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 66)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.33170570354885225234441216.1	x^20 + 12x^18 + 77x^16 + 306x^14 + 761x^12 + 1181x^10 + 1183x^8 + 906x^6 + 660x^4 + 367x^2 + 89	\( 2^{10}\cdot 11^{16}\cdot 89^{3} \)	20T747	Trivial (GRH)
20.4.33170570354885225234441216.1	x^20 - 4x^18 + 11x^16 - 59x^14 + 138x^12 - 59x^10 - 174x^8 + 145x^6 + 165x^4 - 254x^2 + 89	\( 2^{10}\cdot 11^{16}\cdot 89^{3} \)	20T747	Trivial (GRH)
20.0.33170570354885225234441216.2	x^20 + x^18 + 5x^16 - 11x^15 + 2x^14 - 11x^13 + 49x^12 - 33x^11 + 29x^10 - 88x^9 + 130x^8 - 99x^7 + 87x^6 - 110x^5 + 133x^4 - 99x^3 + 47x^2 - 11x + 1	\( 2^{10}\cdot 11^{16}\cdot 89^{3} \)	20T747	Trivial (GRH)
20.4.33170570354885225234441216.2	x^20 - x^19 - 6x^18 + 9x^17 - 14x^15 + 51x^14 - 12x^13 - 145x^12 + 104x^11 + 132x^10 - 185x^9 + 183x^7 - 74x^6 - 127x^5 + 10x^4 + 43x^3 + 9x^2 - 1	\( 2^{10}\cdot 11^{16}\cdot 89^{3} \)	20T747	Trivial (GRH)
20.4.658618684118710741619590144.1	x^20 - 6x^19 + 13x^18 - 3x^17 - 49x^16 + 127x^15 - 169x^14 + 139x^13 - 4x^12 - 455x^11 + 1540x^10 - 2864x^9 + 2801x^8 + 189x^7 - 5095x^6 + 8435x^5 - 7898x^4 + 4764x^3 - 1844x^2 + 420x - 43	\( 2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.8.658618684118710741619590144.1	x^20 - x^19 - 14x^18 + 22x^17 + 75x^16 - 193x^15 - 127x^14 + 818x^13 - 515x^12 - 1362x^11 + 2420x^10 - 684x^9 - 1878x^8 + 2782x^7 - 2143x^6 + 1178x^5 - 533x^4 + 200x^3 - 57x^2 + 11x - 1	\( 2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.4.658618684118710741619590144.2	x^20 - 10x^19 + 44x^18 - 109x^17 + 148x^16 - 38x^15 - 316x^14 + 937x^13 - 1784x^12 + 2717x^11 - 3388x^10 + 3494x^9 - 3097x^8 + 2450x^7 - 1666x^6 + 786x^5 - 32x^4 - 297x^3 + 210x^2 - 30x - 43	\( 2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.8.658618684118710741619590144.2	x^20 - 6x^19 + 11x^18 - 2x^17 + 2x^16 - 69x^15 + 121x^14 + 84x^13 - 547x^12 + 918x^11 - 1067x^10 + 1065x^9 - 471x^8 - 944x^7 + 2035x^6 - 1684x^5 + 530x^4 + 141x^3 - 133x^2 + 13x + 1	\( 2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.4.658618684118710741619590144.3	x^20 + 8x^18 + 3x^16 - 83x^14 - 167x^12 - 38x^10 - 75x^8 - 501x^6 + 195x^4 + 723x^2 + 241	\( 2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.8.658618684118710741619590144.3	x^20 - 9x^19 + 31x^18 - 48x^17 + 8x^16 + 106x^15 - 199x^14 + 99x^13 + 214x^12 - 222x^11 - 130x^10 - 172x^9 + 60x^8 + 425x^7 + 284x^6 + 53x^5 - 136x^4 - 173x^3 - 101x^2 - 25x + 1	\( 2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.4.658618684118710741619590144.4	x^20 - 7x^19 + 14x^18 + 