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 88)

Label	Polynomial	Discriminant	Galois group	Class group
20.4.523132485570902216409088.1	x^20 - 2x^19 + 6x^18 - 8x^17 + 11x^16 - 6x^15 - 4x^14 + 14x^13 - 20x^12 + 14x^11 - 16x^10 + 14x^9 - 20x^8 + 14x^7 - 4x^6 - 6x^5 + 11x^4 - 8x^3 + 6x^2 - 2x + 1	\( 2^{20}\cdot 13^{9}\cdot 19^{6} \)	20T991	Trivial (GRH)
20.2.1940164150557599013535744.1	x^20 - x^18 - 3x^16 + 2x^14 - 7x^12 - 3x^10 + 23x^8 + 6x^6 - 13x^4 - 5x^2 - 1	\( -\,2^{32}\cdot 277^{6} \)	20T991	Trivial (GRH)
20.2.1940164150557599013535744.2	x^20 + x^18 - 3x^16 - 2x^14 - 7x^12 + 3x^10 + 23x^8 - 6x^6 - 13x^4 + 5x^2 - 1	\( -\,2^{32}\cdot 277^{6} \)	20T991	Trivial (GRH)
20.4.8370119769134435462545408.1	x^20 - 3x^18 - 2x^17 - 7x^16 + 34x^15 + 6x^14 - 48x^13 - 75x^12 + 146x^11 - 17x^10 - 88x^9 - 15x^8 + 138x^7 - 34x^6 - 64x^5 + 37x^4 + 22x^3 - 27x^2 + 10x - 1	\( 2^{24}\cdot 13^{9}\cdot 19^{6} \)	20T991	Trivial
20.2.10301685869703920569286656.1	x^20 + 5x^18 + x^16 - 26x^14 - 27x^12 + 31x^10 + 87x^8 + 82x^6 + 23x^4 - 7x^2 - 1	\( -\,2^{28}\cdot 13^{8}\cdot 19^{6} \)	20T991	Trivial (GRH)
20.6.10301685869703920569286656.1	x^20 - 5x^18 + x^16 + 26x^14 - 27x^12 - 31x^10 + 87x^8 - 82x^6 + 23x^4 + 7x^2 - 1	\( -\,2^{28}\cdot 13^{8}\cdot 19^{6} \)	20T991	Trivial (GRH)
20.2.22743500561450963169808384.1	x^20 + 2x^18 - 11x^16 - 25x^14 - 10x^12 - 31x^10 - 67x^8 - 27x^6 - 18x^4 - 21x^2 - 1	\( -\,2^{12}\cdot 19^{8}\cdot 83^{6} \)	20T991	Trivial (GRH)
20.6.22743500561450963169808384.1	x^20 - 2x^16 - 10x^14 - 14x^12 + 11x^10 + 51x^8 - 13x^6 - x^4 - 6x^2 - 1	\( -\,2^{12}\cdot 19^{8}\cdot 83^{6} \)	20T991	Trivial (GRH)
20.0.27104363606861854379873280.1	x^20 + 11x^18 + 53x^16 + 149x^14 + 279x^12 + 386x^10 + 429x^8 + 377x^6 + 217x^4 + 56x^2 + 5	\( 2^{10}\cdot 3^{16}\cdot 5\cdot 223^{6} \)	20T991	Trivial (GRH)
20.0.69444256701301056709723521.1	x^20 - 9x^19 + 43x^18 - 139x^17 + 328x^16 - 582x^15 + 779x^14 - 774x^13 + 547x^12 - 275x^11 + 137x^10 - 90x^9 + 52x^8 + x^7 - 7x^6 - 2x^5 + x^4 + 11x^3 + 6x^2 + 3x + 1	\( 3^{4}\cdot 17^{6}\cdot 97^{6}\cdot 42641 \)	20T991	Trivial (GRH)
20.0.71786073570631163500822528.1	x^20 + 11x^18 + 55x^16 + 168x^14 + 355x^12 + 553x^10 + 651x^8 + 574x^6 + 365x^4 + 157x^2 + 37	\( 2^{32}\cdot 37\cdot 277^{6} \)	20T991	Trivial (GRH)
20.4.71786073570631163500822528.1	x^20 - 11x^18 + 55x^16 - 168x^14 + 355x^12 - 553x^10 + 651x^8 - 574x^6 + 365x^4 - 157x^2 + 37	\( 2^{32}\cdot 37\cdot 277^{6} \)	20T991	Trivial (GRH)
20.4.110997640035709136878436352.1	x^20 - 12x^18 + 64x^16 - 204x^14 + 436x^12 - 664x^10 + 744x^8 - 616x^6 + 364x^4 - 140x^2 + 28	\( 2^{32}\cdot 3^{22}\cdot 7^{7} \)	20T991	Trivial (GRH)
