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 6097)

Label	Polynomial	Discriminant	Galois group	Class group
20.4.10922267596307822265625.1	x^20 - 3x^19 - x^18 + 4x^17 + 13x^16 - 26x^15 + 3x^14 + 16x^13 + 4x^12 - 21x^11 + 21x^10 - 21x^9 + 4x^8 + 16x^7 + 3x^6 - 26x^5 + 13x^4 + 4x^3 - x^2 - 3x + 1	\( 5^{10}\cdot 5783^{4} \)	20T279	Trivial (GRH)
20.4.12010577056389693116416.1	x^20 - x^18 + 3x^16 - 11x^14 + 6x^12 + 6x^10 + 5x^8 - 13x^6 + 7x^4 - 5x^2 + 1	\( 2^{12}\cdot 41381^{4} \)	20T568	Trivial (GRH)
20.4.12646126110965776516096.1	x^20 - x^18 - 4x^16 + 4x^14 + 9x^12 - 11x^10 - 9x^8 + 12x^6 + x^4 - 4x^2 + 1	\( 2^{10}\cdot 47^{2}\cdot 8647^{4} \)	20T994	Trivial (GRH)
20.4.12858618354751897106401.1	x^20 - 2x^19 + 2x^18 + 2x^17 - 9x^16 + 24x^15 - 39x^14 + 48x^13 - 58x^12 + 60x^11 - 59x^10 + 60x^9 - 58x^8 + 48x^7 - 39x^6 + 24x^5 - 9x^4 + 2x^3 + 2x^2 - 2x + 1	\( 11^{16}\cdot 23^{4} \)	$C_2\times C_2^4:C_5$ (as 20T41)	Trivial
20.4.15363369498681819529216.1	x^20 + 3x^18 + x^16 - 3x^14 - 2x^12 + x^10 + 6x^8 - 9x^6 - 7x^4 + 1	\( 2^{24}\cdot 5501^{4} \)	20T568	Trivial (GRH)
20.4.18780357640955901417873.1	x^20 - 2x^19 + 3x^17 - 9x^16 + 20x^15 - 26x^14 + 19x^13 - 5x^12 - 8x^11 + 42x^10 - 89x^9 + 94x^8 - 76x^7 + 75x^6 - 64x^5 + 33x^4 - 14x^3 + 6x^2 - 1	\( 3^{8}\cdot 17^{15} \)	$C_2\times F_5$ (as 20T9)	Trivial
20.4.22905655334132142080000.1	x^20 - 4x^19 + x^18 + 20x^17 - 31x^16 - 18x^15 + 69x^14 - 3x^13 - 95x^12 + 43x^11 + 88x^10 - 135x^9 + 112x^8 - 40x^7 - 44x^6 + 37x^5 + 16x^4 - 9x^3 - 4x^2 - 2x - 1	\( 2^{15}\cdot 5^{4}\cdot 5783^{4} \)	20T992	Trivial (GRH)
20.4.23317004278327158203125.1	x^20 - 3x^19 + 5x^18 - 10x^17 + 4x^16 + x^15 - 12x^14 + 30x^13 - 35x^12 + 39x^11 - 25x^10 + 18x^9 + 4x^8 - 15x^7 + 3x^6 - 18x^5 + 3x^3 + 3x^2 + 5x + 1	\( 5^{10}\cdot 601^{4}\cdot 18301 \)	20T876	Trivial (GRH)
20.4.23382101649260778427129.1	x^20 - x^19 - 5x^18 + 6x^17 + 5x^16 - 7x^15 + 7x^14 - 14x^13 - 5x^12 + 14x^11 + 8x^10 + 14x^9 - 29x^8 - 18x^7 + 23x^6 + 5x^5 - x^4 + x^3 - 5x^2 - x + 1	\( 7^{8}\cdot 43^{2}\cdot 1217^{4} \)	20T669	Trivial (GRH)
20.4.24890784868177585325056.1	x^20 + 5x^18 + 8x^16 + 2x^14 - x^12 - 11x^10 - 37x^8 - 34x^6 - 5x^4 + 4x^2 + 1	\( 2^{10}\cdot 11^{16}\cdot 23^{2} \)	20T751	Trivial
