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 )

Label	Polynomial	Discriminant	Galois group	Class group
20.0.169023218768603112760857.1	x^20 - x^19 + 2x^18 + 3x^17 - 6x^16 + 23x^15 - 13x^14 + 7x^13 + 34x^12 - 50x^11 + 81x^10 - 50x^9 + 34x^8 + 7x^7 - 13x^6 + 23x^5 - 6x^4 + 3x^3 + 2x^2 - x + 1	\( 3^{10}\cdot 17^{15} \)	$F_5$ (as 20T5)	$[2]$
20.0.439234614592946176000000.1	x^20 - 2x^18 - 7x^16 - 2x^14 + 28x^12 + 52x^10 + 55x^8 + 38x^6 + 19x^4 + 2x^2 + 1	\( 2^{20}\cdot 5^{6}\cdot 173^{6} \)	20T201	$[2]$
20.0.1555892820924979549874521.1	x^20 - 4x^19 + 15x^18 - 45x^17 + 88x^16 - 109x^15 + 84x^14 - 29x^13 - 23x^12 + 55x^11 - 65x^10 + 55x^9 - 23x^8 - 29x^7 + 84x^6 - 109x^5 + 88x^4 - 45x^3 + 15x^2 - 4x + 1	\( 11^{18}\cdot 23^{4} \)	$C_2\times C_2^4:C_5$ (as 20T44)	$[2]$
20.0.1555892820924979549874521.2	x^20 - 9x^19 + 39x^18 - 105x^17 + 198x^16 - 298x^15 + 427x^14 - 644x^13 + 952x^12 - 1254x^11 + 1420x^10 - 1386x^9 + 1201x^8 - 964x^7 + 727x^6 - 496x^5 + 297x^4 - 156x^3 + 62x^2 - 12x + 1	\( 11^{18}\cdot 23^{4} \)	$C_2\times C_2^4:C_5$ (as 20T44)	$[2]$
20.0.1860495326773308902342656.2	x^20 - x^18 + x^14 - x^12 + x^10 - x^8 + x^6 - x^2 + 1	\( 2^{20}\cdot 36497^{4} \)	20T669	$[2]$ (GRH)
20.0.2112500000000000000000000.1	x^20 + 5x^16 - 8x^15 + 20x^14 + 10x^13 - 40x^11 + 14x^10 + 50x^9 + 50x^8 + 20x^7 - 42x^5 - 25x^4 + 20x^3 + 30x^2 + 10x + 1	\( 2^{20}\cdot 5^{23}\cdot 13^{2} \)	20T135	$[2]$
20.0.2320349626175642005405696.1	x^20 - x^12 + x^10 - x^8 + 1	\( 2^{20}\cdot 38569^{4} \)	20T669	$[2]$ (GRH)
20.0.2497515382702158081163264.1	x^20 + 2x^18 + x^16 - 18x^12 + 12x^10 - 2x^8 + 81x^4 - 14x^2 + 1	\( 2^{42}\cdot 7^{6}\cdot 13^{6} \)	20T199	$[2]$
20.0.4226880044572534053535744.1	x^20 - 10x^19 + 50x^18 - 162x^17 + 381x^16 - 696x^15 + 1032x^14 - 1242x^13 + 1134x^12 - 648x^11 + 484x^9 - 611x^8 + 428x^7 - 136x^6 - 84x^5 + 164x^4 - 136x^3 + 72x^2 - 24x + 4	\( 2^{30}\cdot 89^{8} \)	20T226	$[2]$
20.0.4226880044572534053535744.4	x^20 + 4x^18 + 2x^16 + 18x^14 - 3x^12 + 20x^10 - 3x^8 + 18x^6 + 2x^4 + 4x^2 + 1	\( 2^{30}\cdot 89^{8} \)	20T555	$[2]$
20.0.5638945908764610561114112.1	x^20 - 9x^19 + 30x^18 - 36x^17 - 34x^16 + 151x^15 - 136x^14 - 126x^13 + 475x^12 - 528x^11 - 8x^10 + 784x^9 - 922x^8 + 254x^7 + 384x^6 - 486x^5 + 321x^4 - 153x^3 + 38x^2 + 1	\( 2^{16}\cdot 13^{15}\cdot 41^{2} \)	20T135	$[2]$
