1298079	\( 13^{14}\cdot 61^{7} \)	16T1281	$[2, 2]$ (GRH)
16.0.30825767705154553478835417397.2	x^16 - 8x^15 + 63x^14 - 301x^13 + 1293x^12 - 4209x^11 + 11966x^10 - 27468x^9 + 52921x^8 - 82593x^7 + 100610x^6 - 92914x^5 + 74142x^4 - 52399x^3 + 24421x^2 - 5525x + 607	\( 13^{7}\cdot 53^{12} \)	16T1281	$[2, 2]$ (GRH)
16.0.30825767705154553478835417397.4	x^16 - 5x^15 + x^14 + 26x^13 - 33x^12 - 5x^11 + 327x^10 - 2346x^9 + 6109x^8 - 5472x^7 - 178x^6 - 1260x^5 + 7718x^4 - 5862x^3 + 1590x^2 - 1833x + 1391	\( 13^{7}\cdot 53^{12} \)	16T1281	$[2, 2]$ (GRH)
16.0.30825767705154553478835417397.7	x^16 - 9x^14 + 8x^12 + 21x^10 + 355x^8 - 351x^6 - 1196x^4 + 1183x^2 + 2197	\( 13^{7}\cdot 53^{12} \)	16T1281	$[2, 2]$ (GRH)
16.0.30825767705154553478835417397.8	x^16 - 3x^15 + 5x^14 + 8x^13 + 106x^12 - 238x^11 + 567x^10 - 1463x^9 + 3412x^8 + 1030x^7 - 6943x^6 + 762x^5 + 16444x^4 - 1667x^3 - 8909x^2 + 4115x + 6229	\( 13^{7}\cdot 53^{12} \)	16T1281	$[2, 2]$ (GRH)
16.0.30825767705154553478835417397.11	x^16 - x^15 + 19x^14 - 57x^13 + 231x^12 - 729x^11 + 2345x^10 - 5425x^9 + 14291x^8 - 30498x^7 + 54301x^6 - 87559x^5 + 134903x^4 - 171186x^3 + 144723x^2 - 63249x + 12073	\( 13^{7}\cdot 53^{12} \)	16T1281	$[2, 2]$ (GRH)
16.0.30825767705154553478835417397.14	x^16 - 7x^15 + 44x^14 - 195x^13 + 773x^12 - 2569x^11 + 7662x^10 - 19679x^9 + 44581x^8 - 85175x^7 + 139863x^6 - 192875x^5 + 227862x^4 - 246054x^3 + 231624x^2 - 139802x + 59137	\( 13^{7}\cdot 53^{12} \)	16T1281	$[2, 2]$ (GRH)
16.0.272451211105578415516403423821.1	x^16 + 24x^14 - 82x^13 + 184x^12 - 735x^11 + 2920x^10 + 1159x^9 + 207x^8 - 25235x^7 - 37310x^6 + 66572x^5 + 903300x^4 - 1053416x^3 - 1608564x^2 + 1962513x + 1756431	\( 13^{12}\cdot 61^{9} \)	16T1281	$[2, 2, 2]$ (GRH)
16.0.512364387477983081195554363717.5	x^16 - 2x^15 - 4x^14 - 67x^13 + 190x^12 + 915x^11 - 1792x^10 - 971x^9 + 2066x^8 + 7255x^7 + 61336x^6 + 92720x^5 + 232223x^4 + 231390x^3 + 307996x^2 + 160664x + 160976	\( 13^{5}\cdot 53^{14} \)	16T1281	$[2]$ (GRH)
16.0.627941159888163345951926403517.1	x^16 - 5x^15 + 14x^14 - 63x^13 + 178x^12 - 320x^11 + 2135x^10 - 995x^9 + 9667x^8 - 14243x^7 + 26932x^6 - 59939x^5 + 74239x^4 - 119420x^3 + 310369x^2 - 4431x + 261513	\( 37^{12}\cdot 157^{5} \)	16T1281	$[2]$ (GRH)
16.0.679738604498925402954951294976.1	x^16 + 48x^14 + 880x^12 + 7992x^10 + 40322x^8 + 118128x^6 + 199036x^4 + 178088x^2 + 65314	\( 2^{65}\cdot 113^{5} \)	16T1281	$[6, 198]$ (GRH)