20.4.25567174371986127192064.1	x^20 - 2x^19 + 2x^18 - 2x^17 - 11x^16 + 24x^15 - 42x^14 + 130x^13 - 131x^12 - 38x^11 + 36x^10 + 68x^9 + 23x^8 - 88x^7 + 32x^6 + 8x^5 - 10x^4 - 6x^3 + 4x^2 + 2x - 1	\( 2^{30}\cdot 47^{8} \)	$C_2^4:D_5$ (as 20T39)	Trivial
20.4.29319238827689141862400.1	x^20 - 2x^19 - 2x^18 + 8x^17 + 7x^16 - 32x^15 - x^14 + 60x^13 + 3x^12 - 108x^11 + 14x^10 + 112x^9 - 4x^8 - 96x^7 - 21x^6 + 52x^5 + 26x^4 - 18x^3 - 22x^2 - 8x - 1	\( 2^{20}\cdot 5^{2}\cdot 5783^{4} \)	20T964	Trivial (GRH)
20.4.31994921266495224201025.1	x^20 - 2x^19 + 7x^18 - 15x^17 + 30x^16 - 54x^15 + 95x^14 - 152x^13 + 221x^12 - 306x^11 + 361x^10 - 364x^9 + 297x^8 - 188x^7 + 58x^6 + 25x^5 - 36x^4 + 23x^3 - x^2 - 2x + 1	\( 5^{2}\cdot 61^{6}\cdot 397^{4} \)	20T799	Trivial (GRH)
20.4.33090677680473274083073.1	x^20 - x^19 - 5x^18 + 12x^16 + 8x^15 - 2x^14 - 21x^13 - 17x^12 + 13x^11 + x^10 + 20x^9 - 23x^8 + 34x^7 - 17x^6 - 10x^5 + 20x^4 - 20x^3 + 11x^2 - 4x + 1	\( 97^{3}\cdot 13799^{4} \)	20T791	Trivial
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)
20.4.46484025093233137504237.1	x^20 - 3x^19 + 3x^18 + 8x^17 - 29x^16 + 42x^15 - 30x^14 - 3x^13 + 4x^12 + 33x^11 - 18x^10 - 83x^9 + 164x^8 - 175x^7 + 134x^6 - 65x^5 + 22x^4 - 2x^3 - 5x^2 + 2x - 1	\( 11^{10}\cdot 13^{11} \)	20T144	Trivial
20.4.47669167735583779323904.1	x^20 - 6x^19 + 17x^18 - 30x^17 + 26x^16 + 12x^15 - 58x^14 + 62x^13 - 20x^12 - 26x^11 + 43x^10 - 26x^9 - 20x^8 + 62x^7 - 58x^6 + 12x^5 + 26x^4 - 30x^3 + 17x^2 - 6x + 1	\( 2^{20}\cdot 7^{2}\cdot 5519^{4} \)	20T964	Trivial (GRH)
20.4.48902390003204345703125.1	x^20 - 2x^15 - 10x^10 + 11x^5 - 1	\( 5^{22}\cdot 29^{5} \)	$D_5^2:C_4$ (as 20T94)	Trivial
20.4.54760506817899727281152.1	x^20 - 8x^19 + 27x^18 - 51x^17 + 57x^16 - 26x^15 - 41x^14 + 134x^13 - 245x^12 + 349x^11 - 403x^10 + 378x^9 - 291x^8 + 195x^7 - 113x^6 + 42x^5 - x^4 - 12x^3 + 8x^2 - 1	\( 2^{10}\cdot 17^{4}\cdot 23\cdot 2297^{4} \)	20T992	Trivial (GRH)
20.4.58350703559923741242112.1	x^20 - 6x^19 + 14x^18 - 12x^17 - 16x^16 + 82x^15 - 189x^14 + 278x^13 - 236x^12 + 82x^11 - 7x^10 + 76x^9 - 107x^8 + 24x^7 + 7x^6 + 76x^5 - 118x^4 + 60x^3 - 3x^2 - 6x + 1	\( 2^{8}\cdot 67^{5}\cdot 641^{4} \)	20T1106	Trivial (GRH)
20.4.59506232715491992087669.1	x^20 - x^19 + 3x^18 - 8x^17 + 16x^16 - 34x^15 + 39x^14 - 30x^13 - 3x^12 + 46x^11 - 57x^10 + 46x^9 - 3x^8 - 30x^7 + 39x^6 - 34x^5 + 16x^4 - 8x^3 + 3x^2 - x + 1	\( 11^{16}\cdot 109^{3} \)	20T303	Trivial
