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 148)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.4042635603271291778125.1	x^20 - 6x^19 + 21x^18 - 55x^17 + 119x^16 - 231x^15 + 429x^14 - 767x^13 + 1287x^12 - 1952x^11 + 2604x^10 - 3005x^9 + 2972x^8 - 2497x^7 + 1763x^6 - 1031x^5 + 490x^4 - 184x^3 + 52x^2 - 10x + 1	\( 5^{5}\cdot 11^{2}\cdot 47^{8}\cdot 449 \)	20T905	Trivial
20.2.4078772064323626845184.1	x^20 - x^18 - 2x^16 + 3x^14 - 3x^12 + x^10 + 5x^8 - 5x^6 + 3x^2 - 1	\( -\,2^{10}\cdot 47^{8}\cdot 409^{2} \)	20T905	Trivial
20.0.4447536889383439569920.1	x^20 + x^18 + 5x^16 + 6x^14 + 7x^12 + 21x^10 + 34x^8 + 37x^6 + 32x^4 + 18x^2 + 5	\( 2^{10}\cdot 5\cdot 47^{8}\cdot 191^{2} \)	20T905	Trivial
20.0.13931879556172069248581.1	x^20 - 3x^19 + 5x^18 - 7x^17 + 6x^16 + x^15 + 7x^14 - 2x^13 + 19x^12 - 36x^11 + 29x^10 - 36x^9 + 19x^8 - 2x^7 + 7x^6 + x^5 + 6x^4 - 7x^3 + 5x^2 - 3x + 1	\( 11^{3}\cdot 47^{10}\cdot 199 \)	20T905	Trivial
20.2.23656760935840835814400.1	x^20 + 5x^18 + 12x^16 + 18x^14 + 19x^12 + 15x^10 + 9x^8 + 4x^6 + x^4 - 1	\( -\,2^{10}\cdot 5^{2}\cdot 47^{8}\cdot 197^{2} \)	20T905	Trivial (GRH)
20.4.42686966776427487214592.1	x^20 - 4x^19 + 2x^18 + 21x^17 - 48x^16 + 5x^15 + 125x^14 - 178x^13 + 7x^12 + 238x^11 - 285x^10 + 121x^9 + 78x^8 - 175x^7 + 153x^6 - 100x^5 + 62x^4 - 29x^3 + 10x^2 - 4x + 1	\( 2^{10}\cdot 47^{9}\cdot 193^{2} \)	20T905	Trivial (GRH)
20.0.42686966776427487214592.1	x^20 - 5x^19 + 16x^18 - 33x^17 + 49x^16 - 55x^15 + 67x^14 - 124x^13 + 225x^12 - 279x^11 + 176x^10 + 62x^9 - 264x^8 + 294x^7 - 161x^6 - 9x^5 + 95x^4 - 85x^3 + 39x^2 - 9x + 1	\( 2^{10}\cdot 47^{9}\cdot 193^{2} \)	20T905	Trivial (GRH)
20.4.135802362058317231106057.1	x^20 - 10x^19 + 53x^18 - 192x^17 + 522x^16 - 1116x^15 + 1920x^14 - 2682x^13 + 3029x^12 - 2704x^11 + 1787x^10 - 680x^9 - 166x^8 + 538x^7 - 523x^6 + 343x^5 - 172x^4 + 69x^3 - 24x^2 + 7x - 1	\( 47^{8}\cdot 269^{3}\cdot 293 \)	20T905	Trivial (GRH)
20.2.197857619840087113364571136.1	x^20 - x^18 - 4x^16 - 15x^14 + 64x^12 - 44x^10 - 4x^8 - 12x^6 - 26x^4 - 9x^2 - 1	\( -\,2^{10}\cdot 17^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.2.362168446004865338996048896.1	x^20 + 14x^18 + 81x^16 + 233x^14 + 320x^12 + 159x^10 - 18x^8 - 25x^6 - 19x^4 + 2x^2 - 1	\( -\,2^{10}\cdot 23^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.2.362168446004865338996048896.2	x^20 + 7x^18 + 16x^16 + 10x^14 - 28x^12 - 86x^10 - 62x^8 - 31x^6 - 50x^4 - 23x^2 - 1	\( -\,2^{10}\cdot 