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 163)

Label	Polynomial	Discriminant	Galois group	Class group
16.4.1078732544346879404306640625.1	x^16 - 6x^15 + 23x^14 - 67x^13 + 189x^12 - 287x^11 + 130x^10 + 54x^9 + 498x^8 + 495x^7 - 5594x^6 + 9181x^5 - 28506x^4 + 77180x^3 - 127780x^2 + 149085x - 80345	\( 5^{10}\cdot 101^{10} \)	16T875	Trivial (GRH)
16.4.1078732544346879404306640625.7	x^16 - 5x^15 + 7x^14 + 61x^13 - 353x^12 + 781x^11 - 846x^10 - 157x^9 - 1542x^8 + 5882x^7 - 10288x^6 - 9000x^5 + 16424x^4 + 12370x^3 - 99040x^2 + 75775x - 15595	\( 5^{10}\cdot 101^{10} \)	16T875	Trivial (GRH)
16.4.1078732544346879404306640625.8	x^16 - 2x^15 - 2x^14 - 34x^13 + 66x^12 + 17x^11 + 320x^10 - 122x^9 + 635x^8 - 3278x^7 - 1424x^6 - 514x^5 - 13702x^4 + 11373x^3 + 26001x^2 - 8805x - 13255	\( 5^{10}\cdot 101^{10} \)	16T875	Trivial (GRH)
16.4.1078732544346879404306640625.11	x^16 - x^15 + x^14 - 22x^13 + 104x^12 - 149x^11 - 63x^10 + 852x^9 - 2384x^8 + 2398x^7 + 4204x^6 - 15498x^5 + 13501x^4 + 8388x^3 - 30356x^2 + 29904x - 9136	\( 5^{10}\cdot 101^{10} \)	16T875	Trivial (GRH)
16.4.1078732544346879404306640625.14	x^16 - 7x^15 + 24x^14 - 63x^13 + 176x^12 - 368x^11 + 381x^10 - 582x^9 + 1574x^8 + 947x^7 - 5494x^6 - 3912x^5 + 819x^4 + 20962x^3 + 1696x^2 - 16050x - 5125	\( 5^{10}\cdot 101^{10} \)	16T875	Trivial (GRH)
16.4.1078732544346879404306640625.20	x^16 - x^15 + 18x^14 - 24x^13 + 144x^12 - 11x^11 + 272x^10 + 792x^9 - 2005x^8 + 1787x^7 - 6709x^6 + 165x^5 - 1064x^4 + 1720x^3 + 585x^2 + 400x + 25	\( 5^{10}\cdot 101^{10} \)	16T875	Trivial (GRH)
16.4.1078732544346879404306640625.25	x^16 - 2x^15 - 17x^14 + 49x^13 - 47x^12 + 199x^11 + 201x^10 - 3069x^9 + 6885x^8 - 12157x^7 + 24259x^6 - 37805x^5 + 30421x^4 - 7299x^3 - 6311x^2 + 2376x + 841	\( 5^{10}\cdot 101^{10} \)	16T875	Trivial (GRH)
16.4.1078732544346879404306640625.27	x^16 - 23x^14 - 21x^13 + 59x^12 - 203x^11 - 381x^10 - 1641x^9 - 14335x^8 - 23689x^7 + 13795x^6 + 36135x^5 - 16895x^4 - 17171x^3 + 15821x^2 - 5940x + 1229	\( 5^{10}\cdot 101^{10} \)	16T875	Trivial (GRH)
16.4.1078732544346879404306640625.29	x^16 - 4x^15 + 4x^14 + 26x^13 - 345x^12 + 1476x^11 - 4833x^10 + 7928x^9 - 11262x^8 - 1792x^7 + 45782x^6 - 100628x^5 + 96324x^4 - 31738x^3 - 16047x^2 + 13682x + 4451	\( 5^{10}\cdot 101^{10} \)	16T875	Trivial (GRH)
16.4.1078732544346879404306640625.33	x^16 - 5x^15 + 8x^14 + 24x^13 - 85x^12 - 29x^11 + 205x^10 - 747x^9 + 34x^8 + 4525x^7 - 5715x^6 - 11950x^5 + 13545x^4 + 16850x^3 - 14825x^2 - 15500x + 11125	\( 5^{10}\cdot 101^{10} \)	16T875	Trivial (GRH)