20.0.6802209109663753569286129.1	x^20 - 8x^19 + 33x^18 - 96x^17 + 225x^16 - 428x^15 + 639x^14 - 722x^13 + 605x^12 - 426x^11 + 458x^10 - 746x^9 + 1001x^8 - 1010x^7 + 873x^6 - 694x^5 + 455x^4 - 214x^3 + 66x^2 - 12x + 1	\( 11^{16}\cdot 23^{6} \)	$C_2^4:C_5$ (as 20T17)	$[2]$
20.0.6802209109663753569286129.2	x^20 - 3x^19 + 14x^18 - 33x^17 + 85x^16 - 156x^15 + 281x^14 - 417x^13 + 590x^12 - 734x^11 + 869x^10 - 875x^9 + 908x^8 - 679x^7 + 668x^6 - 321x^5 + 303x^4 - 77x^3 + 42x^2 - 4x + 1	\( 11^{16}\cdot 23^{6} \)	$C_2\times C_2^4:C_5$ (as 20T46)	$[2]$
20.0.7833215942848814041519681.1	x^20 - 9x^18 + 12x^16 + 96x^14 - 94x^12 + 144x^10 + 416x^8 - 153x^6 + 130x^4 + 135x^2 + 49	\( 7^{2}\cdot 53^{6}\cdot 139^{6} \)	20T664	$[2]$ (GRH)
20.0.9913305541837631770231808.1	x^20 - 4x^19 + 8x^18 - 10x^17 + 12x^16 - 15x^15 + 13x^14 - 15x^13 + 37x^12 - 40x^11 - 76x^10 + 231x^9 - 142x^8 - 227x^7 + 493x^6 - 327x^5 - x^4 + 103x^3 + 65x^2 + 14x + 1	\( 2^{10}\cdot 7^{10}\cdot 17^{11} \)	20T426	$[2]$ (GRH)
20.0.9928207061616528930635776.1	x^20 - 2x^18 - 17x^16 - 3x^14 + 85x^12 + 208x^10 + 439x^8 - 195x^6 + 229x^4 - 17x^2 + 1	\( 2^{20}\cdot 79^{10} \)	$D_{10}$ (as 20T4)	$[3]$
20.0.12800000000000000000000000.1	x^20 + 5x^16 - 4x^15 + 30x^14 + 20x^13 + 25x^12 + 60x^11 + 46x^10 + 60x^9 + 25x^8 + 20x^7 + 30x^6 - 4x^5 + 5x^4 + 1	\( 2^{30}\cdot 5^{23} \)	$F_5$ (as 20T5)	$[2]$
20.0.15233950180173557331984384.1	x^20 - 2x^19 + 6x^18 - 8x^17 + 16x^16 - 14x^15 + 32x^14 - 12x^13 + 32x^12 + 8x^11 + 48x^10 - 16x^9 + 48x^8 + 8x^7 + 24x^6 + 8x^5 + 32x^4 + 16x^3 + 32x^2 + 16x + 16	\( 2^{16}\cdot 3^{10}\cdot 89^{8} \)	$S_5$ (as 20T32)	$[2]$
20.0.15802861880872333999079424.1	x^20 - 4x^19 + 10x^18 - 16x^17 + 15x^16 + 20x^15 - 62x^14 - 36x^13 + 456x^12 - 1288x^11 + 1928x^10 - 862x^9 - 1680x^8 + 1604x^7 + 4435x^6 - 12624x^5 + 15361x^4 - 11076x^3 + 4962x^2 - 1296x + 153	\( 2^{20}\cdot 3^{10}\cdot 761^{5} \)	$C_2\times D_5\wr C_2$ (as 20T92)	$[2]$
20.0.16537062841993940409778176.1	x^20 - 2x^17 - x^16 + 12x^15 + 5x^14 - 112x^13 + 313x^12 - 448x^11 + 442x^10 - 380x^9 + 265x^8 - 104x^7 + 5x^6 + 18x^5 - x^4 - 4x^3 + 1	\( 2^{24}\cdot 3^{16}\cdot 389^{4} \)	20T872	$[2]$
20.0.16907520178290136214142976.1	x^20 - 4x^18 + 7x^16 - 6x^14 - 12x^12 + 69x^10 + 152x^8 + 132x^6 + 59x^4 + 13x^2 + 1	\( 2^{32}\cdot 89^{8} \)	20T664	$[2]$