20.4.59506232715491992087669.2	x^20 - x^19 - 4x^18 + x^17 + 2x^16 - 6x^15 + 5x^14 + 20x^13 - 6x^12 - 39x^11 - 7x^10 + 55x^9 + 36x^8 - 47x^7 - 43x^6 + 21x^5 + 18x^4 - 8x^3 - 3x^2 + 3x + 1	\( 11^{16}\cdot 109^{3} \)	20T303	Trivial
20.4.61453477994727278116864.1	x^20 - 7x^18 + 19x^16 - 37x^14 + 69x^12 - 98x^10 + 94x^8 - 71x^6 + 46x^4 - 18x^2 + 1	\( 2^{26}\cdot 5501^{4} \)	20T567	Trivial (GRH)
20.4.66045000696445844586496.1	x^20 - 4x^18 + 2x^16 + 4x^14 + 10x^12 - 21x^10 - 3x^8 + 28x^4 - 20x^2 + 4	\( 2^{24}\cdot 89^{8} \)	20T567	Trivial (GRH)
20.4.80903040633285021367225.1	x^20 - 7x^19 + 21x^18 - 30x^17 - 4x^16 + 114x^15 - 273x^14 + 403x^13 - 455x^12 + 450x^11 - 441x^10 + 450x^9 - 455x^8 + 403x^7 - 273x^6 + 114x^5 - 4x^4 - 30x^3 + 21x^2 - 7x + 1	\( 5^{2}\cdot 61^{4}\cdot 97^{2}\cdot 397^{4} \)	20T799	Trivial (GRH)
20.4.84663181407790756265984.1	x^20 - 4x^19 + 8x^18 - 6x^17 - 10x^16 + 36x^15 - 57x^14 + 54x^13 - 23x^12 - 18x^11 + 26x^10 + 20x^9 - 90x^8 + 128x^7 - 98x^6 + 24x^5 + 32x^4 - 36x^3 + 19x^2 - 6x + 1	\( 2^{30}\cdot 137^{3}\cdot 313^{3} \)	20T540	Trivial
20.4.109115950462157402855641.1	x^20 - 2x^19 + 2x^18 + 2x^17 - 9x^16 + 2x^15 + 5x^14 - 7x^13 - 3x^12 + 5x^11 + 7x^10 + 5x^9 - 3x^8 - 7x^7 + 5x^6 + 2x^5 - 9x^4 + 2x^3 + 2x^2 - 2x + 1	\( 11^{16}\cdot 23^{2}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.4.109115950462157402855641.2	x^20 - x^19 + 6x^18 - 8x^17 + 18x^16 - 13x^15 + 25x^14 + 10x^13 - 23x^12 + 65x^11 - 103x^10 + 107x^9 - 130x^8 + 94x^7 - 65x^6 + 53x^5 - 12x^4 + 5x^3 - 3x^2 - 4x + 1	\( 11^{16}\cdot 23^{2}\cdot 67^{2} \)	20T341	Trivial (GRH)
20.4.109150463284655166015625.1	x^20 - 5x^19 + 6x^18 + 12x^17 - 31x^16 - x^15 + 58x^14 - 41x^13 - 50x^12 + 88x^11 + 26x^10 - 83x^9 - 17x^8 + 21x^7 + 9x^5 + x^4 - 7x^3 + 5x^2 + 6x + 1	\( 5^{10}\cdot 97^{2}\cdot 1039^{2}\cdot 1049^{2} \)	20T1040	Trivial (GRH)
20.4.135285869682178618505573.1	x^20 - 2x^19 + 2x^18 + 7x^17 - 12x^16 + 8x^15 + 16x^14 - 33x^13 + 4x^12 + 7x^11 - 49x^10 + 7x^9 + 4x^8 - 33x^7 + 16x^6 + 8x^5 - 12x^4 + 7x^3 + 2x^2 - 2x + 1	\( 53^{5}\cdot 4241^{4} \)	20T992	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)
