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 309)

Label	Polynomial	Discriminant	Galois group	Class group
14.14.10260628712958602189.1	x^14 - x^13 - 13x^12 + 12x^11 + 66x^10 - 55x^9 - 165x^8 + 120x^7 + 210x^6 - 126x^5 - 126x^4 + 56x^3 + 28x^2 - 7x - 1	\( 29^{13} \)	$C_{14}$ (as 14T1)	Trivial
14.0.773792930870360792667.1	x^14 - x^13 + 13x^12 - 2x^11 + 123x^10 - 42x^9 + 353x^8 - 132x^7 + 776x^6 - 254x^5 + 455x^4 + 182x^3 + 67x^2 + 9x + 1	\( -\,3^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 2]$
14.0.1341068619663964900807.1	x^14 - 28x^11 + 7x^10 + 14x^9 + 189x^8 - 90x^7 - 98x^6 - 196x^5 + 427x^4 - 217x^3 - 140x^2 + 119x + 79	\( -\,7^{25} \)	$C_{14}$ (as 14T1)	Trivial
14.0.1718264124282290785243.1	x^14 - x^13 + 2x^12 + 24x^11 - 17x^10 + 27x^9 + 143x^8 - 81x^7 + 83x^6 + 209x^5 + 163x^4 - 88x^3 + 235x^2 + 168x + 79	\( -\,43^{13} \)	$C_{14}$ (as 14T1)	Trivial
14.0.5796901408038404767744.1	x^14 + 25x^12 + 214x^10 + 767x^8 + 1194x^6 + 686x^4 + 53x^2 + 1	\( -\,2^{14}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 14]$
14.0.22439994995240462987343.1	x^14 - x^13 + 16x^12 - 17x^11 + 66x^10 - 84x^9 + 38x^8 - 315x^7 + 65x^6 - 503x^5 + 1556x^4 + 665x^3 + 2377x^2 - 3516x + 1681	\( -\,3^{7}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 6]$
14.14.27641779937927268828125.1	x^14 - 5x^13 - 22x^12 + 131x^11 + 90x^10 - 1019x^9 + 223x^8 + 3253x^7 - 1853x^6 - 4170x^5 + 2916x^4 + 1404x^3 - 781x^2 - 168x + 41	\( 5^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	Trivial (GRH)
14.0.87391712553613254588987.1	x^14 - x^13 + 19x^12 - 52x^11 + 321x^10 - 658x^9 + 1819x^8 - 2372x^7 + 5112x^6 - 5324x^5 + 8835x^4 - 4452x^3 + 5145x^2 + 343x + 2401	\( -\,3^{7}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[203]$
14.0.168110140833113738264576.1	x^14 + 29x^12 + 290x^10 + 1247x^8 + 2262x^6 + 1566x^4 + 377x^2 + 29	\( -\,2^{14}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 6]$ (GRH)
14.0.291381688005381590432263.1	x^14 - 5x^13 - x^12 + 41x^11 - 266x^9 + 682x^8 - 1271x^7 + 3346x^6 - 5784x^5 + 12267x^4 - 10251x^3 + 20954x^2 - 13581x + 22271	\( -\,7^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 14]$ (GRH)
14.0.418988153029298748294987.1	x^14 + 21x^12 - 42x^11 + 350x^10 - 553x^9 + 2184x^8 - 2696x^7 + 8869x^6 - 8701x^5 + 18151x^4 - 8246x^3 + 17920x^2 - 8148x + 9409	\( -\,3^{7}\cdot 7^{24} \)	$C_{14}$ (as 14T1)	$[203]$ (GRH)
14.0.654698590982350051753984.1	x^14 + 37x^12 + 470x^10 + 2787x^8 + 8570x^6 + 13714x^4 + 10241x^2 + 2401	\( -\,2^{14}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[43]$ (GRH)
14.0.742003380228915810271232.1	x^14 - 2x^13 - 9x^12 + 14x^11 + 90x^10 - 104x^9 + 267x^8 + 152x^7 + 2022x^6 - 694x^5 + 10130x^4 - 8292x^3 + 29677x^2 - 7326x + 33251	\( -\,2^{21}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 86]$ (GRH)