20.0.16907520178290136214142976.2	x^20 + x^18 - 3x^16 + 17x^14 - 26x^12 + 36x^10 - 26x^8 + 17x^6 - 3x^4 + x^2 + 1	\( 2^{32}\cdot 89^{8} \)	20T664	$[2]$ (GRH)
20.0.22197404920560895031657121.1	x^20 + 3x^18 - 2x^17 + 7x^16 - 4x^15 + 7x^14 - 7x^13 + 5x^12 + x^11 + 3x^10 + 3x^9 + 6x^8 + 7x^7 + 16x^6 - x^5 + 9x^4 + 6x^3 + 9x^2 + 3x + 1	\( 3^{10}\cdot 16493^{2}\cdot 1175561^{2} \)	20T1021	$[2]$ (GRH)
20.0.25488163705013847372857344.1	x^20 + 5x^18 + 4x^16 - 3x^14 + x^12 + 7x^10 + x^8 - 3x^6 + 4x^4 + 5x^2 + 1	\( 2^{20}\cdot 11^{16}\cdot 23^{2} \)	20T263	$[2]$ (GRH)
20.0.26169939318182371097563349.1	x^20 - x^19 + x^18 + x^17 + 7x^16 + 5x^15 + 3x^14 + 10x^13 + 17x^12 + 48x^11 + 34x^10 + 48x^9 + 69x^8 + 113x^7 + 126x^6 + 66x^5 + 31x^4 - 12x^3 + 4x^2 - 5x + 1	\( 29^{7}\cdot 79^{8} \)	20T436	$[2]$ (GRH)
20.0.29740534473574264497719409.1	x^20 - x^19 + 3x^18 + 2x^17 + 5x^16 + 4x^14 + 8x^13 + x^12 + 2x^10 + 16x^9 + 2x^8 + 7x^7 + 8x^6 + 14x^5 + 4x^4 - 4x^3 + 9x^2 - 3x + 1	\( 3^{10}\cdot 277^{2}\cdot 81019273^{2} \)	20T1021	$[2]$ (GRH)
20.0.33626538312268515533112249.1	x^20 - 6x^19 + 13x^18 - 6x^17 - 18x^16 - 18x^15 + 296x^14 - 939x^13 + 1648x^12 - 1689x^11 + 727x^10 + 537x^9 - 1049x^8 + 546x^7 + 156x^6 - 315x^5 + 354x^4 - 399x^3 + 14x^2 + 147x + 49	\( 3^{10}\cdot 7^{10}\cdot 17^{10} \)	$D_{10}$ (as 20T4)	$[2]$
20.0.33626538312268515533112249.2	x^20 - 6x^19 + 18x^18 - 32x^17 + 41x^16 + x^15 - 113x^14 + 222x^13 - 194x^12 - 14x^11 + 723x^10 - 446x^9 + 1142x^8 + 574x^7 + 89x^6 + 2241x^5 + 424x^4 + 340x^3 + 629x^2 + 289	\( 3^{10}\cdot 7^{10}\cdot 17^{10} \)	$D_{10}$ (as 20T4)	$[2]$
20.0.39479125871598264344535849.1	x^20 - 2x^19 + 6x^18 + 8x^17 - x^16 + 7x^15 + 6x^14 - 10x^13 + 11x^12 + 15x^11 - x^10 + 15x^9 + 11x^8 - 10x^7 + 6x^6 + 7x^5 - x^4 + 8x^3 + 6x^2 - 2x + 1	\( 3^{10}\cdot 401^{8} \)	$C_2\times C_2^4:D_5$ (as 20T73)	$[2]$
20.0.39479125871598264344535849.2	x^20 - 3x^19 + 12x^18 - 15x^17 + 40x^16 - 27x^15 + 92x^14 - 43x^13 + 172x^12 - 89x^11 + 249x^10 - 143x^9 + 259x^8 - 173x^7 + 188x^6 - 92x^5 + 96x^4 - 19x^3 + 28x^2 - 5x + 1	\( 3^{10}\cdot 401^{8} \)	$C_2\times C_2^4:D_5$ (as 20T73)	$[2]$
20.0.39479125871598264344535849.3	x^20 - x^19 + x^18 + 2x^16 - 3x^15 - 3x^14 + 2x^13 + 4x^12 - 5x^10 + 4x^8 + 2x^7 - 3x^6 - 3x^5 + 2x^4 + x^2 - x + 1	\( 3^{10}\cdot 401^{8} \)	$C_2\times C_2^4:D_5$ (as 20T73)	$[2]$ (GRH)
