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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.4.1555892820924979549874521.2	x^20 - 4x^19 + 14x^18 - 37x^17 + 87x^16 - 186x^15 + 339x^14 - 555x^13 + 794x^12 - 988x^11 + 1066x^10 - 953x^9 + 679x^8 - 326x^7 + 45x^6 + 76x^5 - 75x^4 + 27x^3 - 2x^2 - 2x + 1	\( 11^{18}\cdot 23^{4} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	Trivial
20.8.1555892820924979549874521.2	x^20 - x^19 - 11x^18 + 12x^17 + 43x^16 - 44x^15 - 76x^14 + 65x^13 + 66x^12 - 32x^11 - 45x^10 - 32x^9 + 66x^8 + 65x^7 - 76x^6 - 44x^5 + 43x^4 + 12x^3 - 11x^2 - x + 1	\( 11^{18}\cdot 23^{4} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	Trivial (GRH)
20.4.1555892820924979549874521.3	x^20 - 2x^19 - 2x^18 + 16x^17 - 9x^16 - 12x^15 - 10x^14 + 81x^13 - 80x^12 + 4x^11 - x^10 + 2x^9 + 24x^8 - 71x^7 + 20x^6 + 23x^5 - 34x^4 + 7x^3 + 3x^2 - 4x + 1	\( 11^{18}\cdot 23^{4} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	Trivial
20.8.1555892820924979549874521.3	x^20 - 5x^19 + 11x^18 - 7x^17 - 31x^16 + 121x^15 - 226x^14 + 239x^13 - 55x^12 - 277x^11 + 527x^10 - 490x^9 + 231x^8 + 7x^7 - 79x^6 + 66x^5 - 60x^4 + 25x^3 + 11x^2 - 9x + 1	\( 11^{18}\cdot 23^{4} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	Trivial (GRH)
20.4.348841672023202139208688921.1	x^20 - 2x^19 - 3x^18 - 2x^17 + 3x^16 + 19x^15 + 40x^14 - 48x^13 - 96x^12 - 44x^11 - 10x^10 + 110x^9 + 4x^8 - 107x^7 - 45x^6 + 69x^5 + x^4 - 34x^3 + 17x^2 - 5x + 1	\( 11^{18}\cdot 89^{4} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	Trivial
20.4.348841672023202139208688921.2	x^20 - 3x^19 + 7x^18 - 15x^17 + 20x^16 - 19x^15 - 5x^14 - 2x^13 + 27x^12 - 10x^10 + 66x^9 - 2x^8 - 49x^7 - 69x^6 + 19x^5 - 7x^4 - 17x^3 + 21x^2 - 7x + 1	\( 11^{18}\cdot 89^{4} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	Trivial
20.12.823067302269314181883621609.1	x^20 - x^19 - 16x^18 + 22x^17 + 96x^16 - 184x^15 - 293x^14 + 814x^13 + 493x^12 - 2154x^11 - 276x^10 + 3939x^9 - 402x^8 - 5522x^7 - 162x^6 + 4485x^5 + 909x^4 - 1760x^3 - 537x^2 + 262x + 89	\( 11^{18}\cdot 23^{6} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	Trivial (GRH)
20.12.823067302269314181883621609.2	x^20 - 7x^19 + 9x^18 + 30x^17 - 53x^16 - 48x^15 - 52x^14 + 227x^13 + 645x^12 - 780x^11 - 1508x^10 + 1074x^9 + 1740x^8 - 558x^7 - 981x^6 + 92x^5 + 261x^4 + 4x^3 - 29x^2 - x + 1	\( 11^{18}\cdot 23^{6} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	Trivial (GRH)
20.4.823067302269314181883621609.3	x^20 - 4x^18 - 11x^17 + 5x^16 - 11x^15 - 53x^14 - 143x^13 - 30x^12 - 176x^11 - 342x^10 - 506x^9 + 103x^8 + 264x^7 + 72x^6 - 176x^5 - 68x^4 + 44x^3 + 30x^2 + 11x + 1	\( 11^{18}\cdot 23^{6} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	$[2]$
20.4.823067302269314181883621609.4	x^20 - 4x^18 + 5x^16 - 9x^14 - 22x^13 - 118x^12 - 154x^11 + 263x^10 + 11x^9 - 986x^8 - 594x^7 + 402x^6 + 385x^5 - 123x^4 - 88x^3 + 52x^2 - 11x + 1	\( 11^{18}\cdot 23^{6} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	$[2]$
20.0.5969915757478328440239161344.2	x^20 - 8x^19 + 22x^18 - 16x^17 + 7x^16 - 264x^15 + 1048x^14 - 1674x^13 + 1331x^12 - 2446x^11 + 8590x^10 - 14490x^9 + 10032x^8 - 5132x^7 + 26778x^6 - 70730x^5 + 91781x^4 - 67450x^3 + 28094x^2 - 5980x + 529	\( 2^{30}\cdot 11^{18} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	$[2]$
20.0.5969915757478328440239161344.3	x^20 - 8x^19 + 22x^18 + 6x^17 - 147x^16 + 198x^15 + 322x^14 - 948x^13 + 44x^12 + 1888x^11 - 1288x^10 - 1752x^9 + 2255x^8 + 522x^7 - 1580x^6 + 286x^5 + 591x^4 - 438x^3 + 132x^2 - 18x + 1	\( 2^{30}\cdot 11^{18} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	$[2]$