14.14.742003380228915810271232.1	x^14 - 2x^13 - 37x^12 + 62x^11 + 450x^10 - 640x^9 - 2333x^8 + 2584x^7 + 5734x^6 - 4278x^5 - 6342x^4 + 2284x^3 + 2429x^2 + 338x - 17	\( 2^{21}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	Trivial (GRH)
14.14.801611618199890796015625.1	x^14 - x^13 - 42x^12 + 41x^11 + 646x^10 - 606x^9 - 4602x^8 + 4383x^7 + 15261x^6 - 16163x^5 - 18628x^4 + 25257x^3 - 1451x^2 - 4386x + 289	\( 5^{7}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[4]$ (GRH)
14.0.1165087474585497590531111.1	x^14 - x^13 + 3x^12 - 11x^11 + 44x^10 + 156x^9 - 250x^8 - 749x^7 + 1560x^6 + 4490x^5 + 3202x^4 + 755x^3 + 4050x^2 + 1750x + 625	\( -\,71^{13} \)	$C_{14}$ (as 14T1)	$[49]$ (GRH)
14.14.2932917071205091238064909.1	x^14 - 42x^12 - 63x^11 + 539x^10 + 1484x^9 - 1386x^8 - 8597x^7 - 7007x^6 + 6734x^5 + 10591x^4 + 490x^3 - 3731x^2 - 1071x + 79	\( 3^{7}\cdot 7^{25} \)	$C_{14}$ (as 14T1)	Trivial
14.14.3121846156036138781328125.1	x^14 - 5x^13 - 34x^12 + 135x^11 + 470x^10 - 1207x^9 - 3159x^8 + 3921x^7 + 9113x^6 - 3280x^5 - 7200x^4 + 698x^3 + 529x^2 - 62x + 1	\( 5^{7}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	Trivial (GRH)
14.0.3138866894939200133545984.1	x^14 + 42x^12 + 623x^10 + 4431x^8 + 16513x^6 + 31906x^4 + 28784x^2 + 9409	\( -\,2^{14}\cdot 7^{24} \)	$C_{14}$ (as 14T1)	$[71]$ (GRH)
14.14.3757843639805369947326441.1	x^14 - x^13 - 41x^12 - 19x^11 + 585x^10 + 887x^9 - 2996x^8 - 7649x^7 + 1803x^6 + 19387x^5 + 16761x^4 - 45x^3 - 4323x^2 - 434x + 337	\( 3^{7}\cdot 43^{13} \)	$C_{14}$ (as 14T1)	Trivial
14.0.6894849182652903337173011.1	x^14 - 5x^13 + 6x^12 + 11x^11 + 54x^10 - 315x^9 + 1275x^8 - 3203x^7 + 9895x^6 - 18010x^5 + 45292x^4 - 47572x^3 + 108523x^2 - 68096x + 130153	\( -\,11^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 86]$ (GRH)
14.0.8450068952156066122535627.1	x^14 - x^13 + 45x^12 - 46x^11 + 646x^10 - 693x^9 + 3489x^8 - 5970x^7 + 7170x^6 - 27038x^5 + 34790x^4 - 15372x^3 + 128440x^2 - 135147x + 77023	\( -\,7^{7}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 116]$ (GRH)
14.14.12677823379379991227056128.1	x^14 - 2x^13 - 44x^12 + 74x^11 + 645x^10 - 924x^9 - 4033x^8 + 4572x^7 + 11777x^6 - 9184x^5 - 15970x^4 + 5098x^3 + 8842x^2 + 1584x - 59	\( 2^{14}\cdot 3^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	Trivial (GRH)
14.14.14967283701606751125078125.1	x^14 - 7x^13 - 28x^12 + 217x^11 + 322x^10 - 2415x^9 - 2149x^8 + 11383x^7 + 8197x^6 - 20622x^5 - 12474x^4 + 12390x^3 + 5201x^2 - 1876x - 589	\( 5^{7}\cdot 7^{24} \)	$C_{14}$ (as 14T1)	Trivial (GRH)
14.0.21518098026638558497865728.1	x^14 + 58x^12 + 1160x^10 + 9976x^8 + 36192x^6 + 50112x^4 + 24128x^2 + 3712	\( -\,2^{21}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 86]$ (GRH)
14.14.21518098026638558497865728.1	x^14 - 58x^12 + 1160x^10 - 9976x^8 + 36192x^6 - 50112x^4 + 24128x^2 - 3712	\( 2^{21}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2]$ (GRH)