7x^17 - 47x^16 + 11x^15 + 44x^14 + 95x^13 - 334x^12 + 597x^11 - 1080x^10 + 1237x^9 - 674x^8 + 218x^7 + 69x^6 - 688x^5 + 836x^4 - 468x^3 + 378x^2 - 319x + 67	\( 2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.8.658618684118710741619590144.4	x^20 - 4x^19 - 5x^18 + 35x^17 + 18x^16 - 232x^15 + 175x^14 + 489x^13 - 598x^12 - 342x^11 + 198x^10 + 520x^9 + 327x^8 - 630x^7 - 81x^6 + 23x^5 + 373x^4 - 315x^3 + 107x^2 - 17x + 1	\( 2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.4.658618684118710741619590144.5	x^20 - x^19 + 6x^18 + 5x^17 - 5x^16 + 47x^15 + 14x^14 - 48x^13 + 138x^12 + 119x^11 - 550x^10 + 1000x^9 - 909x^8 + 171x^7 + 576x^6 - 995x^5 + 661x^4 - 298x^3 - 8x^2 + 32x - 23	\( 2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.4.658618684118710741619590144.6	x^20 - 7x^19 + 15x^18 + 7x^17 - 77x^16 + 100x^15 + 52x^14 - 307x^13 + 324x^12 + 167x^11 - 638x^10 + 200x^9 + 262x^8 + 102x^7 + 592x^6 - 351x^5 - 1101x^4 - 346x^3 + 187x^2 + 83x - 1	\( 2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.2.3830789095830880837568561152.1	x^20 - 3x^18 - 5x^16 + 55x^14 + 26x^12 - 202x^10 - 28x^8 + 275x^6 + 21x^4 - 86x^2 - 43	\( -\,2^{20}\cdot 11^{16}\cdot 43^{3} \)	20T747	Trivial (GRH)
20.6.3830789095830880837568561152.1	x^20 - 3x^18 - 5x^16 + 33x^14 - 7x^12 - 81x^10 - 39x^8 + 165x^6 + 54x^4 - 86x^2 - 43	\( -\,2^{20}\cdot 11^{16}\cdot 43^{3} \)	20T747	Trivial (GRH)
20.2.3830789095830880837568561152.2	x^20 + 6x^18 + 2x^16 - 33x^14 - 13x^12 + 73x^10 - 21x^8 - 99x^6 + 41x^4 + 43x^2 - 43	\( -\,2^{20}\cdot 11^{16}\cdot 43^{3} \)	20T747	Trivial (GRH)
20.6.3830789095830880837568561152.2	x^20 + 2x^18 - 12x^16 - 44x^14 + 16x^12 + 205x^10 + 114x^8 - 242x^6 - 115x^4 + 129x^2 - 43	\( -\,2^{20}\cdot 11^{16}\cdot 43^{3} \)	20T747	Trivial (GRH)
20.10.18079489015266793067734899712.1	x^20 - 8x^19 + 21x^18 - 16x^17 - 45x^16 + 172x^15 - 230x^14 - 18x^13 + 707x^12 - 1150x^11 + 143x^10 + 1840x^9 - 2440x^8 + 532x^7 + 1897x^6 - 2260x^5 + 986x^4 - 96x^3 - 50x^2 + 14x - 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.14.18079489015266793067734899712.1	x^20 - 6x^19 - 3x^18 + 63x^17 - 9x^16 - 282x^15 - 34x^14 + 628x^13 + 532x^12 - 500x^11 - 1656x^10 - 422x^9 + 2972x^8 + 1787x^7 - 3354x^6 - 3144x^5 + 1146x^4 + 2077x^3 + 548x^2 - 102x - 43	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.2.18079489015266793067734899712.1	x^20 - 6x^19 + 13x^18 - 4x^17 - 26x^16 + 55x^15 - 153x^14 + 528x^13 - 1033x^12 + 1368x^11 - 1527x^10 + 1833x^9 - 1759x^8 + 1108x^7 - 199x^6 - 548x^5 + 984x^4 - 777x^3 + 519x^2 - 641x + 463	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.6.18079489015266793067734899712.1	