16.16.679738604498925402954951294976.1	x^16 - 48x^14 + 936x^12 - 9520x^10 + 53528x^8 - 160192x^6 + 215840x^4 - 72320x^2 + 3616	\( 2^{65}\cdot 113^{5} \)	16T1281	Trivial (GRH)
16.0.679738604498925402954951294976.2	x^16 + 48x^14 + 944x^12 + 9904x^10 + 60530x^8 + 220064x^6 + 462212x^4 + 507144x^2 + 217186	\( 2^{65}\cdot 113^{5} \)	16T1281	$[2, 726]$ (GRH)
16.16.679738604498925402954951294976.2	x^16 - 40x^14 + 600x^12 - 4136x^10 + 13042x^8 - 17968x^6 + 10716x^4 - 2712x^2 + 226	\( 2^{65}\cdot 113^{5} \)	16T1281	Trivial (GRH)
16.8.1867887076585120400000000000000.1	x^16 - 8x^15 + 50x^13 - 385x^12 + 2226x^11 - 4508x^10 + 2130x^9 + 18520x^8 - 98840x^7 + 240112x^6 - 238766x^5 - 179065x^4 + 573390x^3 - 337540x^2 - 268022x + 70561	\( 2^{16}\cdot 5^{14}\cdot 1361^{5} \)	16T1281	$[2]$ (GRH)
16.8.1867887076585120400000000000000.2	x^16 - 33x^14 - 120x^13 + 383x^12 + 2720x^11 + 544x^10 - 21980x^9 - 29225x^8 + 135810x^7 - 26896x^6 - 57070x^5 - 213232x^4 + 303520x^3 - 82528x^2 - 25430x + 15541	\( 2^{16}\cdot 5^{14}\cdot 1361^{5} \)	16T1281	$[2]$ (GRH)
16.8.5011286635190625792744365228032.1	x^16 - 336x^12 - 160x^10 + 32650x^8 + 16080x^6 - 808880x^4 + 620080x^2 + 323857	\( 2^{60}\cdot 337^{5} \)	16T1281	$[4]$ (GRH)
16.8.5011286635190625792744365228032.2	x^16 + 12x^14 - 366x^12 - 5004x^10 - 8993x^8 + 64944x^6 + 113696x^4 - 258816x^2 + 86272	\( 2^{60}\cdot 337^{5} \)	16T1281	$[4]$ (GRH)
16.8.5011286635190625792744365228032.3	x^16 - 336x^12 + 160x^10 + 32650x^8 - 16080x^6 - 808880x^4 - 620080x^2 + 323857	\( 2^{60}\cdot 337^{5} \)	16T1281	$[2, 4]$ (GRH)
16.8.5011286635190625792744365228032.4	x^16 - 28x^14 + 62x^12 + 2700x^10 - 7329x^8 - 61712x^6 - 49696x^4 + 86272x^2 + 86272	\( 2^{60}\cdot 337^{5} \)	16T1281	$[4]$ (GRH)
16.0.5209554742171119537923185540093.7	x^16 - 3x^15 + 17x^13 + 106x^12 - 832x^11 - 1091x^10 + 566x^9 + 12072x^8 + 20318x^7 + 28515x^6 - 38510x^5 - 61276x^4 + 256573x^3 + 638850x^2 + 1433943x + 1460143	\( 13^{9}\cdot 53^{12} \)	16T1281	$[2, 2, 2, 2]$ (GRH)
16.0.46044254676842752222272178625749.2	x^16 - x^15 - 9x^14 - 190x^13 + 652x^12 + 642x^11 - 367x^10 - 1671x^9 - 9447x^8 - 61895x^7 + 719684x^6 - 1973002x^5 - 511662x^4 - 8663345x^3 + 10220890x^2 + 59364288x + 143762193	\( 13^{14}\cdot 61^{9} \)	16T1281	$[2, 2, 4]$ (GRH)
16.0.86589581483779140722048687468173.5	x^16 - 3x^15 + 4x^14 + 71x^13 - 352x^12 + 1187x^11 + 4161x^10 - 19742x^9 + 37685x^8 + 140126x^7 - 434369x^6 - 7668x^5 + 1171759x^4 - 1515269x^3 + 996415x^2 - 367208x + 61861	\( 13^{7}\cdot 53^{14} \)	16T1281	$[2, 4]$ (GRH)