14.14.21972068264574400934821888.1	x^14 - 42x^12 + 539x^10 - 2401x^8 + 3773x^6 - 1470x^4 + 196x^2 - 7	\( 2^{14}\cdot 7^{25} \)	$C_{14}$ (as 14T1)	Trivial
14.14.22201352938819688612162197.1	x^14 - 5x^13 - 36x^12 + 191x^11 + 360x^10 - 2271x^9 - 1083x^8 + 11209x^7 - 779x^6 - 23974x^5 + 6292x^4 + 22724x^3 - 7601x^2 - 7796x + 2941	\( 13^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	Trivial (GRH)
14.14.28152039412241052225421312.1	x^14 - 43x^12 + 602x^10 - 3397x^8 + 8514x^6 - 9030x^4 + 3053x^2 - 43	\( 2^{14}\cdot 43^{13} \)	$C_{14}$ (as 14T1)	Trivial (GRH)
14.0.32908474225670013957008743.1	x^14 - 5x^13 - 13x^12 + 45x^11 + 236x^10 - 82x^9 - 828x^8 - 171x^7 + 6224x^6 + 8174x^5 + 5181x^4 + 3227x^3 + 53608x^2 + 87199x + 85141	\( -\,7^{7}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 2, 14]$ (GRH)
14.0.35887976153781453950585067.1	x^14 - x^13 + 31x^12 + 36x^11 + 643x^10 + 844x^9 + 7385x^8 + 14106x^7 + 58178x^6 + 65124x^5 + 122335x^4 + 9326x^3 + 93727x^2 + 33565x + 18769	\( -\,3^{7}\cdot 71^{12} \)	$C_{14}$ (as 14T1)	$[43]$ (GRH)
14.0.60452572724246936927109375.1	x^14 - 5x^13 + 13x^12 - 19x^11 + 150x^10 - 514x^9 + 2438x^8 - 6347x^7 + 22552x^6 - 42720x^5 + 123031x^4 - 143071x^3 + 363084x^2 - 231593x + 499381	\( -\,3^{7}\cdot 5^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 226]$ (GRH)
14.0.83801419645740806624509952.1	x^14 - 2x^13 - 21x^12 + 82x^11 + 138x^10 - 1164x^9 + 2063x^8 - 824x^7 + 4950x^6 - 26778x^5 + 57742x^4 - 70268x^3 + 124449x^2 - 210818x + 208427	\( -\,2^{21}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[203]$ (GRH)
14.14.83801419645740806624509952.1	x^14 - 2x^13 - 49x^12 + 130x^11 + 690x^10 - 2164x^9 - 3225x^8 + 13320x^7 + 86x^6 - 26074x^5 + 20214x^4 - 1996x^3 - 1359x^2 + 78x + 7	\( 2^{21}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	Trivial (GRH)
14.0.104770985911247257875546875.1	x^14 + 42x^12 - 119x^11 + 553x^10 - 2702x^9 + 6174x^8 - 15735x^7 + 36995x^6 - 61572x^5 + 88655x^4 - 58940x^3 + 2863x^2 - 4557x + 30361	\( -\,5^{7}\cdot 7^{25} \)	$C_{14}$ (as 14T1)	$[254]$ (GRH)
14.0.134239384709553967597109375.1	x^14 - x^13 + 45x^12 + 67x^11 + 585x^10 + 2263x^9 + 4916x^8 + 17291x^7 + 36289x^6 + 71331x^5 + 129077x^4 + 181931x^3 + 270017x^2 + 169588x + 119189	\( -\,5^{7}\cdot 43^{13} \)	$C_{14}$ (as 14T1)	$[2842]$ (GRH)
14.14.145183888628314852626522593.1	x^14 - 5x^13 - 43x^12 + 221x^11 + 558x^10 - 3122x^9 - 2666x^8 + 18469x^7 + 3280x^6 - 47088x^5 + 4167x^4 + 51345x^3 - 9196x^2 - 18921x + 2669	\( 17^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	Trivial (GRH)
14.0.199950626296934196778017319.1	x^14 - x^13 + 74x^12 - 75x^11 + 1806x^10 - 1882x^9 + 17670x^8 - 25893x^7 + 68157x^6 - 189003x^5 + 252348x^4 - 306967x^3 + 1166437x^2 - 1133182x + 741761	\( -\,11^{7}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 8, 8, 40]$ (GRH)