x^20 - x^19 - 4x^18 + 23x^17 - 73x^16 + 54x^15 + 141x^14 - 599x^13 + 886x^12 - 454x^11 + 163x^10 - 249x^9 - 324x^8 - 205x^7 + 278x^6 + 507x^5 + 523x^4 + 265x^3 + 60x^2 - 2x - 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.10.18079489015266793067734899712.2	x^20 - 6x^19 + 4x^18 + 40x^17 - 104x^16 + 66x^15 + 93x^14 - 38x^13 - 325x^12 + 256x^11 + 88x^10 - 16x^9 - 24x^8 - 326x^7 - 8x^6 + 110x^5 + 98x^4 - 6x^3 - 43x^2 + 8x + 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.14.18079489015266793067734899712.2	x^20 - 8x^19 + 14x^18 + 40x^17 - 164x^16 + 152x^15 + 112x^14 - 599x^13 + 1522x^12 - 1809x^11 - 838x^10 + 4742x^9 - 4663x^8 + 499x^7 + 2314x^6 - 1661x^5 + 226x^4 + 183x^3 - 64x^2 + x + 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.2.18079489015266793067734899712.2	x^20 - 6x^19 + 30x^18 - 115x^17 + 364x^16 - 1024x^15 + 2406x^14 - 5063x^13 + 9144x^12 - 14742x^11 + 20510x^10 - 24620x^9 + 24238x^8 - 19510x^7 + 12870x^6 - 7868x^5 + 4901x^4 - 3053x^3 + 1481x^2 - 514x + 131	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.6.18079489015266793067734899712.2	x^20 - 4x^19 + x^18 + 20x^17 - 26x^16 - 5x^15 - 63x^14 + 132x^13 + 297x^12 - 1121x^11 + 830x^10 + 1546x^9 - 4251x^8 + 796x^7 + 5614x^6 - 895x^5 - 1472x^4 + 68x^3 + 256x^2 - 54x - 43	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.10.18079489015266793067734899712.3	x^20 - 6x^19 - 5x^18 + 72x^17 - 26x^16 - 276x^15 + 170x^14 + 385x^13 - 279x^12 - 19x^11 + 115x^10 - 622x^9 + 94x^8 + 803x^7 - 74x^6 - 639x^5 - 267x^4 + 57x^3 + 62x^2 + 14x + 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.6.18079489015266793067734899712.3	x^20 - 4x^19 + 7x^18 + 6x^17 - 23x^16 + 45x^15 - 119x^14 + 278x^13 - 210x^12 - 71x^11 - 1089x^10 - 466x^9 + 589x^8 + 1550x^7 + 1240x^6 + 111x^5 - 848x^4 - 388x^3 - 240x^2 + 128x + 32	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.10.18079489015266793067734899712.4	x^20 - 6x^19 + 8x^18 + 14x^17 - 54x^16 + 58x^15 + 44x^14 - 66x^13 - 126x^12 + 139x^11 + 112x^10 - 157x^9 + 299x^8 - 770x^7 + 297x^6 + 311x^5 - 13x^4 - 21x^3 - 31x^2 + 3x + 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.6.18079489015266793067734899712.4	x^20 - 5x^19 + 16x^18 - 7x^17 - 56x^16 + 215x^15 - 120x^14 - 319x^13 + 1056x^12 - 228x^11 - 1128x^10 + 2136x^9 + 459x^8 - 2142x^7 + 1387x^6 + 1250x^5 - 1499x^4 - 595x^3 + 401x^2 + 102x - 43	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.10.18079489015266793067734899712.5	x^20 - x^19 - 13x^18 + 43x^17 + 42x^16 - 375x^15 + 370x^14 + 1230x^13 - 3006x^12 - 376x^11 + 8065x^10 - 6050x^9 - 9004x^8 + 13211x^7 + 3162x^6 - 11252x^5 + 79x^4 + 4257x^3 + 271x^2 - 456x - 67	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.6.18079489015266793067734899712.5	x^20 + 5x^18 - 26x^16 - 134x^14 + 193x^12 + 959x^10 - 745x^8 - 2030x^6 + 1545x^4 + 1002x^2 - 727	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.10.18079489015266793067734899712.6	x^20 - x^19 - 12x^18 + 11x^17 + 36x^16 - 56x^15 - 16x^14 + 320x^13 - 24x^12 - 547x^11 - 200x^10 + 158x^9 - 160x^8 - 1217x^7 - 518x^6 + 54x^5 + 389x^4 - 33x^3 - 37x^2 + 2x + 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.6.18079489015266793067734899712.6	x^20 - 5x^19 + 4x^18 + 16x^17 - 39x^16 + 31x^15 + 84x^14 - 295x^13 + 71x^12 + 751x^11 - 862x^10 - 469x^9 + 1625x^8 - 66x^7 - 1980x^6 + 178x^5 + 1712x^4 - 482x^3 - 1640x^2 - 485x + 67	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.6.18079489015266793067734899712.7	x^20 - 8x^19 + 37x^18 - 125x^17 + 307x^16 - 603x^15 + 937x^14 - 1076x^13 + 1040x^12 - 697x^11 + 357x^10 - 639x^9 + 1189x^8 - 2217x^7 + 2302x^6 - 981x^5 + 49x^4 + 280x^3 - 101x^2 + 16x - 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.12.33966664043402470640067805184.1	x^20 - 2x^19 - 15x^18 + 24x^17 + 74x^16 - 84x^15 - 146x^14 + 36x^13 + 185x^12 + 356x^11 - 524x^10 - 850x^9 + 1083x^8 + 786x^7 - 1252x^6 - 312x^5 + 874x^4 + 46x^3 - 292x^2 - 12x + 23	\( 2^{20}\cdot 11^{16}\cdot 89^{3} \)	20T747	Trivial (GRH)
20.8.33966664043402470640067805184.1	x^20 - 10x^19 + 40x^18 - 52x^17 - 153x^16 + 734x^15 - 1036x^14 - 300x^13 + 2758x^12 - 2972x^11 + 364x^10 - 22x^9 + 3775x^8 - 5428x^7 + 1929x^6 + 1364x^5 - 1201x^4 + 118x^3 + 119x^2 - 26x - 1	\( 2^{20}\cdot 11^{16}\cdot 89^{3} \)	20T747	Trivial (GRH)
20.12.33966664043402470640067805184.2	x^20 - 10x^19 + 47x^18 - 138x^17 + 241x^16 - 92x^15 - 728x^14 + 2218x^13 - 3155x^12 + 1380x^11 + 3249x^10 - 6912x^9 + 5386x^8 + 534x^7 - 4750x^6 + 3768x^5 - 704x^4 - 730x^3 + 479x^2 - 84x - 1	\( 2^{20}\cdot 11^{16}\cdot 89^{3} \)	20T747	Trivial (GRH)
20.8.33966664043402470640067805184.2	x^20 - 8x^19 + 22x^18 - 104x^16 + 40x^15 + 657x^14 - 1318x^13 + 175x^12 + 1196x^11 + 1860x^10 - 6248x^9 + 3080x^8 + 4438x^7 - 5650x^6 + 1534x^5 + 730x^4 - 576x^3 + 175x^2 - 26x - 1	\( 2^{20}\cdot 11^{16}\cdot 89^{3} \)	20T747	Trivial (GRH)