20.0.6113193735657808322804901216256.1	x^20 - 12x^18 + 67x^16 - 232x^14 + 551x^12 - 826x^10 + 364x^8 + 1352x^6 - 2903x^4 + 2166x^2 + 1	\( 2^{40}\cdot 11^{18} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	$[2]$ (GRH)
20.8.6113193735657808322804901216256.1	x^20 + 2x^18 - 7x^16 - 14x^14 - 28x^12 + 32x^10 + 31x^8 + 150x^6 - 85x^4 - 16x^2 + 1	\( 2^{40}\cdot 11^{18} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	Trivial (GRH)
20.0.6113193735657808322804901216256.2	x^20 + 6x^18 + 14x^16 + 62x^14 + 185x^12 + 340x^10 + 808x^8 + 1350x^6 + 1764x^4 + 1212x^2 + 529	\( 2^{40}\cdot 11^{18} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	$[2]$ (GRH)
20.8.6113193735657808322804901216256.2	x^20 - 4x^18 - 6x^16 + 90x^14 - 283x^12 + 406x^10 - 480x^8 + 226x^6 + 20x^4 - 14x^2 + 1	\( 2^{40}\cdot 11^{18} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	Trivial (GRH)
20.4.6113193735657808322804901216256.3	x^20 + 8x^18 + 31x^16 + 94x^14 + 15x^12 - 518x^10 - 173x^8 + 200x^6 - 94x^4 - 4x^2 + 1	\( 2^{40}\cdot 11^{18} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	Trivial (GRH)
20.4.6113193735657808322804901216256.4	x^20 + 6x^18 + 3x^16 + 62x^14 - 13x^12 - 320x^10 - 424x^8 - 256x^6 - 51x^4 + 2x^2 + 1	\( 2^{40}\cdot 11^{18} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	Trivial (GRH)
20.0.13806836326351181066487331815424.1	x^20 - 4x^19 + 18x^18 - 18x^17 + 81x^16 - 52x^15 + 324x^14 + 740x^13 + 1872x^12 + 430x^11 + 5848x^10 - 9186x^9 + 28503x^8 - 33322x^7 + 53696x^6 - 59590x^5 + 72747x^4 - 49020x^3 + 12646x^2 - 414x + 529	\( 2^{30}\cdot 11^{16}\cdot 23^{4} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	$[4, 8]$ (GRH)
20.0.13806836326351181066487331815424.2	x^20 - 4x^19 + 18x^18 - 40x^17 + 103x^16 - 338x^15 + 500x^14 - 140x^13 + 5007x^12 + 3444x^11 + 11502x^10 - 1420x^9 + 14599x^8 - 5866x^7 + 18276x^6 - 7274x^5 + 13842x^4 - 4690x^3 + 5254x^2 - 2944x + 529	\( 2^{30}\cdot 11^{16}\cdot 23^{4} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	$[4, 8]$ (GRH)
20.0.1670627195488492909044967149666304.1	x^20 - 4x^19 + 8x^18 + 200x^16 - 1328x^15 + 4372x^14 - 12254x^13 + 31178x^12 - 63948x^11 + 140920x^10 - 242876x^9 + 288907x^8 - 566126x^7 + 836746x^6 - 287708x^5 - 119520x^4 - 97790x^3 + 56910x^2 + 37372x + 5039	\( 2^{30}\cdot 11^{18}\cdot 23^{4} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	$[2, 2, 12]$ (GRH)
20.20.1670627195488492909044967149666304.1	x^20 - 4x^19 - 42x^18 + 158x^17 + 759x^16 - 2520x^15 - 7938x^14 + 21338x^13 + 52829x^12 - 104808x^11 - 227556x^10 + 305624x^9 + 621926x^8 - 519716x^7 - 1030838x^6 + 485792x^5 + 956087x^4 - 221306x^3 - 422874x^2 + 38132x + 58147	\( 2^{30}\cdot 11^{18}\cdot 23^{4} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	Trivial (GRH)
20.0.1670627195488492909044967149666304.2	x^20 - 2x^19 + 10x^18 + 12x^17 + 14x^16 + 44x^15 - 268x^14 + 668x^13 + 6945x^12 + 11260x^11 + 21262x^10 + 61954x^9 + 99859x^8 + 97580x^7 + 101736x^6 - 18128x^5 - 201043x^4 - 289242x^3 - 17626x^2 + 111368x + 145993	\( 2^{30}\cdot 11^{18}\cdot 23^{4} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	$[2, 2, 12]$ (GRH)
20.20.1670627195488492909044967149666304.2	x^20 - 4x^19 - 50x^18 + 222x^17 + 597x^16 - 3334x^15 - 1756x^14 + 20532x^13 - 7328x^12 - 55058x^11 + 44056x^10 + 60786x^9 - 64339x^8 - 29546x^7 + 38280x^6 + 6028x^5 - 9317x^4 - 396x^3 + 638x^2 - 11	\( 2^{30}\cdot 11^{18}\cdot 23^{4} \)	$C_2^2\times C_2^4:C_5$ (as 20T74)	Trivial (GRH)