20.0.46465044146768981515042816.1	x^20 + 2x^18 - 7x^16 + 5x^14 + 11x^12 - 20x^10 + 11x^8 + 5x^6 - 7x^4 + 2x^2 + 1	\( 2^{20}\cdot 83^{4}\cdot 983^{4} \)	20T669	$[2]$ (GRH)
20.0.46465044146768981515042816.2	x^20 + 3x^18 - x^16 - 2x^14 + 5x^12 - 8x^10 + 5x^8 - 2x^6 - x^4 + 3x^2 + 1	\( 2^{20}\cdot 83^{4}\cdot 983^{4} \)	20T669	$[2]$ (GRH)
20.0.48807303526718226903859200.1	x^20 + x^18 - 2x^17 - 6x^16 + 4x^15 + 30x^14 - 36x^13 - 15x^12 + 12x^11 + 48x^10 + 12x^9 - 123x^8 + 36x^7 + 153x^6 - 124x^5 - 66x^4 + 110x^3 - 11x^2 - 30x + 10	\( 2^{20}\cdot 3^{14}\cdot 5^{2}\cdot 17\cdot 389^{4} \)	20T925	$[2]$
20.0.51200000000000000000000000.2	x^20 + 5x^16 + 20x^14 + 10x^12 - 10x^8 - 20x^6 + 5x^4 + 5	\( 2^{32}\cdot 5^{23} \)	$C_2^4:C_5:C_4$ (as 20T88)	$[2]$
20.0.54296067514572573056640625.1	x^20 - x^19 + 2x^18 - 3x^17 + 5x^16 - 8x^15 + 13x^14 - 21x^13 + 34x^12 - 55x^11 + 89x^10 + 55x^9 + 34x^8 + 21x^7 + 13x^6 + 8x^5 + 5x^4 + 3x^3 + 2x^2 + x + 1	\( 5^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[2]$
20.0.56477888187717354967269376.1	x^20 - 2x^19 - 2x^18 + 12x^17 - 21x^16 + 26x^15 + 78x^14 - 18x^13 + 360x^12 + 482x^11 + 614x^10 + 594x^9 + 565x^8 + 686x^7 + 1552x^6 + 1286x^5 - 133x^4 - 970x^3 - 402x^2 + 102x + 115	\( 2^{30}\cdot 47^{10} \)	$C_2^4:D_5$ (as 20T45)	$[2]$ (GRH)
20.0.56477888187717354967269376.3	x^20 + 22x^18 + 208x^16 + 1112x^14 + 3856x^12 + 9184x^10 + 15424x^8 + 17792x^6 + 13312x^4 + 5632x^2 + 1024	\( 2^{30}\cdot 47^{10} \)	$D_{10}$ (as 20T4)	$[4]$
20.0.57722337794481266110634089.1	x^20 - 5x^19 + 15x^18 - 24x^17 + 15x^16 + 22x^15 - 57x^14 + 64x^13 - 10x^12 - 57x^11 + 95x^10 - 57x^9 - 10x^8 + 64x^7 - 57x^6 + 22x^5 + 15x^4 - 24x^3 + 15x^2 - 5x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T263	$[2]$ (GRH)
20.0.57722337794481266110634089.2	x^20 - 3x^19 + 10x^18 - 31x^17 + 95x^16 - 194x^15 + 426x^14 - 662x^13 + 1038x^12 - 1221x^11 + 1283x^10 - 1067x^9 + 753x^8 - 401x^7 + 172x^6 + 7x^5 - 14x^4 - 8x^3 + 8x^2 + 4x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T263	$[2]$
20.0.57722337794481266110634089.3	x^20 - 5x^19 + 17x^18 - 29x^17 + 27x^16 - 2x^15 - 36x^14 + 32x^13 + 3x^12 - 45x^11 + 88x^10 - 95x^9 + 136x^8 - 123x^7 + 101x^6 - 31x^5 + 64x^4 - 9x^3 + 21x^2 - 7x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T263	$[2]$
