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 26 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.7.1387347928027439932553142925836288.1	x^21 - 3x^19 - 2x^18 - 27x^17 - 36x^16 + 15x^15 + 54x^14 + 360x^13 + 872x^12 + 621x^11 - 426x^10 - 1745x^9 - 3636x^8 - 2913x^7 + 5854x^6 + 18252x^5 + 22104x^4 + 15056x^3 + 6048x^2 + 1344x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 13^{6}\cdot 109^{6} \)	21T147	Trivial (GRH)
21.7.1387347928027439932553142925836288.2	x^21 - 3x^19 - 10x^18 - 36x^17 - 18x^16 + 124x^15 + 252x^14 + 618x^13 + 982x^12 - 144x^11 - 1332x^10 - 2358x^9 - 4626x^8 - 2493x^7 + 4586x^6 + 5472x^5 + 1344x^4 + 624x^3 + 576x^2 - 192x - 128	\( -\,2^{14}\cdot 3^{21}\cdot 13^{6}\cdot 109^{6} \)	21T147	Trivial (GRH)
21.5.9711435496192079527872000480854016.1	x^21 - 21x^19 - 12x^18 + 189x^17 + 216x^16 - 897x^15 - 1620x^14 + 2115x^13 + 6440x^12 - 783x^11 - 14100x^10 - 8033x^9 + 15336x^8 + 18837x^7 - 4012x^6 - 16416x^5 - 5736x^4 + 4368x^3 + 3744x^2 + 1152x + 128	\( 2^{14}\cdot 3^{21}\cdot 7\cdot 13^{6}\cdot 109^{6} \)	21T147	Trivial (GRH)
21.3.15260827208301839258084572184199168.1	x^21 + 18x^19 - 12x^18 + 108x^17 - 144x^16 + 210x^15 - 324x^14 - 351x^13 + 1464x^12 - 3213x^11 + 6342x^10 - 8401x^9 + 7956x^8 - 4353x^7 - 5662x^6 + 18252x^5 - 22104x^4 + 15056x^3 - 6048x^2 + 1344x - 128	\( -\,2^{14}\cdot 3^{21}\cdot 11\cdot 13^{6}\cdot 109^{6} \)	21T147	Trivial (GRH)
21.3.26359610632521358718509715590889472.1	x^21 + 15x^19 - 10x^18 + 72x^17 - 96x^16 + 140x^15 - 216x^14 + 225x^13 - 248x^12 + 702x^11 - 1716x^10 + 1447x^9 + 1476x^8 - 6567x^7 + 14462x^6 - 22572x^5 + 23256x^4 - 15184x^3 + 6048x^2 - 1344x + 128	\( -\,2^{14}\cdot 3^{21}\cdot 13^{6}\cdot 19\cdot 109^{6} \)	21T147	Trivial (GRH)
21.5.45589180307529253293163107814735872.1	x^21 - 6x^19 - 4x^18 + 54x^15 + 108x^14 - 90x^13 - 416x^12 + 54x^11 + 1428x^10 + 2128x^9 + 1440x^8 - 3894x^7 - 20348x^6 - 40824x^5 - 45360x^4 - 30240x^3 - 12096x^2 - 2688x - 256	\( 2^{32}\cdot 3^{21}\cdot 317^{6} \)	21T147	Trivial (GRH)
21.9.45589180307529253293163107814735872.1	x^21 - 18x^19 - 24x^18 + 90x^17 + 252x^16 - 256x^15 - 1368x^14 - 102x^13 + 4096x^12 + 2556x^11 - 6780x^10 - 3112x^9 + 12384x^8 + 6666x^7 - 11436x^6 - 8712x^5 + 6192x^4 + 4576x^3 - 2880x^2 - 384x + 256	\( 2^{32}\cdot 3^{21}\cdot 317^{6} \)	21T147	Trivial (GRH)
21.5.51331873337015277504466288255942656.1	x^21 - 21x^19 - 16x^18 + 189x^17 + 288x^16 - 845x^15 - 2160x^14 + 1335x^13 + 8328x^12 + 3897x^11 - 15696x^10 - 21465x^9 + 6480x^8 + 34425x^7 + 22352x^6 - 12636x^5 - 27192x^4 - 13840x^3 + 2880x^2 + 6528x + 2432	\( 2^{14}\cdot 3^{21}\cdot 13^{6}\cdot 37\cdot 109^{6} \)	21T147	Trivial (GRH)
21.5.91178360615058506586326215629471744.1	x^21 + 3x^19 - 14x^18 - 45x^17 + 12x^16 - 99x^15 + 522x^14 + 171x^13 + 272x^12 - 513x^11 - 954x^10 - 4555x^9 + 4032x^8 + 5343x^7 - 770x^6 - 4356x^5 - 1224x^4 - 880x^3 + 288x^2 + 576x + 128	\( 2^{33}\cdot 3^{21}\cdot 317^{6} \)	21T147	Trivial (GRH)