23^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.6.2224357809205685229486130176.1	x^20 + 11x^18 + 48x^16 + 74x^14 - 104x^12 - 450x^10 - 211x^8 + 473x^6 + 200x^4 - 4x^2 - 1	\( -\,2^{10}\cdot 3^{2}\cdot 19^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.6.2224357809205685229486130176.2	x^20 + 5x^18 + 20x^16 + 50x^14 - 44x^12 - 286x^10 - 121x^8 + 283x^6 + 266x^4 + 70x^2 - 1	\( -\,2^{10}\cdot 3^{2}\cdot 19^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.10.4766727535631841356595299203.1	x^20 - 10x^19 + 38x^18 - 57x^17 - 26x^16 + 208x^15 - 231x^14 - 85x^13 + 404x^12 - 253x^11 - 216x^10 + 381x^9 - 80x^8 - 219x^7 + 189x^6 - x^5 - 76x^4 + 38x^3 + x^2 - 6x + 1	\( -\,13^{2}\cdot 401^{8}\cdot 42187 \)	20T905	Trivial (GRH)
20.6.6309535724727483864248745984.1	x^20 - 2x^18 - 13x^16 - 6x^14 + 60x^12 + 105x^10 + 25x^8 - 64x^6 - 30x^4 + 6x^2 - 1	\( -\,2^{20}\cdot 3^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.6.6309535724727483864248745984.2	x^20 - 11x^18 + 54x^16 - 156x^14 + 292x^12 - 365x^10 + 299x^8 - 146x^6 + 29x^4 + 5x^2 - 1	\( -\,2^{20}\cdot 3^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.4.6673073427617055688458390528.1	x^20 + 7x^18 + 18x^16 + 17x^14 - 12x^12 - 44x^10 - 38x^8 - 2x^6 + 22x^4 + 15x^2 + 3	\( 2^{10}\cdot 3^{3}\cdot 19^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.0.8329874258111902796909124608.1	x^20 - 8x^19 + 40x^18 - 152x^17 + 481x^16 - 1306x^15 + 3034x^14 - 5982x^13 + 9933x^12 - 13864x^11 + 16300x^10 - 16242x^9 + 13886x^8 - 10360x^7 + 6900x^6 - 4154x^5 + 2231x^4 - 1010x^3 + 350x^2 - 78x + 9	\( 2^{10}\cdot 23^{3}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.0.10353635933708087942603492352.1	x^20 + 17x^18 + 106x^16 + 324x^14 + 547x^12 + 563x^10 + 423x^8 + 276x^6 + 133x^4 + 34x^2 + 3	\( 2^{10}\cdot 3\cdot 71^{2}\cdot 401^{8} \)	20T905	$[2]$ (GRH)
20.8.11918011924485247299136520192.1	x^20 - 10x^19 + 51x^18 - 164x^17 + 345x^16 - 492x^15 + 514x^14 - 422x^13 + 235x^12 + 122x^11 - 907x^10 + 1868x^9 - 1822x^8 + 1050x^7 - 1275x^6 + 1484x^5 - 143x^4 - 894x^3 + 535x^2 - 66x - 9	\( 2^{20}\cdot 17\cdot 401^{8} \)	20T905	Trivial (GRH)
20.8.15835320149390464670771579317.1	x^20 - 3x^19 + 4x^18 - 3x^17 - 14x^16 - 43x^15 + 138x^14 - 406x^13 + 344x^12 - 15x^11 - 437x^10 + 599x^9 + 82x^8 + 227x^7 + 350x^6 - 405x^5 - 321x^4 + 39x^3 + 36x^2 - x - 1	\( 23^{2}\cdot 401^{8}\cdot 44773 \)	20T905	Trivial (GRH)