20.4.79692860778363999735970407424.1	x^20 - 4x^19 + 8x^18 - 33x^17 + 90x^16 - 140x^15 + 357x^14 - 737x^13 + 961x^12 - 1545x^11 + 2617x^10 - 1767x^9 - 998x^8 + 2299x^7 - 4391x^6 + 15848x^5 - 31388x^4 + 29238x^3 - 8023x^2 - 5187x + 2861	\( 2^{10}\cdot 11^{18}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.8.79692860778363999735970407424.1	x^20 - 2x^19 + 2x^18 - 48x^16 + 41x^15 - 173x^14 - 165x^13 + 324x^12 - 197x^11 + 483x^10 + 871x^9 + 2385x^8 - 3718x^7 + 3205x^6 + 1851x^5 - 1290x^4 - 572x^3 - 38x^2 + 10x + 1	\( 2^{10}\cdot 11^{18}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.8.79692860778363999735970407424.2	x^20 - 10x^19 + 39x^18 - 66x^17 - 25x^16 + 371x^15 - 722x^14 + 396x^13 + 559x^12 - 1443x^11 + 505x^10 + 1693x^9 - 666x^8 - 968x^7 + 1257x^6 - 580x^5 - 950x^4 + 198x^3 - 196x^2 + 13x + 1	\( 2^{10}\cdot 11^{18}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.8.79692860778363999735970407424.3	x^20 - 2x^19 - 9x^18 + 11x^17 + 29x^16 + 41x^15 - 129x^14 - 374x^13 + 49x^12 + 1607x^11 + 1660x^10 - 2011x^9 - 3885x^8 - 11x^7 + 4195x^6 + 1213x^5 - 2126x^4 - 1672x^3 + 248x^2 + 208x - 32	\( 2^{10}\cdot 11^{18}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.0.674425532537559799418460307456.1	x^20 + 18x^18 + 141x^16 + 636x^14 + 1841x^12 + 3603x^10 + 4883x^8 + 4602x^6 + 2958x^4 + 1205x^2 + 241	\( 2^{20}\cdot 11^{16}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.12.674425532537559799418460307456.1	x^20 - 6x^19 - 3x^18 + 98x^17 - 268x^16 + 190x^15 + 640x^14 - 2478x^13 + 4090x^12 - 1614x^11 - 7310x^10 + 16026x^9 - 11895x^8 - 5222x^7 + 16697x^6 - 10778x^5 - 864x^4 + 4278x^3 - 1694x^2 - 20x + 89	\( 2^{20}\cdot 11^{16}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.4.674425532537559799418460307456.1	x^20 + 15x^18 + 86x^16 + 200x^14 - 7x^12 - 809x^10 - 1761x^8 - 840x^6 + 1825x^4 + 1446x^2 + 241	\( 2^{20}\cdot 11^{16}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.8.674425532537559799418460307456.1	x^20 - 4x^19 + 4x^18 + 10x^17 - 65x^16 - 44x^15 - 131x^14 + 116x^13 + 314x^12 + 72x^11 + 1696x^10 + 944x^9 - 1888x^8 - 3398x^7 - 321x^6 + 1382x^5 + 347x^4 - 206x^3 - 121x^2 - 26x - 1	\( 2^{20}\cdot 11^{16}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.0.674425532537559799418460307456.2	x^20 + 13x^18 + 49x^16 - 30x^14 - 569x^12 - 885x^10 + 1172x^8 + 4401x^6 + 4319x^4 + 1737x^2 + 241	\( 2^{20}\cdot 11^{16}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.12.674425532537559799418460307456.2	x^20 - 18x^18 + 141x^16 - 636x^14 + 1841x^12 - 3603x^10 + 4883x^8 - 4602x^6 + 2958x^4 - 1205x^2 + 241	\( 2^{20}\cdot 11^{16}\cdot 241^{3} \)	20T747	Trivial (GRH)
20.8.674425532537559799418460307456.2	x^20 - 2x^19 - 5x^18 + 6x^17 - 32x^16 + 28x^15 + 72x^14 - 12x^13 + 330x^12 + 104x^11 + 156x^10 + 450x^9 - 601x^8 + 498x^7 + 1191x^6 - 94x^5 - 314x^4 - 206x^3 - 138x^2 - 112x - 23	\( 2^{20}\cdot 11^{16}\cdot 241^{3} \)	20T747	Trivial (GRH)