21.9.17715045692982380498771082020003561472.1	x^21 - 45x^19 - 30x^18 + 837x^17 + 1116x^16 - 7971x^15 - 16686x^14 + 37152x^13 + 126264x^12 - 34803x^11 - 487914x^10 - 411853x^9 + 737244x^8 + 1627689x^7 + 635266x^6 - 1401516x^5 - 2321496x^4 - 1681744x^3 - 683424x^2 - 151872x - 14464	\( 2^{14}\cdot 3^{21}\cdot 13^{6}\cdot 109^{6}\cdot 113^{2} \)	21T147	Trivial (GRH)
21.17.7002806587576722456817460320710948814848.1	x^21 - 21x^19 - 44x^18 + 189x^17 + 792x^16 - 833x^15 - 5940x^14 + 1155x^13 + 23916x^12 + 4977x^11 - 55332x^10 - 26001x^9 + 72576x^8 + 50949x^7 - 47772x^6 - 50544x^5 + 5724x^4 + 22688x^3 + 10368x^2 + 1920x + 128	\( 2^{34}\cdot 3^{21}\cdot 139\cdot 809^{6} \)	21T147	Trivial (GRH)
21.13.8866863017363332031653762708238323679232.1	x^21 + 24x^19 - 16x^18 - 36x^17 + 48x^16 - 3472x^15 + 6912x^14 - 11088x^13 + 18304x^12 + 107136x^11 - 407040x^10 + 691648x^9 - 928512x^8 - 63744x^7 + 4379648x^6 - 10036224x^5 + 11501568x^4 - 7729152x^3 + 3096576x^2 - 688128x + 65536	\( 2^{38}\cdot 3^{21}\cdot 11\cdot 809^{6} \)	21T147	Trivial (GRH)
21.13.12897255297983028409678200302892107169792.1	x^21 - 9x^19 - 6x^18 - 36x^17 - 48x^16 + 362x^15 + 756x^14 + 828x^13 + 976x^12 - 3024x^11 - 12576x^10 - 18674x^9 - 17352x^8 - 9186x^7 + 11260x^6 + 36504x^5 + 44208x^4 + 30112x^3 + 12096x^2 + 2688x + 256	\( 2^{42}\cdot 3^{21}\cdot 809^{6} \)	21T147	Trivial (GRH)
21.17.14307892596199922141986753461020931391488.1	x^21 - 21x^19 - 23x^18 + 189x^17 + 414x^16 - 813x^15 - 3105x^14 + 855x^13 + 12212x^12 + 6777x^11 - 25449x^10 - 30665x^9 + 22302x^8 + 52425x^7 + 6305x^6 - 35532x^5 - 20496x^4 + 2944x^3 + 5472x^2 + 1536x + 128	\( 2^{36}\cdot 3^{21}\cdot 71\cdot 809^{6} \)	21T147	Trivial (GRH)
21.15.24988432139842117543751513086853457641472.1	x^21 - 21x^19 - 8x^18 + 189x^17 + 144x^16 - 945x^15 - 1080x^14 + 2835x^13 + 4432x^12 - 5103x^11 - 11064x^10 + 4903x^9 + 17712x^8 - 387x^7 - 17960x^6 - 5400x^5 + 9264x^4 + 5656x^3 - 288x^2 - 768x - 128	\( -\,2^{38}\cdot 3^{21}\cdot 31\cdot 809^{6} \)	21T147	Trivial (GRH)
21.9.25794510595966056819356400605784214339584.1	x^21 - 21x^19 - 11x^18 + 189x^17 + 198x^16 - 961x^15 - 1485x^14 + 3075x^13 + 6400x^12 - 6543x^11 - 18885x^10 + 8607x^9 + 40878x^8 - 1323x^7 - 60851x^6 - 18144x^5 + 56172x^4 + 28560x^3 - 28368x^2 - 19584x + 3904	\( 2^{43}\cdot 3^{21}\cdot 809^{6} \)	21T147	Trivial (GRH)
21.15.60189691870465817637946777639383944134656.1	x^21 - 24x^19 - 16x^18 + 153x^17 + 204x^16 + 365x^15 + 594x^14 - 4545x^13 - 13088x^12 - 9774x^11 + 5484x^10 + 48407x^9 + 147132x^8 + 233967x^7 + 213694x^6 + 121932x^5 + 49752x^4 + 18128x^3 + 6048x^2 + 1344x + 128	\( -\,2^{27}\cdot 3^{21}\cdot 11\cdot 3967^{6} \)	21T147	Trivial (GRH)
21.11.103178042383864227277425602423136857358336.1	x^21 - 72x^17 - 96x^16 - 86x^15 - 108x^14 + 1143x^13 + 3224x^12 + 4212x^11 + 4680x^10 + 186x^9 - 14616x^8 - 32574x^7 - 46204x^6 - 53784x^5 - 48816x^4 - 30624x^3 - 12096x^2 - 2688x - 256	\( -\,2^{45}\cdot 3^{21}\cdot 809^{6} \)	21T147	Trivial (GRH)