20.0.57722337794481266110634089.4	x^20 - x^19 + 6x^18 - x^17 + 10x^16 - 48x^15 + 49x^14 - 24x^13 + 58x^12 - 161x^11 + 114x^10 - 49x^9 + 136x^8 - 224x^7 + 356x^6 - 315x^5 + 194x^4 - 83x^3 + 21x^2 + 3x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T263	$[2]$
20.0.57722337794481266110634089.5	x^20 - 2x^19 + 3x^18 + 3x^16 + 12x^15 + 16x^14 + 69x^13 + 79x^12 + 29x^11 + 37x^10 - 29x^9 + 79x^8 - 69x^7 + 16x^6 - 12x^5 + 3x^4 + 3x^2 + 2x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T341	$[2]$ (GRH)
20.0.57722337794481266110634089.6	x^20 + 13x^18 + 73x^16 + 235x^14 + 481x^12 + 660x^10 + 633x^8 + 445x^6 + 296x^4 + 43x^2 + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T341	$[2]$ (GRH)
20.0.57722337794481266110634089.7	x^20 - 10x^19 + 52x^18 - 180x^17 + 461x^16 - 899x^15 + 1328x^14 - 1354x^13 + 507x^12 + 1410x^11 - 3813x^10 + 5599x^9 - 5270x^8 + 2768x^7 + 1115x^6 - 4240x^5 + 5356x^4 - 4383x^3 + 2573x^2 - 1021x + 197	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T341	$[2]$ (GRH)
20.0.57722337794481266110634089.8	x^20 - 2x^19 + 8x^18 - 8x^17 + 19x^16 + 22x^15 + x^14 + 90x^13 - 10x^12 + 102x^11 + 95x^10 - 124x^9 + 320x^8 - 431x^7 + 694x^6 - 363x^5 + 591x^4 - 322x^3 + 195x^2 - 20x + 1	\( 11^{16}\cdot 23^{4}\cdot 67^{2} \)	20T341	$[2]$ (GRH)
20.0.92463633619402804697265625.1	x^20 - 6x^19 + 17x^18 - 34x^17 + 72x^16 - 142x^15 + 230x^14 - 374x^13 + 667x^12 - 926x^11 + 1464x^10 - 4142x^9 + 10155x^8 - 17489x^7 + 24262x^6 - 26479x^5 + 20704x^4 - 10840x^3 + 3907x^2 - 1407x + 441	\( 5^{10}\cdot 79^{10} \)	$D_{10}$ (as 20T4)	$[4]$
20.0.99984128957797575628203125.1	x^20 - 3x^19 + 14x^18 - 42x^17 + 118x^16 - 271x^15 + 620x^14 - 1111x^13 + 2016x^12 - 3054x^11 + 4174x^10 - 5147x^9 + 5378x^8 - 4516x^7 + 3536x^6 - 1447x^5 + 525x^4 + 131x^3 - 270x^2 + 28x + 29	\( 5^{7}\cdot 61^{6}\cdot 397^{4} \)	20T790	$[2]$ (GRH)
20.0.100564814293580902500000000.1	x^20 - 6x^19 + 14x^18 - 24x^17 + 80x^16 - 266x^15 + 553x^14 - 784x^13 + 1007x^12 - 1370x^11 + 1591x^10 - 1370x^9 + 1007x^8 - 784x^7 + 553x^6 - 266x^5 + 80x^4 - 24x^3 + 14x^2 - 6x + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{10}\cdot 19^{10} \)	$D_5\wr C_2$ (as 20T55)	$[4]$
20.0.104226732560060708467769344.1	x^20 - 2x^16 + 2x^14 - 3x^12 + 5x^10 - 3x^8 + 2x^6 - 2x^4 + 1	\( 2^{20}\cdot 17^{2}\cdot 61^{4}\cdot 397^{4} \)	20T368	$[3]$ (GRH)

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