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 27 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.3.273379262499112817938520460419.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 51x^16 - 901x^15 - 354x^14 + 2589x^13 + 1292x^12 - 4479x^11 - 2667x^10 + 4522x^9 + 3132x^8 - 2424x^7 - 2026x^6 + 438x^5 + 534x^4 - 63x^2 - 15x - 1	\( -\,23^{7}\cdot 113\cdot 710546119470924629 \)	21T162	Trivial (GRH)
21.7.878578378205789250788964411993263.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 58x^16 - 894x^15 - 452x^14 + 2477x^13 + 1803x^12 - 3795x^11 - 3826x^10 + 2581x^9 + 3988x^8 - 3x^7 - 1577x^6 - 413x^5 + 231x^4 + 106x^3 - 5x^2 - 8x - 1	\( -\,11\cdot 23^{7}\cdot 59\cdot 64079789\cdot 6204687157589 \)	21T162	Trivial (GRH)
21.5.933167608477540848840155096819053.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 49x^16 - 903x^15 - 326x^14 + 2621x^13 + 1146x^12 - 4665x^11 - 2317x^10 + 5020x^9 + 2746x^8 - 3078x^7 - 1856x^6 + 916x^5 + 648x^4 - 62x^3 - 89x^2 - 17x - 1	\( 23^{7}\cdot 7013\cdot 101221\cdot 386091589202563 \)	21T162	Trivial (GRH)
21.7.1392812522681068857210837676949039.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 53x^16 - 899x^15 - 382x^14 + 2557x^13 + 1438x^12 - 4286x^11 - 3003x^10 + 3982x^9 + 3413x^8 - 1742x^7 - 1959x^6 + 181x^5 + 487x^4 + 54x^3 - 44x^2 - 13x - 1	\( -\,23^{7}\cdot 709\cdot 743\cdot 681493\cdot 1139465977607 \)	21T162	Trivial (GRH)
21.5.11499163537178564173557477003259625.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 52x^16 - 900x^15 - 368x^14 + 2573x^13 + 1365x^12 - 4381x^11 - 2832x^10 + 4243x^9 + 3250x^8 - 2077x^7 - 1933x^6 + 383x^5 + 551x^4 + 34x^3 - 55x^2 - 14x - 1	\( 5^{3}\cdot 31^{7}\cdot 3343677482854966554307 \)	21T162	Trivial (GRH)
21.3.31914857731384305486967984384473527.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 58x^16 - 894x^15 - 452x^14 + 2477x^13 + 1803x^12 - 3795x^11 - 3826x^10 + 2581x^9 + 3988x^8 - 3x^7 - 1575x^6 - 407x^5 + 237x^4 + 108x^3 - 5x^2 - 8x - 1	\( -\,31^{7}\cdot 167\cdot 16447\cdot 422335795817826193 \)	21T162	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)
21.19.102724782506109615033478690865109188608.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 52x^16 - 900x^15 - 368x^14 + 2573x^13 + 1365x^12 - 4384x^11 - 2838x^10 + 4261x^9 + 3295x^8 - 2089x^7 - 2019x^6 + 335x^5 + 569x^4 + 53x^3 - 52x^2 - 14x - 1	\( -\,2^{14}\cdot 37^{7}\cdot 66045498523363396992439 \)	21T162	Trivial (GRH)
21.11.145147030291169283887309482380107366400.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 56x^16 - 896x^15 - 424x^14 + 2509x^13 + 1657x^12 - 4006x^11 - 3526x^10 + 3229x^9 + 3977x^8 - 757x^7 - 2159x^6 - 441x^5 + 389x^4 + 167x^3 - 6x^2 - 10x - 1	\( -\,2^{14}\cdot 3^{3}\cdot 5^{2}\cdot 37^{7}\cdot 138252302841813371149 \)	21T162	Trivial (GRH)
21.1.264940694864400738400104636932918870016.1	x^21 - 12x^14 - 49x^9 - 126x^8 + 36x^7 - 343x^3 + 252x - 216	\( 2^{18}\cdot 3^{12}\cdot 7^{21}\cdot 23^{7} \)	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)
21.17.1859129620558936360977052492338516111661.1	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)
21.15.3481801648751785241682752893736008859648.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 46x^16 - 906x^15 - 284x^14 + 2669x^13 + 927x^12 - 4946x^11 - 1796x^10 + 5779x^9 + 2197x^8 - 4067x^7 - 1691x^6 + 1503x^5 + 733x^4 - 175x^3 - 126x^2 - 20x - 1	\( -\,2^{14}\cdot 37^{7}\cdot 349\cdot 10765241\cdot 595830643430851 \)	21T162	Trivial (GRH)
21.15.4805855121304884104682343436580598366208.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 58x^16 - 894x^15 - 452x^14 + 2477x^13 + 1803x^12 - 3798x^11 - 3832x^10 + 2599x^9 + 4033x^8 - 15x^7 - 1667x^6 - 473x^5 + 237x^4 + 121x^3 - 2x^2 - 8x - 1	\( -\,2^{14}\cdot 37^{7}\cdot 3089859034734508131528239 \)	21T162	Trivial (GRH)