16.4.1078732544346879404306640625.34	x^16 - x^15 + 2x^14 + 69x^12 - 292x^11 + 103x^10 + 2388x^9 - 6741x^8 + 8350x^7 - 4614x^6 - 4715x^5 + 16470x^4 - 15055x^3 - 18895x^2 + 16525x + 11125	\( 5^{10}\cdot 101^{10} \)	16T875	Trivial (GRH)
16.4.1078732544346879404306640625.40	x^16 - 7x^15 + 19x^14 - 28x^13 - 92x^12 + 601x^11 - 1022x^10 + 1444x^9 - 867x^8 - 11142x^7 + 17564x^6 + 8227x^5 + 24936x^4 - 83730x^3 - 2495x^2 - 7535x + 93845	\( 5^{10}\cdot 101^{10} \)	16T875	Trivial (GRH)
16.4.24109722907876309716269637601.3	x^16 - 2x^15 - 46x^14 + 122x^13 + 776x^12 - 2418x^11 - 5049x^10 + 19682x^9 + 5275x^8 - 56614x^7 + 39776x^6 + 29248x^5 - 75936x^4 + 12064x^3 - 13312x^2 + 9984x - 29952	\( 13^{10}\cdot 53^{10} \)	16T875	Trivial (GRH)
16.4.24109722907876309716269637601.4	x^16 - 5x^15 + 12x^14 + 29x^13 - 289x^12 + 1464x^11 - 5843x^10 + 19773x^9 - 52032x^8 + 99384x^7 - 126683x^6 + 81320x^5 + 28279x^4 - 110890x^3 + 92734x^2 - 21014x - 25437	\( 13^{10}\cdot 53^{10} \)	16T875	Trivial (GRH)
16.4.24109722907876309716269637601.8	x^16 - x^15 + 13x^14 + 2x^13 - 133x^12 + 233x^11 + 1693x^10 + 9x^9 - 7953x^8 - 10209x^7 + 579x^6 + 14278x^5 + 10911x^4 + 22319x^3 + 78008x^2 + 59010x - 11651	\( 13^{10}\cdot 53^{10} \)	16T875	Trivial (GRH)
16.4.24109722907876309716269637601.9	x^16 - 3x^15 - 17x^14 + 56x^13 + 18x^12 - 638x^11 + 598x^10 + 2586x^9 + 5404x^8 + 20483x^7 - 4851x^6 - 109361x^5 - 109880x^4 + 131265x^3 + 199153x^2 + 107820x - 5931	\( 13^{10}\cdot 53^{10} \)	16T875	$[2]$ (GRH)
16.4.24109722907876309716269637601.10	x^16 - 4x^15 + 36x^14 - 71x^13 + 220x^12 + 346x^11 - 1091x^10 + 3336x^9 - 698x^8 - 1069x^7 - 736x^6 + 3336x^5 + 17005x^4 + 13064x^3 + 9564x^2 - 144x - 1296	\( 13^{10}\cdot 53^{10} \)	16T875	$[2]$ (GRH)
16.4.24109722907876309716269637601.12	x^16 - 8x^15 + 44x^14 - 168x^13 + 320x^12 - 100x^11 - 870x^10 + 2216x^9 - 1703x^8 - 2436x^7 + 4908x^6 - 1178x^5 - 2139x^4 + 1136x^3 - 127x^2 + 104x - 39	\( 13^{10}\cdot 53^{10} \)	16T875	Trivial (GRH)
16.4.24109722907876309716269637601.21	x^16 - 4x^15 - 27x^14 + 55x^13 + 375x^12 + 209x^11 - 2041x^10 - 6103x^9 - 3829x^8 + 12985x^7 + 22381x^6 - 929x^5 - 23079x^4 - 11471x^3 + 3537x^2 + 1532x + 207	\( 13^{10}\cdot 53^{10} \)	16T875	Trivial (GRH)
16.4.24109722907876309716269637601.23	x^16 - 7x^15 + 6x^14 + 63x^13 - 183x^12 + 296x^11 - 1386x^10 + 4329x^9 - 5557x^8 + 5374x^7 - 14606x^6 + 17036x^5 + 23158x^4 - 64340x^3 + 49123x^2 - 10015x + 919	\( 13^{10}\cdot 53^{10} \)	16T875	Trivial (GRH)
