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 29 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.17.38289048631639269472806869479351853.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 55x^16 - 897x^15 - 410x^14 + 2525x^13 + 1584x^12 - 4093x^11 - 3339x^10 + 3442x^9 + 3694x^8 - 1060x^7 - 1902x^6 - 106x^5 + 410x^4 + 98x^3 - 25x^2 - 11x - 1	\( 7^{14}\cdot 13\cdot 97\cdot 8914877\cdot 5021940620101 \)	21T159	Trivial (GRH)
21.17.295273090543420857732075123373712153.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 46x^16 - 906x^15 - 284x^14 + 2669x^13 + 927x^12 - 4945x^11 - 1794x^10 + 5773x^9 + 2182x^8 - 4063x^7 - 1665x^6 + 1511x^5 + 719x^4 - 184x^3 - 127x^2 - 20x - 1	\( 7^{14}\cdot 27427\cdot 15873511208841403811 \)	21T159	Trivial (GRH)
21.17.380273806833409289291563492222717957.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 49x^16 - 903x^15 - 326x^14 + 2621x^13 + 1146x^12 - 4667x^11 - 2321x^10 + 5032x^9 + 2776x^8 - 3086x^7 - 1910x^6 + 894x^5 + 670x^4 - 46x^3 - 87x^2 - 17x - 1	\( 7^{14}\cdot 757\cdot 1373\cdot 537599\cdot 1003457499787 \)	21T159	Trivial (GRH)
21.17.1398884674421463279959586376937816064.1	x^21 - 18x^19 - 16x^18 + 36x^17 + 300x^16 + 1080x^15 - 990x^14 - 9240x^13 - 8424x^12 + 32616x^11 + 61062x^10 - 62433x^9 - 127386x^8 + 78735x^7 + 98312x^6 - 51048x^5 - 27456x^4 + 14400x^3 + 1728x^2 - 1344x + 128	\( 2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 283583^{3} \)	21T152	Trivial (GRH)
21.17.12467389482269010020495422048363303168.1	x^21 - 3x^20 - 17x^19 + 52x^18 + 120x^17 - 368x^16 - 466x^15 + 1380x^14 + 1119x^13 - 2978x^12 - 1768x^11 + 3759x^10 + 1869x^9 - 2699x^8 - 1272x^7 + 1022x^6 + 510x^5 - 168x^4 - 104x^3 + 4x^2 + 8x + 1	\( 2^{8}\cdot 1009\cdot 81515745041\cdot 592110678165795251537 \)	21T164	Trivial (GRH)
21.17.14830935213726926366667234918428262400.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 55x^16 - 897x^15 - 410x^14 + 2525x^13 + 1584x^12 - 4094x^11 - 3341x^10 + 3448x^9 + 3709x^8 - 1064x^7 - 1931x^6 - 123x^5 + 415x^4 + 104x^3 - 24x^2 - 11x - 1	\( 2^{14}\cdot 5^{2}\cdot 37^{7}\cdot 381413904556105579993 \)	21T162	Trivial (GRH)
21.17.693779639215282549858830138256037368621.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 54x^16 - 898x^15 - 396x^14 + 2541x^13 + 1511x^12 - 4192x^11 - 3176x^10 + 3727x^9 + 3591x^8 - 1411x^7 - 1998x^6 + 10x^5 + 476x^4 + 96x^3 - 32x^2 - 12x - 1	\( 229^{7}\cdot 45112649\cdot 465666337416281 \)	21T162	Trivial (GRH)
21.17.740009992768954075098621193400104697856.1	x^21 - 24x^19 - 16x^18 + 117x^17 + 156x^16 + 889x^15 + 1674x^14 - 8037x^13 - 24160x^12 + 135x^11 + 70962x^10 + 105085x^9 + 63972x^8 - 40641x^7 - 244466x^6 - 475956x^5 - 523368x^4 - 347952x^3 - 139104x^2 - 30912x - 2944	\( 2^{14}\cdot 3^{21}\cdot 23^{2}\cdot 71^{3}\cdot 283583^{3} \)	21T152	Trivial (GRH)
21.17.1859129620558936360977052492338516111661.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 51x^16 - 901x^15 - 354x^14 + 2589x^13 + 1292x^12 - 4480x^11 - 2669x^10 + 4528x^9 + 3147x^8 - 2428x^7 - 2028x^6 + 502x^5 + 620x^4 + 33x^3 - 62x^2 - 15x - 1	\( 67\cdot 229^{7}\cdot 4447\cdot 13291\cdot 2106919\cdot 6747049 \)	21T162	Trivial (GRH)