20.4.157092982407310367598961.1	x^20 - 2x^18 - 11x^15 - 39x^14 - 55x^13 - 67x^12 - 66x^11 - 51x^10 - 66x^9 - 67x^8 - 55x^7 - 39x^6 - 11x^5 - 2x^2 + 1	\( 11^{16}\cdot 43^{4} \)	$C_2\times C_2^4:C_5$ (as 20T41)	Trivial
20.4.157418066211172801132861.1	x^20 - 10x^19 + 52x^18 - 183x^17 + 481x^16 - 992x^15 + 1649x^14 - 2241x^13 + 2504x^12 - 2297x^11 + 1713x^10 - 1014x^9 + 446x^8 - 109x^7 - 34x^6 + 66x^5 - 55x^4 + 34x^3 - 18x^2 + 7x - 1	\( 7^{4}\cdot 61^{2}\cdot 230101\cdot 276721^{2} \)	20T1110	Trivial (GRH)
20.4.164475020247040000000000.1	x^20 - 6x^19 + 15x^18 - 18x^17 + x^16 + 46x^15 - 138x^14 + 300x^13 - 521x^12 + 716x^11 - 763x^10 + 598x^9 - 273x^8 - 58x^7 + 250x^6 - 272x^5 + 199x^4 - 110x^3 + 43x^2 - 10x + 1	\( 2^{28}\cdot 5^{10}\cdot 89^{4} \)	20T1013	Trivial (GRH)
20.4.197550394506345032237009.1	x^20 - 2x^18 - 5x^17 + x^16 + 12x^15 - 4x^14 - 27x^13 + 19x^11 + 6x^10 + 18x^9 + 20x^8 - 7x^7 - 29x^6 - 27x^5 - 4x^4 + 12x^3 + 11x^2 + 5x + 1	\( 1609^{4}\cdot 3089^{3} \)	20T791	Trivial (GRH)
20.4.202312357996686362657792.1	x^20 - 4x^19 + x^18 + 12x^17 - 12x^16 + 4x^15 - 7x^14 - 9x^12 + 23x^11 - 33x^10 + 45x^9 - 25x^8 + 7x^7 - 14x^6 + 28x^5 - 33x^4 + 19x^3 - 2x^2 - 3x + 1	\( 2^{10}\cdot 7^{8}\cdot 17^{11} \)	20T426	Trivial (GRH)
20.4.214377296883203134765625.1	x^20 - x^19 + 2x^18 + x^17 - 6x^16 + 9x^15 - 8x^14 - 13x^13 + 21x^12 - 18x^11 - 16x^10 + 28x^9 - 16x^8 - 8x^7 + 21x^6 - 9x^5 - 2x^4 + 8x^3 - 4x^2 - 2x + 1	\( 5^{10}\cdot 280001^{3} \)	20T540	Trivial (GRH)
20.4.223904745130829775390625.1	x^20 - 4x^18 - 4x^17 - x^16 + 15x^15 + 33x^14 - 21x^13 - 80x^12 + 16x^11 + 108x^10 - 15x^9 - 97x^8 + 34x^7 + 55x^6 - 35x^5 - 15x^4 + 13x^3 + 2x^2 - 5x + 1	\( 5^{10}\cdot 13^{6}\cdot 41^{6} \)	$C_2\times S_5$ (as 20T62)	Trivial
20.4.223904745130829775390625.2	x^20 - 2x^19 - x^18 + 15x^17 - 23x^16 - 39x^15 + 68x^14 + 25x^13 - 74x^12 + 12x^11 + 59x^10 - 20x^9 - 85x^8 + 52x^7 + 47x^6 - 35x^5 - 3x^4 - 4x^3 + 9x^2 - 4x + 1	\( 5^{10}\cdot 13^{6}\cdot 41^{6} \)	20T288	Trivial (GRH)
20.4.230921785379186176385189.1	x^20 - 2x^19 + 5x^18 - 10x^17 + 17x^16 - 34x^15 + 32x^14 - 30x^13 + 16x^12 - 9x^11 - 27x^10 + 89x^9 - 18x^8 - 74x^7 + 53x^6 + 24x^5 - 7x^4 + 19x^3 + 4x^2 - 7x - 1	\( 29^{3}\cdot 79^{10} \)	20T418	Trivial (GRH)