16.4.24109722907876309716269637601.24	x^16 - x^15 - 2x^14 + 23x^13 - 309x^12 + 2063x^11 - 6918x^10 + 12394x^9 - 20469x^8 + 41789x^7 - 46181x^6 + 6504x^5 + 13705x^4 - 9702x^3 + 15417x^2 - 2376x + 2187	\( 13^{10}\cdot 53^{10} \)	16T875	$[2]$ (GRH)
16.4.24109722907876309716269637601.25	x^16 - x^15 - 2x^14 - 61x^13 + 137x^12 + 338x^11 - 413x^10 + 3385x^9 - 8388x^8 + 13057x^7 - 12633x^6 + 1672x^5 + 11790x^4 - 17069x^3 + 14105x^2 - 8164x + 2249	\( 13^{10}\cdot 53^{10} \)	16T875	$[2]$ (GRH)
16.4.24109722907876309716269637601.26	x^16 - 3x^15 - 21x^14 + 94x^13 + 74x^12 - 1053x^11 + 1929x^10 + 1398x^9 - 18360x^8 + 58816x^7 - 100244x^6 + 90186x^5 - 25355x^4 - 24142x^3 + 26008x^2 - 10384x + 2928	\( 13^{10}\cdot 53^{10} \)	16T875	$[2]$ (GRH)
16.4.24109722907876309716269637601.42	x^16 - x^15 - 3x^14 + x^13 + 80x^12 - 211x^11 - 744x^10 + 1073x^9 + 3409x^8 - 6056x^7 + 27073x^6 - 21992x^5 - 201687x^4 + 197845x^3 + 712532x^2 - 1315048x + 608357	\( 13^{10}\cdot 53^{10} \)	16T875	$[2]$ (GRH)
16.4.26968313608671985107666015625.5	x^16 - 4x^15 + 13x^14 - 33x^13 - 17x^12 + 535x^11 - 2146x^10 + 4031x^9 - 6252x^8 + 25258x^7 - 114094x^6 + 325461x^5 - 596497x^4 + 725871x^3 - 554378x^2 + 237091x - 17599	\( 5^{12}\cdot 101^{10} \)	16T875	$[2]$ (GRH)
16.4.26968313608671985107666015625.9	x^16 - 2x^15 + 8x^14 - 18x^13 + 83x^12 - 212x^11 - 1826x^10 + 13011x^9 - 39252x^8 + 73938x^7 - 108099x^6 + 142360x^5 - 187742x^4 + 216921x^3 - 183478x^2 + 73797x - 3259	\( 5^{12}\cdot 101^{10} \)	16T875	$[2]$ (GRH)
16.4.26968313608671985107666015625.14	x^16 - x^15 - 20x^14 - 25x^13 + 201x^12 + 525x^11 - 746x^10 - 4000x^9 + 596x^8 + 11585x^7 + 10530x^6 - 28211x^5 - 7799x^4 + 7825x^3 + 30875x^2 - 20460x + 355	\( 5^{12}\cdot 101^{10} \)	16T875	$[2]$ (GRH)
16.4.26968313608671985107666015625.16	x^16 - 5x^15 + 32x^14 - 108x^13 + 82x^12 - 157x^11 - 1821x^10 + 4291x^9 - 13100x^8 + 16329x^7 - 36393x^6 + 23186x^5 + 2332x^4 - 55357x^3 + 20132x^2 - 21644x + 1511	\( 5^{12}\cdot 101^{10} \)	16T875	$[2]$ (GRH)
16.4.26968313608671985107666015625.17	x^16 - 3x^15 - 10x^14 + 65x^13 - 194x^12 + 420x^11 - 339x^10 - 840x^9 + 2036x^8 + 315x^7 - 4650x^6 + 2158x^5 + 4681x^4 - 2050x^3 - 4650x^2 + 1760x + 1655	\( 5^{12}\cdot 101^{10} \)	16T875	$[2]$ (GRH)
16.4.26968313608671985107666015625.20	x^16 - 3x^15 + 13x^14 + 12x^13 - 66x^12 + 717x^11 - 2578x^10 + 7578x^9 - 3507x^8 - 45982x^7 + 206202x^6 - 448959x^5 + 541710x^4 - 375564x^3 + 149429x^2 - 31859x + 2861	\( 5^{12}\cdot 101^{10} \)	16T875	$[2]$ (GRH)