16.0.86589581483779140722048687468173.6	x^16 - 6x^15 - 37x^13 + 303x^12 + 579x^11 - 2977x^10 + 7846x^9 + 33896x^8 - 81985x^7 + 114611x^6 + 73668x^5 - 369459x^4 + 284099x^3 + 132447x^2 - 318402x + 295517	\( 13^{7}\cdot 53^{14} \)	16T1281	$[2, 4]$ (GRH)
16.0.86589581483779140722048687468173.9	x^16 - 2x^15 - 4x^14 - 14x^13 + 243x^12 + 1180x^11 + 11458x^10 + 26165x^9 + 134036x^8 + 160425x^7 + 1006697x^6 + 681868x^5 + 3992202x^4 - 70551x^3 + 5230901x^2 + 878761x + 1083017	\( 13^{7}\cdot 53^{14} \)	16T1281	$[2, 4]$ (GRH)
16.0.86589581483779140722048687468173.10	x^16 - x^15 - 12x^14 - 118x^13 + 15x^12 + 843x^11 + 8514x^10 + 2841x^9 - 32309x^8 - 250859x^7 - 108397x^6 + 372455x^5 + 3630390x^4 + 655026x^3 - 1263417x^2 + 1397596x + 1199909	\( 13^{7}\cdot 53^{14} \)	16T1281	$[2, 4]$ (GRH)
16.0.86589581483779140722048687468173.12	x^16 - 2x^15 - 4x^14 + 39x^13 + 243x^12 - 569x^11 + 1441x^10 + 6608x^9 + 13620x^8 - 5041x^7 + 152284x^6 + 535111x^5 + 398643x^4 + 349050x^3 + 6533111x^2 + 1603589x + 4864249	\( 13^{7}\cdot 53^{14} \)	16T1281	$[2, 4]$ (GRH)
16.0.86589581483779140722048687468173.16	x^16 - x^15 - 102x^13 + 483x^12 + 979x^11 + 5581x^10 - 39994x^9 - 26277x^8 + 143486x^7 + 1574742x^6 - 1546998x^5 - 7251219x^4 - 9106744x^3 + 70841602x^2 - 60725949x + 51239197	\( 13^{7}\cdot 53^{14} \)	16T1281	$[2, 4]$ (GRH)
16.0.859651447886895620608187246414773.2	x^16 - 4x^15 - 13x^14 + 100x^13 + 116x^12 - 2576x^11 + 1396x^10 + 15756x^9 - 33125x^8 - 35431x^7 + 390010x^6 + 1336286x^5 + 4531102x^4 + 14668620x^3 + 29685377x^2 + 32060193x + 14157391	\( 37^{14}\cdot 157^{5} \)	16T1281	$[2]$ (GRH)
16.0.14633639270758674782026228182121237.3	x^16 - 5x^15 - 2x^14 + 98x^13 + 1049x^12 - 12712x^11 + 52171x^10 - 65359x^9 + 137931x^8 - 3540860x^7 + 21459942x^6 - 87176508x^5 + 248541840x^4 - 454458628x^3 + 740541568x^2 - 723490612x + 600584543	\( 13^{9}\cdot 53^{14} \)	16T1281	$[2, 2, 2, 4]$ (GRH)
16.0.15478121650083338314369033920290533.1	x^16 - 5x^15 + 66x^14 - 192x^13 + 1465x^12 - 2188x^11 + 15250x^10 - 6042x^9 + 91904x^8 + 133932x^7 + 317208x^6 + 1246339x^5 + 1728007x^4 + 3416917x^3 + 5720470x^2 + 4064538x + 1048347	\( 37^{12}\cdot 157^{7} \)	16T1281	$[2, 2]$ (GRH)
16.0.15478121650083338314369033920290533.2	x^16 - 7x^15 - 5x^14 - 45x^13 + 315x^12 + 1879x^11 - 9624x^10 + 89874x^9 + 25265x^8 + 1212x^7 - 288961x^6 - 4208135x^5 + 49678870x^4 - 54019469x^3 + 418519900x^2 + 325469946x + 1236119787	\( 37^{12}\cdot 157^{7} \)	16T1281	$[2, 2]$ (GRH)