21.17.2725960527801648753674435845823096440269.1	x^21 - 2x^20 - 19x^19 + 34x^18 + 151x^17 - 233x^16 - 653x^15 + 831x^14 + 1676x^13 - 1665x^12 - 2626x^11 + 1895x^10 + 2517x^9 - 1184x^8 - 1458x^7 + 363x^6 + 489x^5 - 33x^4 - 86x^3 - 6x^2 + 6x + 1	\( 3\cdot 683\cdot 1240271\cdot 39356833\cdot 49784320121\cdot 547454828827 \)	21T164	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)
21.17.14307892596199922141986753461020931391488.1	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)
21.17.15148388514038533069337142710227794542592.1	x^21 - 48x^19 - 32x^18 + 927x^17 + 1236x^16 - 8795x^15 - 18414x^14 + 37539x^13 + 130112x^12 - 10044x^11 - 417240x^10 - 431286x^9 + 352296x^8 + 1057599x^7 + 691446x^6 - 303156x^5 - 822024x^4 - 633136x^3 - 260064x^2 - 57792x - 5504	\( 2^{14}\cdot 3^{25}\cdot 43^{2}\cdot 8388019^{3} \)	21T149	Trivial (GRH)
21.17.43978192433421249509929797067247084063789.1	x^21 - 8x^20 - x^19 + 83x^18 + 31x^17 - 219x^16 - 433x^15 - 960x^14 - 206x^13 + 2604x^12 + 2808x^11 + 2203x^10 + 1933x^9 - 7087x^8 - 12004x^7 + 1523x^6 + 9926x^5 + 2591x^4 - 2172x^3 - 923x^2 - 78x - 1	\( 29^{18}\cdot 389\cdot 463^{2}\cdot 1583^{2} \)	21T123	Trivial (GRH)
21.17.330985239322495312738299332696447755321344.1	x^21 - 48x^19 - 32x^18 + 909x^17 + 1212x^16 - 8209x^15 - 17226x^14 + 31284x^13 + 111496x^12 + 7614x^11 - 304092x^10 - 350139x^9 + 142452x^8 + 622908x^7 + 500928x^6 + 12528x^5 - 272448x^4 - 231872x^3 - 96768x^2 - 21504x - 2048	\( 2^{15}\cdot 3^{21}\cdot 149^{6}\cdot 211^{6} \)	21T151	Trivial (GRH)
21.17.780359536423698568398593575601369133108096.1	x^21 - 21x^19 - 41x^18 + 189x^17 + 738x^16 - 1010x^15 - 5535x^14 + 3810x^13 + 22384x^12 - 10953x^11 - 52743x^10 + 23361x^9 + 72954x^8 - 34884x^7 - 55577x^6 + 34911x^5 + 15780x^4 - 18860x^3 + 5976x^2 - 768x + 32	\( 2^{7}\cdot 3^{21}\cdot 2029^{9} \)	21T131	Trivial (GRH)
21.17.1028917447801689921253623397415199700942848.1	x^21 - 42x^19 - 28x^18 + 684x^17 + 912x^16 - 5150x^15 - 10908x^14 + 14760x^13 + 57136x^12 + 17442x^11 - 111588x^10 - 154462x^9 - 23256x^8 + 128814x^7 + 161852x^6 + 114264x^5 + 64944x^4 + 32416x^3 + 12096x^2 + 2688x + 256	\( 2^{32}\cdot 3^{21}\cdot 73^{12} \)	21T137	Trivial (GRH)
21.17.1437253422311392754840506463696646924091392.1	x^21 - 48x^19 - 32x^18 + 909x^17 + 1212x^16 - 8236x^15 - 17280x^14 + 31653x^13 + 112568x^12 + 8208x^11 - 305232x^10 - 359509x^9 + 111852x^8 + 580389x^7 + 488282x^6 + 52164x^5 - 210168x^4 - 187152x^3 - 78624x^2 - 17472x - 1664	\( 2^{14}\cdot 3^{21}\cdot 7\cdot 13^{2}\cdot 577^{9} \)	21T131	Trivial (GRH)
21.17.29714264728113325207242631362078816000000000.1	x^21 - 42x^19 - 28x^18 + 639x^17 + 852x^16 - 3955x^15 - 8478x^14 + 5445x^13 + 28336x^12 + 28863x^11 + 10722x^10 - 26563x^9 - 104220x^8 - 181755x^7 - 202326x^6 - 177660x^5 - 133560x^4 - 77840x^3 - 30240x^2 - 6720x - 640	\( 2^{14}\cdot 3^{21}\cdot 5^{9}\cdot 6679^{6} \)	21T151	Trivial (GRH)
21.17.51445872390084496062681169870759985047142400.1	x^21 - 63x^19 - 42x^18 + 1413x^17 + 1884x^16 - 12359x^15 - 25974x^14 + 15327x^13 + 83200x^12 + 223371x^11 + 493098x^10 + 63391x^9 - 1791828x^8 - 3514005x^7 - 3183978x^6 - 1524420x^5 - 320328x^4 + 27408x^3 + 30240x^2 + 6720x + 640	\( 2^{33}\cdot 3^{21}\cdot 5^{2}\cdot 73^{12} \)	21T137	Trivial (GRH)