21.9.111312903718645565236549669222820006068224.1	x^21 - 21x^19 - 5x^18 + 189x^17 + 90x^16 - 1009x^15 - 675x^14 + 3795x^13 + 2880x^12 - 10863x^11 - 8235x^10 + 23615x^9 + 17010x^8 - 39195x^7 - 24541x^6 + 48816x^5 + 23316x^4 - 40304x^3 - 13104x^2 + 21120x + 1216	\( 2^{31}\cdot 3^{21}\cdot 4129^{6} \)	21T147	Trivial (GRH)
21.7.6293860585415717863922961747811348298858496.1	x^21 + 33x^19 - 22x^18 + 396x^17 - 528x^16 + 2174x^15 - 3996x^14 + 5580x^13 - 8368x^12 + 1944x^11 + 15984x^10 - 38466x^9 + 69768x^8 - 97614x^7 + 98940x^6 - 79704x^5 + 55728x^4 - 31392x^3 + 12096x^2 - 2688x + 256	\( -\,2^{45}\cdot 3^{21}\cdot 61\cdot 809^{6} \)	21T147	Trivial (GRH)
21.19.476572123064963750340948413604798767327870976.1	x^21 - 90x^19 - 48x^18 + 3114x^17 + 2736x^16 - 55436x^15 - 59544x^14 + 556140x^13 + 626528x^12 - 3161016x^11 - 3364128x^10 + 9540856x^9 + 9086400x^8 - 12948624x^7 - 11248992x^6 + 4643712x^5 + 5262720x^4 + 208896x^3 - 734976x^2 - 200448x - 14848	\( -\,2^{38}\cdot 3^{21}\cdot 19\cdot 29^{2}\cdot 37\cdot 809^{6} \)	21T147	Trivial (GRH)
21.7.9349065598444321497834811261162853782096183296.1	x^21 + 42x^19 - 28x^18 + 684x^17 - 912x^16 + 5650x^15 - 10692x^14 + 26487x^13 - 53208x^12 + 70578x^11 - 86124x^10 + 39950x^9 + 136296x^8 - 385146x^7 + 670452x^6 - 918216x^5 + 899856x^4 - 578784x^3 + 229824x^2 - 51072x + 4864	\( -\,2^{45}\cdot 3^{21}\cdot 19^{2}\cdot 251\cdot 809^{6} \)	21T147	Trivial (GRH)
21.19.14820597186060641470356690957661801327808741376.1	x^21 - 63x^19 - 42x^18 + 1629x^17 + 2172x^16 - 21605x^15 - 44658x^14 + 144702x^13 + 458648x^12 - 307962x^11 - 2370636x^10 - 1613130x^9 + 4864824x^8 + 9505014x^7 + 2763308x^6 - 10171656x^5 - 15777936x^4 - 11303904x^3 - 4584384x^2 - 1018752x - 97024	\( -\,2^{45}\cdot 3^{21}\cdot 379^{2}\cdot 809^{6} \)	21T147	Trivial (GRH)
21.11.20999001542048815263956213456361659483283259392.1	x^21 + 21x^19 - 14x^18 - 99x^17 + 132x^16 - 3851x^15 + 7614x^14 - 13905x^13 + 24672x^12 + 86535x^11 - 356466x^10 + 760871x^9 - 1419660x^8 + 1233567x^7 + 1621218x^6 - 5701428x^5 + 7018920x^4 - 4799280x^3 + 1929312x^2 - 428736x + 40832	\( -\,2^{46}\cdot 3^{21}\cdot 11^{2}\cdot 29^{2}\cdot 809^{6} \)	21T147	Trivial (GRH)
21.21.73753831434876210806676646549709111513743097856.1	x^21 - 72x^19 - 48x^18 + 2151x^17 + 2868x^16 - 33496x^15 - 68904x^14 + 272475x^13 + 838888x^12 - 843156x^11 - 5263464x^10 - 2685461x^9 + 14076972x^8 + 24653316x^7 + 2422720x^6 - 37133424x^5 - 53201088x^4 - 37562432x^3 - 15192576x^2 - 3376128x - 321536	\( 2^{45}\cdot 3^{21}\cdot 29\cdot 157^{2}\cdot 809^{6} \)	21T147	Trivial (GRH)
21.21.4264783997834323604464194715279742546743696293888.1	x^21 - 69x^19 - 46x^18 + 1935x^17 + 2580x^16 - 27679x^15 - 57078x^14 + 200736x^13 + 628312x^12 - 497070x^11 - 3496452x^10 - 2158489x^9 + 7974972x^8 + 14886327x^7 + 3180814x^6 - 18527508x^5 - 27676008x^4 - 19694512x^3 - 7977312x^2 - 1772736x - 168832	\( 2^{33}\cdot 3^{21}\cdot 7\cdot 1319^{2}\cdot 3967^{6} \)	21T147	Trivial (GRH)