16.4.26968313608671985107666015625.23	x^16 - 3x^15 + 13x^14 - 98x^13 + 354x^12 - 933x^11 + 2477x^10 - 6347x^9 + 14113x^8 - 25062x^7 + 37732x^6 - 60434x^5 + 97795x^4 - 118419x^3 + 89289x^2 - 36714x + 6241	\( 5^{12}\cdot 101^{10} \)	16T875	$[2]$ (GRH)
16.4.26968313608671985107666015625.25	x^16 - 3x^15 - 31x^14 + 16x^13 + 414x^12 + 735x^11 - 2048x^10 - 11318x^9 - 12187x^8 + 44042x^7 + 190822x^6 + 369725x^5 + 461474x^4 + 402296x^3 + 240669x^2 + 88567x + 14951	\( 5^{12}\cdot 101^{10} \)	16T875	$[2]$ (GRH)
16.4.26968313608671985107666015625.27	x^16 - x^15 - 3x^14 + 62x^13 - 143x^12 + 134x^11 + 497x^10 - 1309x^9 - 985x^8 + 5289x^7 - 10986x^6 - 13458x^5 + 13857x^4 - 3342x^3 - 60193x^2 - 8150x + 20141	\( 5^{12}\cdot 101^{10} \)	16T875	$[2]$ (GRH)
16.4.26968313608671985107666015625.29	x^16 - 4x^15 - 39x^14 + 134x^13 + 397x^12 - 1516x^11 - 384x^10 + 6427x^9 - 10296x^8 - 493x^7 + 18943x^6 - 3005x^5 + 10896x^4 - 10360x^3 + 64840x^2 - 41745x + 53605	\( 5^{12}\cdot 101^{10} \)	16T875	$[2]$ (GRH)
16.4.26968313608671985107666015625.30	x^16 - 3x^15 + 34x^14 - 89x^13 + 222x^12 - 693x^11 - 952x^10 + 1446x^9 - 5579x^8 + 26349x^7 + 3333x^6 - 71567x^5 + 43327x^4 + 61869x^3 - 95211x^2 - 17847x + 63261	\( 5^{12}\cdot 101^{10} \)	16T875	$[2]$ (GRH)
16.4.26968313608671985107666015625.33	x^16 - 2x^15 + 13x^14 - 10x^13 + 125x^12 - 198x^11 + 529x^10 - 1845x^9 + 374x^8 - 13295x^7 - 15289x^6 - 42171x^5 - 52860x^4 - 47230x^3 - 135503x^2 + 182831x + 278501	\( 5^{12}\cdot 101^{10} \)	16T875	$[2]$ (GRH)
16.4.98340377973019428085802419249.4	x^16 - 6x^15 + x^14 + 113x^13 - 457x^12 - 259x^11 + 4268x^10 - 6485x^9 - 7128x^8 + 48936x^7 - 31338x^6 + 29159x^5 + 324725x^4 - 471125x^3 + 188282x^2 + 744165x - 231183	\( 13^{10}\cdot 61^{10} \)	16T875	Trivial (GRH)
16.4.98340377973019428085802419249.6	x^16 - 23x^14 - 4x^13 + 333x^12 + 402x^11 - 2195x^10 - 4987x^9 + 3181x^8 + 27549x^7 + 28831x^6 + 1820x^5 + 137646x^4 + 222204x^3 - 500920x^2 - 1079850x - 138069	\( 13^{10}\cdot 61^{10} \)	16T875	Trivial (GRH)
16.4.98340377973019428085802419249.7	x^16 - 7x^15 + 9x^14 + 24x^13 - 57x^12 - 3x^11 + 1710x^10 - 12640x^9 + 32512x^8 + 7903x^7 - 302960x^6 + 1046722x^5 - 2002372x^4 + 2356494x^3 - 1671346x^2 + 648024x - 104221	\( 13^{10}\cdot 61^{10} \)	16T875	Trivial (GRH)
16.4.98340377973019428085802419249.9	x^16 + 24x^14 - 16x^13 + 134x^12 - 689x^11 + 644x^10 - 4155x^9 + 7346x^8 + 5842x^7 - 24017x^6 + 65468x^5 - 32548x^4 - 148827x^3 + 111824x^2 + 69589x - 53507	\( 13^{10}\cdot 61^{10} \)	16T875	Trivial (GRH)