21.13.21658684236689624719937096086082755356533.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 57x^16 - 895x^15 - 438x^14 + 2493x^13 + 1730x^12 - 3910x^11 - 3695x^10 + 2962x^9 + 4125x^8 - 418x^7 - 2147x^6 - 599x^5 + 347x^4 + 190x^3 + 4x^2 - 9x - 1	\( 229^{7}\cdot 92077\cdot 82827653\cdot 85991827177 \)	21T162	Trivial (GRH)
21.11.21976304547105974485649436224048259658411.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 45x^16 - 907x^15 - 270x^14 + 2685x^13 + 854x^12 - 5050x^11 - 1643x^10 + 6094x^9 + 2169x^8 - 4438x^7 - 1895x^6 + 1645x^5 + 935x^4 - 110x^3 - 128x^2 - 21x - 1	\( -\,53\cdot 229^{7}\cdot 12555396112941725258843 \)	21T162	Trivial (GRH)
21.13.30442588627548161668838591975407708094464.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 44x^16 - 908x^15 - 256x^14 + 2701x^13 + 781x^12 - 5138x^11 - 1458x^10 + 6313x^9 + 1901x^8 - 4745x^7 - 1695x^6 + 1879x^5 + 877x^4 - 201x^3 - 146x^2 - 22x - 1	\( 2^{14}\cdot 37^{7}\cdot 113\cdot 8273\cdot 385537\cdot 54305277821449 \)	21T162	Trivial (GRH)
21.13.70218440916863154295349403985322359078912.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 50x^16 - 902x^15 - 340x^14 + 2605x^13 + 1219x^12 - 4584x^11 - 2516x^10 + 4843x^9 + 3119x^8 - 2799x^7 - 2259x^6 + 563x^5 + 741x^4 + 71x^3 - 64x^2 - 16x - 1	\( 2^{14}\cdot 37^{7}\cdot 3637897767851\cdot 12409911498371 \)	21T162	Trivial (GRH)
21.9.945176990061050853553422483248682925113344.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 45x^16 - 907x^15 - 270x^14 + 2685x^13 + 854x^12 - 5064x^11 - 1671x^10 + 6178x^9 + 2379x^8 - 4494x^7 - 2265x^6 + 1515x^5 + 1113x^4 + 10x^3 - 114x^2 - 21x - 1	\( 2^{14}\cdot 17^{2}\cdot 37^{7}\cdot 43\cdot 67\cdot 89\cdot 139\cdot 58997719491683443 \)	21T162	Trivial (GRH)
21.1.965708832780740691468381401620489281208320.1	x^21 + 14x^15 - 12x^14 + 49x^9 - 84x^8 + 36x^7 + 343x^3 - 882x^2 + 756x - 216	\( 2^{18}\cdot 3^{18}\cdot 5\cdot 7^{21}\cdot 23^{7} \)	21T162	Trivial (GRH)
21.3.1058356817313571731164941409972240999941668864.1	x^21 + 35x^15 - 30x^14 + 196x^9 - 336x^8 + 144x^7 - 343x^3 + 882x^2 - 756x + 216	\( -\,2^{18}\cdot 3^{14}\cdot 7^{19}\cdot 257^{7} \)	21T162	Trivial (GRH)
21.3.1210279916577068953435441844027700814188380160.1	x^21 + 35x^15 - 30x^14 + 245x^9 - 420x^8 + 180x^7 - 343x^3 + 882x^2 - 756x + 216	\( -\,2^{33}\cdot 3^{12}\cdot 5\cdot 7^{21}\cdot 37^{7} \)	21T162	Trivial (GRH)
21.9.2060977840404216682757858217498617316303388672.1	x^21 - 21x^19 - 3x^18 + 186x^17 + 37x^16 - 915x^15 - 158x^14 + 2813x^13 + 270x^12 - 5744x^11 - 143x^10 + 7786x^9 - 125x^8 - 6854x^7 - 29x^6 + 3615x^5 + 349x^4 - 922x^3 - 282x^2 - 29x - 1	\( 2^{14}\cdot 37^{7}\cdot 5743\cdot 1508471\cdot 152955653138364850217 \)	21T162	Trivial (GRH)
21.7.5514337869904270419090231901851211834645807104.1	x^21 - 77x^15 - 66x^14 + 1323x^9 + 2268x^8 + 972x^7 - 343x^3 - 882x^2 - 756x - 216	\( -\,2^{28}\cdot 3^{18}\cdot 7^{21}\cdot 37^{7} \)	21T162	Trivial (GRH)
21.5.41117071763962069755227219080867949870560837632.1	x^21 - 21x^15 - 18x^14 - 49x^9 - 84x^8 - 36x^7 + 686x^3 + 1764x^2 + 1512x + 432	\( 2^{22}\cdot 3^{12}\cdot 7^{21}\cdot 229^{7} \)	21T162	Trivial (GRH)
21.5.176458811836936653410887420859238778708665827328.1	x^21 - 7x^15 - 6x^14 - 147x^9 - 252x^8 - 108x^7 + 343x^3 + 882x^2 + 756x + 216	\( 2^{33}\cdot 3^{18}\cdot 7^{21}\cdot 37^{7} \)	21T162	Trivial (GRH)
21.7.374974975153490388498135769325882404755914883072.1	x^21 - 56x^15 - 48x^14 + 392x^9 + 672x^8 + 288x^7 + 5488x^3 + 14112x^2 + 12096x + 3456	\( -\,2^{30}\cdot 3^{18}\cdot 7^{21}\cdot 17\cdot 37^{7} \)	21T162	Trivial (GRH)