20.0.173467927083915868031188992.1	x^20 + 5x^18 + 23x^16 + 65x^14 + 150x^12 + 263x^10 + 360x^8 + 476x^6 + 496x^4 + 128x^2 + 32	\( 2^{15}\cdot 3^{16}\cdot 223^{6} \)	20T991	Trivial (GRH)
20.0.2142750660898415478411624448.1	x^20 + 3x^18 + 3x^16 + 14x^14 - 31x^12 - 27x^10 + 237x^8 - 238x^6 - 117x^4 + 143x^2 + 13	\( 2^{32}\cdot 13^{9}\cdot 19^{6} \)	20T991	Trivial (GRH)
20.4.2142750660898415478411624448.1	x^20 + 3x^18 - 5x^16 - 16x^14 + 43x^12 + 73x^10 - 37x^8 - 6x^6 + 13x^4 - 39x^2 + 13	\( 2^{32}\cdot 13^{9}\cdot 19^{6} \)	20T991	Trivial (GRH)
20.8.2142750660898415478411624448.1	x^20 - 3x^18 + 3x^16 - 14x^14 - 31x^12 + 27x^10 + 237x^8 + 238x^6 - 117x^4 - 143x^2 + 13	\( 2^{32}\cdot 13^{9}\cdot 19^{6} \)	20T991	Trivial (GRH)
20.0.2142750660898415478411624448.2	x^20 + 9x^16 + 4x^14 - 14x^12 + 228x^10 + 450x^8 + 100x^6 - 91x^4 + 52x^2 + 13	\( 2^{32}\cdot 13^{9}\cdot 19^{6} \)	20T991	Trivial (GRH)
20.4.2142750660898415478411624448.2	x^20 - 3x^18 - 5x^16 + 16x^14 + 43x^12 - 73x^10 - 37x^8 + 6x^6 + 13x^4 + 39x^2 + 13	\( 2^{32}\cdot 13^{9}\cdot 19^{6} \)	20T991	Trivial (GRH)
20.8.2142750660898415478411624448.2	x^20 + 9x^16 - 4x^14 - 14x^12 - 228x^10 + 450x^8 - 100x^6 - 91x^4 - 52x^2 + 13	\( 2^{32}\cdot 13^{9}\cdot 19^{6} \)	20T991	Trivial (GRH)
20.4.142432138540189229008893575168.1	x^20 - 10x^19 + 48x^18 - 147x^17 + 313x^16 - 464x^15 + 432x^14 - 106x^13 - 370x^12 + 608x^11 - 370x^10 - 92x^9 + 285x^8 - 56x^7 - 224x^6 + 225x^5 - 62x^4 - 32x^3 + 30x^2 - 9x + 1	\( 2^{16}\cdot 11^{8}\cdot 157^{6}\cdot 677 \)	20T991	Trivial (GRH)
20.2.206548481879697235603429344256.2	x^20 - 2x^19 - 4x^18 + 16x^17 - 8x^16 - 17x^15 + 49x^14 - 73x^13 - 73x^12 + 346x^11 + 33x^10 - 639x^9 + 224x^8 + 652x^7 - 163x^6 - 235x^5 + 138x^4 + 111x^3 + 5x^2 - 9x + 1	\( -\,2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T991	$[2]$ (GRH)
20.2.206548481879697235603429344256.3	x^20 - x^18 - 34x^16 + 22x^14 + 517x^12 + 391x^10 - 3831x^8 - 9046x^6 - 5787x^4 - 232x^2 - 1	\( -\,2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T991	$[2]$ (GRH)
20.6.206548481879697235603429344256.5	x^20 - 5x^19 + 10x^18 + 3x^17 - 75x^16 + 317x^15 - 895x^14 + 1510x^13 - 435x^12 - 5019x^11 + 15608x^10 - 27590x^9 + 34510x^8 - 32558x^7 + 23555x^6 - 12793x^5 + 4869x^4 - 1113x^3 + 91x^2 + 11x - 1	\( -\,2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T991	Trivial (GRH)
20.6.206548481879697235603429344256.6	x^20 - 2x^18 - 70x^16 - 65x^14 + 322x^12 + 8x^10 - 2099x^8 - 353x^6 + 1783x^4 - 452x^2 - 1	\( -\,2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T991	Trivial (GRH)
20.6.206548481879697235603429344256.7	x^20 - 8x^16 - 11x^14 - 38x^12 + 51x^10 + 149x^8 - 12x^6 + 35x^4 - 15x^2 - 1	\( -\,2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T991	Trivial (GRH)