14.0.268856242022659049623404544.1	x^14 + 61x^12 + 1402x^10 + 15247x^8 + 80418x^6 + 185798x^4 + 127429x^2 + 18769	\( -\,2^{14}\cdot 71^{12} \)	$C_{14}$ (as 14T1)	$[3277]$ (GRH)
14.0.316265035547780605989332299.1	x^14 - 5x^13 + 20x^12 - 49x^11 + 288x^10 - 863x^9 + 4381x^8 - 11303x^7 + 44797x^6 - 86598x^5 + 279108x^4 - 343260x^3 + 959807x^2 - 625188x + 1493501	\( -\,19^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[4, 4, 284]$ (GRH)
14.14.367656878002019745584627712.1	x^14 - 87x^12 + 2610x^10 - 33669x^8 + 183222x^6 - 380538x^4 + 274833x^2 - 63423	\( 2^{14}\cdot 3^{7}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2]$ (GRH)
14.0.401774962552217617093885952.1	x^14 - 28x^12 - 42x^11 + 371x^10 + 1022x^9 - 791x^8 - 4240x^7 + 8057x^6 + 35938x^5 + 35840x^4 + 6146x^3 + 123060x^2 + 334516x + 420353	\( -\,2^{21}\cdot 7^{24} \)	$C_{14}$ (as 14T1)	$[953]$ (GRH)
14.14.401774962552217617093885952.1	x^14 - 56x^12 - 42x^11 + 1043x^10 + 1190x^9 - 7987x^8 - 11184x^7 + 22169x^6 + 37282x^5 - 5292x^4 - 22190x^3 - 3164x^2 + 3500x + 881	\( 2^{21}\cdot 7^{24} \)	$C_{14}$ (as 14T1)	Trivial (GRH)
14.0.452882922503000372480000000.1	x^14 - 2x^13 + 12x^12 - 22x^11 + 261x^10 - 332x^9 + 3687x^8 - 2596x^7 + 35841x^6 - 17536x^5 + 240758x^4 - 110934x^3 + 986314x^2 - 244032x + 1783541	\( -\,2^{14}\cdot 5^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 406]$ (GRH)
14.14.489801110321660601428677553.1	x^14 - x^13 - 52x^12 + 31x^11 + 908x^10 - 162x^9 - 6351x^8 - 856x^7 + 16495x^6 + 3600x^5 - 18257x^4 - 3381x^3 + 8945x^2 + 874x - 1583	\( 113^{13} \)	$C_{14}$ (as 14T1)	Trivial (GRH)
14.14.637251751667769538275359181.1	x^14 - 5x^13 - 50x^12 + 251x^11 + 798x^10 - 4123x^9 - 5149x^8 + 28717x^7 + 12607x^6 - 86298x^5 - 7172x^4 + 104780x^3 - 6213x^2 - 34448x - 2999	\( 3^{7}\cdot 7^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	Trivial (GRH)
14.14.643839235225770969752703713.1	x^14 - x^13 - 100x^12 + 99x^11 + 3546x^10 - 3448x^9 - 56106x^8 + 60585x^7 + 392145x^6 - 556143x^5 - 905100x^4 + 1955033x^3 - 820295x^2 - 98752x + 40193	\( 13^{7}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2]$ (GRH)
14.0.778700158443122158226851571.1	x^14 - 5x^13 - 6x^12 + 15x^11 + 242x^10 - 7x^9 + 149x^8 - 135x^7 + 11005x^6 + 13904x^5 + 39776x^4 + 35930x^3 + 201521x^2 + 257594x + 376249	\( -\,11^{7}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[743]$ (GRH)
14.0.1204677577382769220367486327.1	x^14 - 5x^13 + 27x^12 - 79x^11 + 468x^10 - 1362x^9 + 7314x^8 - 18671x^7 + 80950x^6 - 158128x^5 + 561187x^4 - 714115x^3 + 2179894x^2 - 1446221x + 3780979	\( -\,23^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 1806]$ (GRH)
14.14.1282006464112563369862578125.1	x^14 - 5x^13 - 58x^12 + 331x^11 + 992x^10 - 7505x^9 - 2735x^8 + 69297x^7 - 53449x^6 - 249558x^5 + 357294x^4 + 220050x^3 - 546085x^2 + 155950x + 42725	\( 5^{7}\cdot 71^{12} \)	$C_{14}$ (as 14T1)	Trivial (GRH)