20.6.16124369074303569875302350848.1	x^20 - 3x^18 - 18x^17 + 12x^16 + 24x^15 - 65x^14 + 28x^13 - 434x^12 + 842x^11 - 460x^10 + 212x^9 - 1170x^8 + 1934x^7 - 1755x^6 + 1256x^5 - 660x^4 + 432x^3 - 214x^2 + 24x + 1	\( -\,2^{20}\cdot 23\cdot 401^{8} \)	20T905	Trivial (GRH)
20.6.16124369074303569875302350848.2	x^20 + 10x^18 - 28x^17 + 21x^16 - 182x^15 + 184x^14 - 152x^13 + 463x^12 + 256x^11 - 514x^10 + 878x^9 - 624x^8 - 490x^7 + 1020x^6 - 908x^5 + 79x^4 + 398x^3 - 160x^2 - 12x + 9	\( -\,2^{20}\cdot 23\cdot 401^{8} \)	20T905	Trivial (GRH)
20.6.16550177879236441175248853331.1	x^20 - 3x^19 + 5x^18 - 20x^17 + 40x^16 - 53x^15 + 64x^14 - 25x^13 - 84x^12 + 450x^11 - 946x^10 + 1539x^9 - 2318x^8 + 2721x^7 - 2669x^6 + 2548x^5 - 1646x^4 + 969x^3 - 431x^2 - 12x + 39	\( -\,3^{2}\cdot 19^{3}\cdot 401^{9} \)	20T905	Trivial (GRH)
20.2.16550177879236441175248853331.1	x^20 - 3x^19 + 11x^18 - 14x^17 + 25x^16 - 9x^15 - 19x^14 + 45x^13 - 196x^12 + 11x^11 - 431x^10 - 259x^9 - 562x^8 - 660x^7 - 278x^6 - 501x^5 - 152x^4 + 45x^3 - 36x^2 + 32x - 13	\( -\,3^{2}\cdot 19^{3}\cdot 401^{9} \)	20T905	Trivial (GRH)
20.8.21766898184661311538405001589.1	x^20 - 10x^19 + 34x^18 - 21x^17 - 132x^16 + 240x^15 + 180x^14 - 666x^13 - 83x^12 + 1070x^11 - 31x^10 - 1160x^9 - 9x^8 + 858x^7 + 115x^6 - 393x^5 - 110x^4 + 88x^3 + 34x^2 - 5x - 1	\( 3^{3}\cdot 31\cdot 97\cdot 401^{9} \)	20T905	Trivial (GRH)
20.4.36704134911573623445289589641.1	x^20 - 10x^19 + 63x^18 - 282x^17 + 995x^16 - 2860x^15 + 6888x^14 - 14078x^13 + 24641x^12 - 37060x^11 + 47880x^10 - 52923x^9 + 49592x^8 - 38832x^7 + 24788x^6 - 12392x^5 + 4485x^4 - 961x^3 + 11x^2 + 54x - 9	\( 13\cdot 83^{2}\cdot 401^{8}\cdot 613 \)	20T905	Trivial (GRH)
20.4.39960392923274064473575391232.1	x^20 + 3x^18 - 2x^17 + 5x^16 - 16x^15 - 33x^14 + 86x^13 - 287x^12 + 64x^11 - 640x^10 - 1116x^9 + 391x^8 - 2350x^7 - 1033x^6 + 260x^5 - 1091x^4 - 552x^3 + 558x^2 + 432x + 81	\( 2^{20}\cdot 3\cdot 19\cdot 401^{8} \)	20T905	Trivial (GRH)
20.4.39960392923274064473575391232.2	x^20 + 5x^18 - 4x^17 + 13x^16 + 46x^15 + 30x^14 - 4x^13 + 188x^12 + 154x^11 + 393x^10 - 582x^9 + 115x^8 + 1720x^7 - 1502x^6 - 2246x^5 + 1423x^4 + 924x^3 - 276x^2 - 152x - 3	\( 2^{20}\cdot 3\cdot 19\cdot 401^{8} \)	20T905	Trivial (GRH)