20.6.206548481879697235603429344256.8	x^20 - 5x^18 + 22x^16 - 10x^14 + 30x^12 - 204x^10 - 866x^8 + 369x^6 + 466x^4 - 29x^2 - 25	\( -\,2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T991	Trivial (GRH)
20.10.12599457394661531371809189999616.1	x^20 - 13x^18 + 11x^16 + 451x^14 - 2685x^12 + 5672x^10 - 3972x^8 + 1199x^6 - 3518x^4 + 1891x^2 - 61	\( -\,2^{10}\cdot 61^{7}\cdot 397^{6} \)	20T991	Trivial (GRH)
20.2.12599457394661531371809189999616.1	x^20 + 2x^18 - 30x^16 - 330x^14 - 1971x^12 - 6098x^10 - 12557x^8 - 21228x^6 - 16165x^4 - 9272x^2 - 61	\( -\,2^{10}\cdot 61^{7}\cdot 397^{6} \)	20T991	Trivial (GRH)
20.10.12599457394661531371809189999616.2	x^20 + x^18 - 68x^16 - 183x^14 + 1140x^12 + 4350x^10 - 1914x^8 - 15336x^6 - 948x^4 + 965x^2 - 61	\( -\,2^{10}\cdot 61^{7}\cdot 397^{6} \)	20T991	Trivial (GRH)
20.2.12599457394661531371809189999616.2	x^20 - 5x^19 + 9x^18 - 46x^17 + 131x^16 - 132x^15 + 453x^14 - 604x^13 + 589x^12 - 941x^11 + 503x^10 - 987x^9 + 720x^8 - 113x^7 + 12x^6 + 414x^5 + 17x^4 + 16x^3 + 23x^2 - 2x + 1	\( -\,2^{10}\cdot 61^{7}\cdot 397^{6} \)	20T991	Trivial (GRH)
20.0.12599457394661531371809189999616.1	x^20 - 5x^19 + 14x^18 - 15x^17 + 6x^16 - 54x^15 + 291x^14 - 498x^13 + 253x^12 - 140x^11 + 2013x^10 - 4914x^9 + 3660x^8 + 492x^7 + 5176x^6 - 21807x^5 + 29715x^4 - 20227x^3 + 7520x^2 - 1847x + 383	\( 2^{10}\cdot 61^{7}\cdot 397^{6} \)	20T991	$[2]$ (GRH)
20.4.12599457394661531371809189999616.4	x^20 - 5x^19 + 22x^18 - 59x^17 + 98x^16 - 152x^15 - x^14 - 185x^13 + 56x^12 - 286x^11 - 408x^10 + 4051x^9 - 396x^8 - 4433x^7 + 440x^6 + 865x^5 + 1291x^4 - 958x^3 + 234x^2 - 41x + 5	\( 2^{10}\cdot 61^{7}\cdot 397^{6} \)	20T991	Trivial (GRH)
20.12.12599457394661531371809189999616.6	x^20 - 6x^19 - 2x^18 + 66x^17 - 96x^16 - 103x^15 + 550x^14 - 908x^13 - 475x^12 + 3076x^11 - 2806x^10 + 166x^9 + 6114x^8 - 9527x^7 + 310x^6 + 6221x^5 - 5696x^4 + 5176x^3 - 2626x^2 + 335x + 25	\( 2^{10}\cdot 61^{7}\cdot 397^{6} \)	20T991	Trivial (GRH)
20.8.12599457394661531371809189999616.6	x^20 - 3x^18 - 13x^16 + 40x^14 + 59x^12 - 159x^10 - 200x^8 + 243x^6 + 515x^4 - 549x^2 + 61	\( 2^{10}\cdot 61^{7}\cdot 397^{6} \)	20T991	Trivial (GRH)
20.8.12599457394661531371809189999616.7	x^20 - 14x^18 + 31x^16 + 314x^14 - 1598x^12 + 1750x^10 + 779x^8 - 2002x^6 + 5573x^4 + 6954x^2 + 1525	\( 2^{10}\cdot 61^{7}\cdot 397^{6} \)	20T991	Trivial (GRH)
20.0.57897378198158198109548515679232.1	x^20 - 2x^19 + 4x^18 - 16x^17 + 15x^16 - 17x^15 + 62x^14 + 6x^13 + 62x^12 - 286x^11 - 273x^10 - 59x^9 + 785x^8 + 1332x^7 + 1247x^6 + 797x^5 + 294x^4 + 148x^3 + 88x^2 + 14x + 1	\( 2^{10}\cdot 3^{24}\cdot 7^{7}\cdot 79^{6} \)	20T991	$[2]$ (GRH)
