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 17 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.19.20096043902376756274484831980765619159040.1	x^21 - 21x^19 - 48x^18 + 189x^17 + 864x^16 - 793x^15 - 6480x^14 + 555x^13 + 25912x^12 + 8577x^11 - 58224x^10 - 36449x^9 + 69552x^8 + 63981x^7 - 33392x^6 - 50760x^5 - 5064x^4 + 13440x^3 + 6624x^2 + 1152x + 64	\( -\,2^{24}\cdot 3^{21}\cdot 5\cdot 73^{12} \)	21T137	Trivial (GRH)
21.13.960590898533608949920374968680596595802112.1	x^21 - 21x^19 - 20x^18 + 189x^17 + 360x^16 - 801x^15 - 2700x^14 + 675x^13 + 10344x^12 + 7857x^11 - 18828x^10 - 33233x^9 + 4536x^8 + 51237x^7 + 34828x^6 - 20304x^5 - 37896x^4 - 15392x^3 + 1440x^2 + 2112x + 320	\( 2^{24}\cdot 3^{21}\cdot 73^{12}\cdot 239 \)	21T137	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)
21.15.1270069974630210996547441381184387130851328.1	x^21 - 21x^19 - 4x^18 + 189x^17 + 72x^16 - 1001x^15 - 540x^14 + 3675x^13 + 2512x^12 - 10143x^11 - 9084x^10 + 19679x^9 + 24840x^8 - 19971x^7 - 40932x^6 - 1080x^5 + 28512x^4 + 15200x^3 - 1536x - 256	\( -\,2^{26}\cdot 3^{21}\cdot 73^{12}\cdot 79 \)	21T137	Trivial (GRH)
21.13.2057834895603379842507246794830399401885696.1	x^21 - 21x^19 - 14x^18 + 117x^17 + 156x^16 + 133x^15 + 162x^14 - 1593x^13 - 4512x^12 - 3321x^11 + 2034x^10 + 8709x^9 + 18180x^8 + 23313x^7 + 11554x^6 - 9612x^5 - 19800x^4 - 14800x^3 - 6048x^2 - 1344x - 128	\( 2^{33}\cdot 3^{21}\cdot 73^{12} \)	21T137	Trivial (GRH)
21.11.5144587239008449606268116987075998504714240.1	x^21 - 72x^17 - 96x^16 - 86x^15 - 108x^14 + 1224x^13 + 3440x^12 + 4914x^11 + 6396x^10 + 2362x^9 - 13176x^8 - 32094x^7 - 46140x^6 - 53784x^5 - 48816x^4 - 30624x^3 - 12096x^2 - 2688x - 256	\( -\,2^{32}\cdot 3^{21}\cdot 5\cdot 73^{12} \)	21T137	Trivial (GRH)
21.15.37882475204146041371729236303551933137891328.1	x^21 - 21x^19 - 17x^18 + 189x^17 + 306x^16 - 1007x^15 - 2295x^14 + 3765x^13 + 9292x^12 - 10683x^11 - 21999x^10 + 22299x^9 + 30834x^8 - 31401x^7 - 24457x^6 + 27378x^5 + 8880x^4 - 13080x^3 + 288x^2 + 2304x - 512	\( -\,2^{12}\cdot 3^{21}\cdot 313^{12} \)	21T137	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)
21.11.139466544682494688544924733946513396963737600.1	x^21 + 12x^19 - 60x^18 - 288x^17 - 840x^16 - 3726x^15 + 594x^14 + 366x^13 + 17192x^12 + 75906x^11 - 86412x^10 + 32126x^9 + 10296x^8 - 447726x^7 + 531832x^6 - 214920x^5 + 43176x^4 - 2352x^3 - 5760x^2 + 1440x + 160	\( -\,2^{26}\cdot 3^{21}\cdot 5^{2}\cdot 73^{12}\cdot 347 \)	21T137	Trivial (GRH)
21.7.370406424218316848968019199412507790681604096.1	x^21 - 21x^19 + 189x^17 - 1253x^15 + 7455x^13 - 2856x^12 - 32823x^11 + 34272x^10 + 80055x^9 - 154224x^8 - 53055x^7 + 311072x^6 - 146772x^5 - 247080x^4 + 270064x^3 + 23616x^2 - 145344x + 58752	\( -\,2^{15}\cdot 3^{19}\cdot 11\cdot 313^{12} \)	21T137	Trivial (GRH)