21.17.1030734672607869933507362803637337302271442944.1	x^21 - 45x^19 - 30x^18 + 756x^17 + 1008x^16 - 5415x^15 - 11502x^14 + 9504x^13 + 44088x^12 + 54054x^11 + 47892x^10 - 77257x^9 - 444996x^8 - 684633x^7 - 275986x^6 + 489132x^5 + 837144x^4 + 609616x^3 + 247968x^2 + 55104x + 5248	\( 2^{14}\cdot 3^{21}\cdot 17\cdot 29^{18}\cdot 41^{2} \)	21T123	Trivial (GRH)
21.17.22434675424853910351209350075254473907901710336.1	x^21 - 30x^19 - 20x^18 + 261x^17 + 348x^16 + 386x^15 + 540x^14 - 14058x^13 - 38368x^12 + 21573x^11 + 182982x^10 + 238397x^9 + 75780x^8 - 257349x^7 - 827098x^6 - 1443204x^5 - 1539720x^4 - 1015280x^3 - 405216x^2 - 90048x - 8576	\( 2^{14}\cdot 3^{40}\cdot 29^{6}\cdot 59^{6}\cdot 67^{2} \)	21T148	Trivial (GRH)
21.17.190320484737840382843602696822539522453290057728.1	x^21 - 45x^19 - 30x^18 + 756x^17 + 1008x^16 - 5361x^15 - 11394x^14 + 9009x^13 + 42592x^12 + 48168x^11 + 32640x^10 - 38489x^9 - 224676x^8 - 426999x^7 - 522910x^6 - 521964x^5 - 432216x^4 - 262224x^3 - 102816x^2 - 22848x - 2176	\( 2^{15}\cdot 3^{21}\cdot 7^{12}\cdot 17^{2}\cdot 173^{9} \)	21T142	Trivial (GRH)
21.17.210302543645345736468562461003484609741021790208.1	x^21 - 93x^19 - 62x^18 + 3186x^17 + 4248x^16 - 45699x^15 - 94230x^14 + 151668x^13 + 558008x^12 + 1909683x^11 + 4713258x^10 - 6558322x^9 - 46220760x^8 - 64186983x^7 + 10446906x^6 + 132062292x^5 + 178126920x^4 + 124258480x^3 + 50143968x^2 + 11143104x + 1061248	\( 2^{14}\cdot 3^{28}\cdot 71^{3}\cdot 8291^{2}\cdot 283583^{3} \)	21T149	Trivial (GRH)
21.17.889138920626346923563285121178114921239572119552.1	x^21 - 21x^19 - 63x^18 + 189x^17 + 1134x^16 - 825x^15 - 8505x^14 + 1035x^13 + 34584x^12 + 5697x^11 - 83313x^10 - 29457x^9 + 122310x^8 + 65853x^7 - 104151x^6 - 87480x^5 + 29556x^4 + 56976x^3 + 24192x^2 + 4032x + 192	\( 2^{33}\cdot 3^{39}\cdot 13^{15}\cdot 499 \)	21T142	Trivial (GRH)
21.17.1368454290663395665925056058246076672368720216064.1	x^21 - 48x^19 - 32x^18 + 891x^17 + 1188x^16 - 7596x^15 - 15984x^14 + 24498x^13 + 91376x^12 + 26676x^11 - 181896x^10 - 255415x^9 - 55836x^8 + 176274x^7 + 223260x^6 + 146664x^5 + 73584x^4 + 33376x^3 + 12096x^2 + 2688x + 256	\( 2^{41}\cdot 3^{40}\cdot 13^{15} \)	21T133	Trivial (GRH)
21.17.10322551559300386187871072331953642204421617893376.1	x^21 - 48x^19 - 32x^18 + 846x^17 + 1128x^16 - 5726x^15 - 12204x^14 - 3924x^13 + 9424x^12 + 186678x^11 + 589812x^10 - 71609x^9 - 2888964x^8 - 4329267x^7 + 474058x^6 + 8477028x^5 + 11551176x^4 + 8074864x^3 + 3259872x^2 + 724416x + 68992	\( 2^{14}\cdot 3^{22}\cdot 7^{4}\cdot 11^{2}\cdot 1601^{9} \)	21T122	Trivial (GRH)
21.17.437180092667948699568301352361682597084807166951424.1	x^21 - 48x^19 - 32x^18 + 846x^17 + 1128x^16 - 6536x^15 - 13824x^14 + 16542x^13 + 66640x^12 + 42444x^11 - 56952x^10 - 180078x^9 - 351864x^8 - 355914x^7 + 182412x^6 + 980856x^5 + 1261296x^4 + 870944x^3 + 350784x^2 + 77952x + 7424	\( 2^{32}\cdot 3^{22}\cdot 29^{2}\cdot 199^{12} \)	21T127	Trivial (GRH)
21.17.4975666366370275989555247135363664150377068540985344.1	x^21 - 84x^19 - 56x^18 + 2376x^17 + 3168x^16 - 22002x^15 - 46116x^14 - 63144x^13 - 93232x^12 + 1201014x^11 + 4252980x^10 + 3168314x^9 - 6373944x^8 - 22213458x^7 - 45277188x^6 - 68252328x^5 - 69462864x^4 - 45190496x^3 - 17986752x^2 - 3997056x - 380672	\( 2^{32}\cdot 3^{28}\cdot 73^{12}\cdot 1487^{2} \)	21T127	Trivial (GRH)