20.4.57897378198158198109548515679232.1	x^20 - 7x^18 + 38x^16 - 183x^14 + 194x^12 + 196x^10 - 135x^8 - 539x^6 - 553x^4 - 203x^2 + 7	\( 2^{10}\cdot 3^{24}\cdot 7^{7}\cdot 79^{6} \)	20T991	Trivial (GRH)
20.0.81999747306239802534561449669632.1	x^20 - 9x^18 - 10x^16 - 106x^14 + 724x^12 + 6232x^10 + 23175x^8 + 83273x^6 + 121430x^4 + 199264x^2 + 210013	\( 2^{10}\cdot 61^{6}\cdot 397^{7} \)	20T991	$[2]$ (GRH)
20.4.81999747306239802534561449669632.1	x^20 - 2x^19 + 2x^17 - 10x^16 + 101x^15 - 129x^14 + 632x^13 + 853x^12 + 998x^11 + 2603x^10 - 5099x^9 + 4759x^8 - 9811x^7 - 26495x^6 + 40318x^5 - 85758x^4 + 83418x^3 - 46331x^2 + 25091x - 5141	\( 2^{10}\cdot 61^{6}\cdot 397^{7} \)	20T991	Trivial (GRH)
20.0.81999747306239802534561449669632.2	x^20 - 2x^19 + 12x^18 - 32x^17 + 94x^16 - 270x^15 + 691x^14 - 1172x^13 + 1047x^12 - 50x^11 - 204x^10 + 526x^9 - 2582x^8 + 6414x^7 - 5598x^6 - 4576x^5 + 11756x^4 - 6856x^3 + 1997x^2 - 320x + 25	\( 2^{10}\cdot 61^{6}\cdot 397^{7} \)	20T991	$[2]$ (GRH)
20.4.81999747306239802534561449669632.2	x^20 + 8x^18 + 8x^16 + 370x^14 + 2095x^12 - 6581x^10 - 15355x^8 + 20686x^6 + 35254x^4 - 64370x^2 + 397	\( 2^{10}\cdot 61^{6}\cdot 397^{7} \)	20T991	Trivial (GRH)
20.10.97182738115842943341316071817216.1	x^20 + 12x^18 - 17x^16 - 369x^14 + 374x^12 + 1239x^10 - 2070x^8 + 837x^6 + 17x^4 - 39x^2 - 1	\( -\,2^{16}\cdot 33769^{6} \)	20T991	Trivial (GRH)
20.14.97182738115842943341316071817216.1	x^20 - 10x^18 - 49x^16 + 213x^14 + 134x^12 - 1182x^10 + 1488x^8 - 660x^6 + 38x^4 + 29x^2 - 1	\( -\,2^{16}\cdot 33769^{6} \)	20T991	Trivial (GRH)
20.6.97182738115842943341316071817216.1	x^20 + 21x^18 + 122x^16 + 150x^14 - 384x^12 - 564x^10 + 418x^8 + 331x^6 - 91x^4 - 46x^2 - 1	\( -\,2^{16}\cdot 33769^{6} \)	20T991	Trivial (GRH)
20.10.97182738115842943341316071817216.2	x^20 + x^18 - 118x^16 + 256x^14 + 1392x^12 - 1812x^10 - 3970x^8 + 3271x^6 + 3173x^4 - 1636x^2 - 1	\( -\,2^{16}\cdot 33769^{6} \)	20T991	Trivial (GRH)
20.14.97182738115842943341316071817216.2	x^20 - 3x^18 - 55x^16 + 113x^14 + 841x^12 - 944x^10 - 1796x^8 + 2544x^6 - 1152x^4 + 224x^2 - 16	\( -\,2^{16}\cdot 33769^{6} \)	20T991	Trivial (GRH)
20.10.523384101330090034436064084345856.1	x^20 - 5x^18 - 60x^16 + 262x^14 + 617x^12 - 1609x^10 - 2261x^8 + 1804x^6 + 1429x^4 - 754x^2 - 1	\( -\,2^{10}\cdot 89417^{6} \)	20T991	Trivial (GRH)
20.6.523384101330090034436064084345856.1	x^20 + 21x^18 + 91x^16 - 89x^14 - 617x^12 + 70x^10 + 1071x^8 - 23x^6 - 151x^4 - 26x^2 - 1	\( -\,2^{10}\cdot 89417^{6} \)	20T991	Trivial (GRH)
20.10.523384101330090034436064084345856.2	x^20 - x^18 - 61x^16 + 51x^14 + 1064x^12 - 1025x^10 - 5285x^8 + 4560x^6 + 5489x^4 - 3623x^2 - 9	\( -\,2^{10}\cdot 89417^{6} \)	20T991	Trivial (GRH)