20.4.231472847376679145996221.1	x^20 - 3x^19 + 3x^18 - 9x^17 + 16x^16 - 18x^15 + 26x^14 - 36x^13 + 36x^12 - 39x^11 + 47x^10 - 39x^9 + 36x^8 - 36x^7 + 26x^6 - 18x^5 + 16x^4 - 9x^3 + 3x^2 - 3x + 1	\( 17^{4}\cdot 421^{3}\cdot 439^{4} \)	20T990	Trivial (GRH)
20.4.238121705371228558065664.1	x^20 - 8x^18 + 28x^16 - 58x^14 + 80x^12 - 78x^10 + 53x^8 - 20x^6 - 2x^4 + 4x^2 + 1	\( 2^{30}\cdot 17^{4}\cdot 227^{4} \)	20T1100	Trivial (GRH)
20.4.252040366516203798224329.1	x^20 - 7x^19 + 27x^18 - 83x^17 + 203x^16 - 404x^15 + 677x^14 - 958x^13 + 1122x^12 - 1101x^11 + 925x^10 - 680x^9 + 536x^8 - 546x^7 + 546x^6 - 422x^5 + 249x^4 - 118x^3 + 39x^2 - 4x - 1	\( 11^{2}\cdot 47^{10}\cdot 199^{2} \)	20T412	Trivial (GRH)
20.4.289274162775135942344704.1	x^20 - 2x^19 + 6x^17 - 9x^16 - x^15 + 16x^14 - 9x^13 - 20x^12 + 36x^11 - 8x^10 - 38x^9 + 48x^8 - 13x^7 - 20x^6 + 13x^5 + 16x^4 - 29x^3 + 20x^2 - 7x + 1	\( 2^{18}\cdot 32411^{4} \)	20T994	Trivial (GRH)
20.4.304226899738556884765625.1	x^20 - x^19 - 2x^18 + 6x^17 + 2x^16 - 7x^15 - 7x^14 + 17x^13 - 5x^12 + x^11 + 6x^10 - 28x^9 - 54x^8 + 28x^7 + 95x^6 + 14x^5 - 48x^4 - 34x^3 + 11x^2 + 3x + 1	\( 5^{12}\cdot 1039^{2}\cdot 1049^{3} \)	20T1045	Trivial (GRH)
20.4.324864479268392294429293.1	x^20 - 3x^19 + 7x^18 - 16x^17 + 26x^16 - 31x^15 + 40x^14 - 46x^13 + 43x^12 - 36x^11 - 40x^10 + 134x^9 - 101x^8 + 33x^7 - 44x^6 + 37x^5 - 2x^4 + 2x^3 - 6x^2 + 1	\( 277^{3}\cdot 11119^{4} \)	20T990	Trivial (GRH)
20.4.337385929308761961864713.1	x^20 + 3x^18 - 2x^17 + x^16 - 2x^15 - 13x^14 + 48x^13 - 2x^12 + 125x^11 - 18x^10 + 17x^9 - 141x^8 - 168x^7 - 166x^6 - 128x^5 - 52x^4 - 15x^3 + 3x^2 + 5x + 1	\( 2297^{7} \)	20T671	Trivial (GRH)
20.4.337783263126326508704161.1	x^20 - 2x^19 + x^18 + x^17 - 8x^16 + 6x^15 - 4x^14 - 10x^13 + 9x^12 - 11x^11 + 16x^10 + 19x^9 - 23x^8 - x^7 + 4x^6 - 2x^5 + 7x^4 - 3x^3 - 4x^2 + 2x + 1	\( 13^{12}\cdot 347^{4} \)	20T279	Trivial (GRH)
20.4.343697048162735885972621.1	x^20 - 3x^19 + 3x^18 + 3x^17 - 14x^16 + 21x^15 - 19x^14 - 3x^13 + 37x^12 - 50x^11 + 46x^10 - 32x^9 + 5x^8 + 2x^7 - 20x^6 + 10x^5 + 2x^4 + 8x^3 + 3x^2 + 1	\( 17^{4}\cdot 23\cdot 2297^{4}\cdot 6427 \)	20T992	Trivial (GRH)
20.4.344359285812922275390625.1	x^20 - 3x^19 + 12x^17 - 10x^16 - 35x^15 + 55x^14 + 39x^13 - 130x^12 + 10x^11 + 206x^10 - 130x^9 - 143x^8 + 201x^7 - 31x^6 - 78x^5 + 14x^4 + 9x^3 - 18x^2 - x + 1	\( 5^{10}\cdot 13^{4}\cdot 41^{4}\cdot 661^{2} \)	20T368	Trivial (GRH)