20.2.57180852133785175762361058304.1	x^20 - 3x^19 + 10x^18 - 26x^17 + 58x^16 - 110x^15 + 282x^14 - 600x^13 + 655x^12 + 27x^11 - 504x^10 + 79x^9 + 352x^8 - 1483x^7 + 5339x^6 - 10096x^5 + 10787x^4 - 7002x^3 + 2754x^2 - 604x + 57	\( -\,2^{10}\cdot 17^{4}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.10.60057660848553501196125514752.1	x^20 - 14x^18 + 81x^16 - 258x^14 + 471x^12 - 416x^10 - 47x^8 + 486x^6 - 474x^4 + 198x^2 - 27	\( -\,2^{10}\cdot 3^{5}\cdot 19^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.6.60057660848553501196125514752.1	x^20 - 4x^18 - 31x^16 + 232x^14 - 535x^12 + 317x^10 + 307x^8 + 510x^6 - 1086x^4 - 387x^2 - 27	\( -\,2^{10}\cdot 3^{5}\cdot 19^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.2.60057660848553501196125514752.1	x^20 + 8x^18 + 29x^16 + 31x^14 - 321x^12 - 1772x^10 - 3875x^8 - 4095x^6 - 2013x^4 - 387x^2 - 27	\( -\,2^{10}\cdot 3^{5}\cdot 19^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.6.60057660848553501196125514752.2	x^20 - 8x^18 - 11x^16 + 231x^14 - 353x^12 - 1624x^10 + 4465x^8 + 1353x^6 - 8241x^4 + 1665x^2 - 27	\( -\,2^{10}\cdot 3^{5}\cdot 19^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.8.60057660848553501196125514752.1	x^20 - 15x^18 + 73x^16 - 98x^14 - 181x^12 + 583x^10 - 430x^8 - 201x^6 + 663x^4 - 819x^2 + 27	\( 2^{10}\cdot 3^{5}\cdot 19^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.4.60057660848553501196125514752.1	x^20 - 4x^19 + 9x^18 + 5x^17 - 58x^16 + 122x^15 - 16x^14 - 320x^13 + 486x^12 + 379x^11 - 1572x^10 + 976x^9 + 1856x^8 - 2988x^7 - 2747x^6 + 7730x^5 - 3593x^4 - 940x^3 + 621x^2 + 51x + 1	\( 2^{10}\cdot 3^{5}\cdot 19^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.8.60057660848553501196125514752.2	x^20 + x^18 - 44x^16 + 44x^14 + 463x^12 - 1217x^10 + 761x^8 + 354x^6 - 309x^4 - 90x^2 + 27	\( 2^{10}\cdot 3^{5}\cdot 19^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.0.101480361958019790381623019561.1	x^20 - 4x^19 + 6x^18 + x^17 - 13x^16 + 10x^15 + 20x^14 - 45x^13 + 17x^12 + 60x^11 - 77x^10 - 91x^9 + 416x^8 - 701x^7 + 765x^6 - 604x^5 + 356x^4 - 156x^3 + 49x^2 - 10x + 1	\( 3^{7}\cdot 401^{8}\cdot 69403 \)	20T905	$[2]$ (GRH)
20.2.126788395124724058080709420032.1	x^20 - 6x^18 - 18x^16 + 47x^14 + 2x^12 - 324x^10 - 1267x^8 - 1949x^6 - 1381x^4 - 456x^2 - 57	\( -\,2^{10}\cdot 3^{3}\cdot 19^{3}\cdot 401^{8} \)	20T905	$[2]$ (GRH)
20.10.126788395124724058080709420032.1	x^20 - 4x^18 - 77x^16 + 722x^14 - 2833x^12 + 6481x^10 - 9557x^8 + 9418x^6 - 6202x^4 + 2565x^2 - 513	\( -\,2^{10}\cdot 3^{3}\cdot 19^{3}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.4.190534537838645617076563552453.1	x^20 - 10x^19 + 54x^18 - 201x^17 + 560x^16 - 1216x^15 + 2092x^14 - 2850x^13 + 3020x^12 - 2364x^11 + 1176x^10 - 122x^9 - 322x^8 + 228x^7 - 12x^6 - 55x^5 + 14x^4 + 16x^3 - 9x^2 + 1	\( 71^{2}\cdot 401^{8}\cdot 56533 \)	20T905	Trivial (GRH)