16.4.98340377973019428085802419249.10	x^16 - 5x^15 - 23x^14 + 148x^13 + 120x^12 - 1653x^11 + 1011x^10 + 7477x^9 - 11167x^8 - 2939x^7 + 13407x^6 - 55190x^5 + 97603x^4 - 16198x^3 - 137891x^2 + 583609x - 39533	\( 13^{10}\cdot 61^{10} \)	16T875	Trivial (GRH)
16.4.98340377973019428085802419249.13	x^16 - 7x^15 + 46x^14 - 161x^13 + 364x^12 - 424x^11 + 54x^10 + 1362x^9 - 4615x^8 + 3784x^7 - 2342x^6 + 7090x^5 + 2886x^4 + 6799x^3 - 45506x^2 + 37051x - 8641	\( 13^{10}\cdot 61^{10} \)	16T875	Trivial (GRH)
16.4.98340377973019428085802419249.16	x^16 - 7x^15 + 3x^14 + 68x^13 - 158x^12 - 87x^11 + 442x^10 + 1190x^9 - 4885x^8 + 3958x^7 + 4458x^6 - 8437x^5 - 1248x^4 + 13858x^3 - 15223x^2 + 7605x - 1521	\( 13^{10}\cdot 61^{10} \)	16T875	Trivial (GRH)
16.4.98340377973019428085802419249.24	x^16 - 5x^15 - 4x^14 + 54x^13 - 135x^12 + 98x^11 + 49x^10 - 2057x^9 + 4881x^8 - 6069x^7 + 10465x^6 - 3270x^5 + 1261x^4 + 3548x^3 - 5472x^2 + 10360x + 7472	\( 13^{10}\cdot 61^{10} \)	16T875	Trivial (GRH)
16.4.98340377973019428085802419249.28	x^16 - 5x^15 - 3x^14 - 36x^13 + 597x^12 - 1056x^11 - 3613x^10 + 12035x^9 + 1951x^8 - 73509x^7 + 200582x^6 - 221534x^5 - 9053x^4 + 313284x^3 - 522759x^2 + 266626x + 21493	\( 13^{10}\cdot 61^{10} \)	16T875	Trivial (GRH)
16.4.98340377973019428085802419249.30	x^16 - 4x^15 - 8x^14 + 78x^13 - 222x^12 + 380x^11 - 344x^10 - 1326x^9 + 7780x^8 - 21854x^7 + 43374x^6 - 68932x^5 + 93551x^4 - 112974x^3 + 113084x^2 - 77640x + 27504	\( 13^{10}\cdot 61^{10} \)	16T875	Trivial (GRH)
16.4.98340377973019428085802419249.33	x^16 - 2x^15 - 44x^14 + 92x^13 + 650x^12 - 1812x^11 - 3987x^10 + 16065x^9 + 4974x^8 - 68206x^7 + 38442x^6 + 151108x^5 - 173006x^4 - 211551x^3 + 531328x^2 - 379452x + 95481	\( 13^{10}\cdot 61^{10} \)	16T875	Trivial (GRH)
16.4.98340377973019428085802419249.36	x^16 - 8x^15 + 2x^14 + 126x^13 - 644x^12 + 1862x^11 + 224x^10 - 14232x^9 + 26238x^8 - 5942x^7 - 56404x^6 + 116978x^5 - 93281x^4 + 19720x^3 + 156920x^2 - 151560x + 168464	\( 13^{10}\cdot 61^{10} \)	16T875	Trivial (GRH)
16.4.4074543171431096342049568754569.7	x^16 - 4x^15 + 3x^14 + 136x^13 - 415x^12 + 444x^11 + 5717x^10 - 17437x^9 + 16465x^8 + 114933x^7 - 307004x^6 - 123952x^5 + 953906x^4 - 614407x^3 - 714532x^2 + 1148831x - 469741	\( 13^{12}\cdot 53^{10} \)	16T875	$[2]$ (GRH)
16.4.4074543171431096342049568754569.9	x^16 - 2x^15 - 16x^14 - 46x^13 + 97x^12 + 160x^11 - 290x^10 - 1315x^9 + 3107x^8 + 10716x^7 + 4204x^6 + 23057x^5 - 19090x^4 - 242564x^3 - 1147948x^2 - 998151x - 239067	\( 13^{12}\cdot 53^{10} \)	16T875	$[2]$ (GRH)