21.9.565904596290929456689492868578359835518566400.1	x^21 + 21x^19 - 14x^18 + 117x^17 - 156x^16 - 137x^15 + 378x^14 - 3249x^13 + 8048x^12 - 12123x^11 + 17322x^10 - 9475x^9 - 25668x^8 + 70035x^7 - 106646x^6 + 130140x^5 - 120888x^4 + 76432x^3 - 30240x^2 + 6720x - 640	\( 2^{33}\cdot 3^{21}\cdot 5^{2}\cdot 11\cdot 73^{12} \)	21T137	Trivial (GRH)
21.7.1336905397440735612565123035386017427050463232.1	x^21 + 84x^19 - 56x^18 + 2736x^17 - 3648x^16 + 43984x^15 - 85536x^14 + 368064x^13 - 842112x^12 + 1498176x^11 - 2597760x^10 + 887424x^9 + 6603264x^8 - 19805952x^7 + 41370112x^6 - 63839232x^5 + 65562624x^4 - 42766336x^3 + 17031168x^2 - 3784704x + 360448	\( -\,2^{24}\cdot 3^{21}\cdot 11^{2}\cdot 73^{12}\cdot 2749 \)	21T137	Trivial (GRH)
21.9.8260747249204096146622706591443293419881427712.1	x^21 - 21x^19 - 7x^18 + 189x^17 + 126x^16 - 1001x^15 - 945x^14 + 3675x^13 + 4487x^12 - 10143x^11 - 16989x^10 + 17547x^9 + 48384x^8 - 783x^7 - 77111x^6 - 58644x^5 + 31179x^4 + 69828x^3 + 39132x^2 + 7272x - 352	\( 2^{8}\cdot 3^{22}\cdot 313^{12}\cdot 1163 \)	21T137	Trivial (GRH)
21.19.460953958284049031411201347341619922421861679104.1	x^21 - 45x^19 - 30x^18 + 729x^17 + 972x^16 - 4266x^15 - 9180x^14 - 6687x^13 - 2872x^12 + 131652x^11 + 443208x^10 + 46436x^9 - 1786608x^8 - 2821416x^7 - 29552x^6 + 4752864x^5 + 6645312x^4 + 4669568x^3 + 1886976x^2 + 419328x + 39936	\( -\,2^{15}\cdot 3^{23}\cdot 13^{2}\cdot 313^{12} \)	21T137	Trivial (GRH)
21.15.2435730551244745508335671328116066872049480499200.1	x^21 - 42x^19 - 28x^18 + 108x^17 + 144x^16 + 10470x^15 + 20844x^14 - 34056x^13 - 124784x^12 - 741690x^11 - 2102892x^10 - 1453054x^9 + 3319272x^8 + 10472130x^7 + 19267908x^6 + 27279720x^5 + 27096912x^4 + 17500768x^3 + 6955200x^2 + 1545600x + 147200	\( -\,2^{32}\cdot 3^{21}\cdot 5^{2}\cdot 23^{2}\cdot 73^{12}\cdot 179 \)	21T137	Trivial (GRH)
21.21.18960041871195105474676737728264432549221525094400.1	x^21 - 84x^19 - 56x^18 + 2952x^17 + 3936x^16 - 54902x^15 - 112428x^14 + 551016x^13 + 1652592x^12 - 2403918x^11 - 12835332x^10 - 3648630x^9 + 45254088x^8 + 70497930x^7 - 13693484x^6 - 153698040x^5 - 206631792x^4 - 144045088x^3 - 58121280x^2 - 12915840x - 1230080	\( 2^{32}\cdot 3^{21}\cdot 5^{2}\cdot 13\cdot 31^{2}\cdot 59\cdot 73^{12} \)	21T137	Trivial (GRH)
21.21.32494270821316278152580568528050655148435682172600320.1	x^21 - 105x^19 - 70x^18 + 4653x^17 + 6204x^16 - 110711x^15 - 225558x^14 + 1464039x^13 + 4271680x^12 - 9341541x^11 - 43575414x^10 + 2732237x^9 + 211825764x^8 + 284052741x^7 - 201624790x^6 - 960233724x^5 - 1224718776x^4 - 844162064x^3 - 339879456x^2 - 75528768x - 7193216	\( 2^{33}\cdot 3^{21}\cdot 5\cdot 73^{12}\cdot 56197^{2} \)	21T137	Trivial (GRH)