20.12.193623132083128153402974623269.1	x^20 - 10x^19 + 34x^18 - 21x^17 - 144x^16 + 336x^15 - 51x^14 - 729x^13 + 921x^12 + 233x^11 - 1502x^10 + 926x^9 + 861x^8 - 1179x^7 - 3x^6 + 516x^5 - 153x^4 - 72x^3 + 37x^2 - x - 1	\( 13\cdot 139^{2}\cdot 401^{8}\cdot 1153 \)	20T905	Trivial (GRH)
20.12.355437179159648257686012690432.1	x^20 - 17x^18 + 124x^16 - 507x^14 + 1269x^12 - 1988x^10 + 1915x^8 - 1079x^6 + 329x^4 - 49x^2 + 3	\( 2^{20}\cdot 3\cdot 13^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.0.355437179159648257686012690432.1	x^20 + 17x^18 + 124x^16 + 507x^14 + 1269x^12 + 1988x^10 + 1915x^8 + 1079x^6 + 329x^4 + 49x^2 + 3	\( 2^{20}\cdot 3\cdot 13^{2}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.10.380365185374172174242128260096.1	x^20 - x^19 - 14x^18 + 29x^17 + 31x^16 - 209x^15 + 428x^14 + 90x^13 - 2666x^12 + 3732x^11 + 4101x^10 - 11900x^9 + 2409x^8 + 10448x^7 - 5839x^6 - 2276x^5 + 1472x^4 + 219x^3 - 40x^2 - 23x - 1	\( -\,2^{10}\cdot 3^{4}\cdot 19^{3}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.6.380365185374172174242128260096.1	x^20 - 9x^19 + 37x^18 - 97x^17 + 183x^16 - 236x^15 + 108x^14 + 275x^13 - 719x^12 + 1122x^11 - 1221x^10 + 999x^9 - 472x^8 - 732x^7 + 1681x^6 - 2609x^5 + 2325x^4 - 1300x^3 + 759x^2 + 43x + 1	\( -\,2^{10}\cdot 3^{4}\cdot 19^{3}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.2.380365185374172174242128260096.1	x^20 - x^19 + 12x^18 - 7x^17 + 21x^16 - 20x^15 - 152x^14 - 219x^13 - 487x^12 - 948x^11 - 406x^10 - 491x^9 - 487x^8 + 914x^7 + 373x^6 - 1449x^5 - 200x^4 + 392x^3 - 17x^2 - 75x + 9	\( -\,2^{10}\cdot 3^{4}\cdot 19^{3}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.8.380365185374172174242128260096.1	x^20 - 12x^18 + 21x^16 + 189x^14 - 530x^12 - 693x^10 + 1260x^8 + 2283x^6 + 1621x^4 + 1026x^2 + 171	\( 2^{10}\cdot 3^{4}\cdot 19^{3}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.4.380365185374172174242128260096.1	x^20 - 3x^19 - x^18 + 16x^17 - x^16 - 38x^15 + 23x^14 + 84x^13 + 59x^12 - 135x^11 - 816x^10 + 366x^9 - 1450x^8 - 580x^7 + 2426x^6 - 3889x^5 + 1666x^4 - 2018x^3 + 1594x^2 - 11x + 1523	\( 2^{10}\cdot 3^{4}\cdot 19^{3}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.4.380365185374172174242128260096.2	x^20 + 6x^18 + 7x^16 - 19x^14 - 300x^12 - 1235x^10 - 2166x^8 - 1673x^6 - 205x^4 + 456x^2 + 171	\( 2^{10}\cdot 3^{4}\cdot 19^{3}\cdot 401^{8} \)	20T905	Trivial (GRH)