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 74)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.1744047395068446282612736.1	x^20 - 4x^19 + 13x^18 - 28x^17 + 48x^16 - 66x^15 + 74x^14 - 74x^13 + 72x^12 - 68x^11 + 50x^10 - 28x^9 - 13x^8 + 34x^7 - 50x^6 + 50x^5 - 51x^4 + 40x^3 - 31x^2 + 16x - 5	\( -\,2^{32}\cdot 67^{8} \)	20T693	Trivial
20.0.5004686909648354265792512.1	x^20 - 2x^18 + 4x^16 + 6x^14 - 17x^12 + 4x^10 + 39x^8 - 6x^6 - 8x^4 + 8x^2 + 2	\( 2^{33}\cdot 17^{12} \)	20T693	Trivial
20.2.29212793867396475233763328.1	x^20 - 2x^19 - 4x^18 + 10x^17 + 18x^16 - 30x^15 - 58x^14 + 26x^13 + 57x^12 - 140x^11 - 292x^10 - 140x^9 + 57x^8 + 26x^7 - 58x^6 - 30x^5 + 18x^4 + 10x^3 - 4x^2 - 2x + 1	\( -\,2^{30}\cdot 67^{9} \)	20T693	Trivial (GRH)
20.0.116851175469585900935053312.1	x^20 - 6x^18 + 24x^16 - 64x^14 + 80x^12 + 44x^10 - 243x^8 + 110x^6 + 133x^4 + 67	\( 2^{32}\cdot 67^{9} \)	20T693	Trivial (GRH)
20.4.233702350939171801870106624.1	x^20 - 4x^19 + x^18 + 32x^17 - 91x^16 + 64x^15 + 196x^14 - 590x^13 + 715x^12 - 362x^11 - 156x^10 + 444x^9 - 457x^8 + 312x^7 - 34x^6 - 212x^5 + 180x^4 - 12x^3 - 40x^2 + 16x - 2	\( 2^{33}\cdot 67^{9} \)	20T693	Trivial (GRH)
20.4.320299962217494673010720768.2	x^20 - 12x^18 + 51x^16 - 80x^14 - 26x^12 + 208x^10 - 153x^8 - 102x^6 + 122x^4 - 28x^2 + 2	\( 2^{39}\cdot 17^{12} \)	20T693	Trivial (GRH)
20.10.17527637043047950664019640604179.1	x^20 - 13x^18 - 16x^17 + 58x^16 + 143x^15 - 16x^14 - 557x^13 - 608x^12 + 1173x^11 + 1844x^10 - 885x^9 - 3604x^8 + 1846x^7 + 1418x^6 - 1040x^5 + 244x^4 + 306x^3 - 179x^2 - 103x - 11	\( -\,19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.10.17527637043047950664019640604179.2	x^20 - 4x^19 + 16x^18 - 26x^17 - 32x^16 + 64x^15 - 151x^14 + 68x^13 + 450x^12 - 1335x^11 - 79x^10 + 3966x^9 - 979x^8 - 4820x^7 + 1269x^6 + 2851x^5 - 678x^4 - 848x^3 + 157x^2 + 110x - 7	\( -\,19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.16.270294613348055239187250247211813.1	x^20 - 5x^19 - 17x^18 + 135x^17 - 55x^16 - 1090x^15 + 2060x^14 + 2325x^13 - 10630x^12 + 5091x^11 + 20552x^10 - 25659x^9 - 16814x^8 + 35240x^7 + 10446x^6 - 21367x^5 - 11712x^4 + 3875x^3 + 6531x^2 + 1995x + 167	\( 19^{8}\cdot 293^{9} \)	20T693	Trivial (GRH)
20.4.270294613348055239187250247211813.1	x^20 - 2x^19 - 20x^18 + 26x^17 + 137x^16 - 61x^15 - 168x^14 - 653x^13 - 1575x^12 + 4080x^11 + 3744x^10 - 8765x^9 + 7934x^8 + 909x^7 - 17947x^6 + 26997x^5 - 27032x^4 + 19516x^3 - 9704x^2 + 3536x - 736	\( 19^{8}\cdot 293^{9} \)	20T693	Trivial (GRH)
20.12.270294613348055239187250247211813.3	x^20 - 2x^19 - 18x^18 + 43x^17 + 165x^16 - 289x^15 - 1200x^14 + 752x^13 + 5503x^12 - 80x^11 - 13888x^10 - 4107x^9 + 20683x^8 + 10594x^7 - 20943x^6 - 11019x^5 + 14058x^4 + 3795x^3 - 4379x^2 + 301x + 49	\( 19^{8}\cdot 293^{9} \)	20T693	Trivial (GRH)
20.8.270294613348055239187250247211813.3	x^20 - 3x^19 - 6x^18 + 37x^17 + 68x^16 - 311x^15 + 54x^14 + 833x^13 - 1010x^12 + 3497x^11 + 446x^10 - 8547x^9 + 5632x^8 - 8219x^7 - 1262x^6 + 1140x^5 - 11817x^4 + 15645x^3 + 9678x^2 - 4306x - 1741	\( 19^{8}\cdot 293^{9} \)	20T693	Trivial (GRH)
20.12.270294613348055239187250247211813.4	x^20 - 10x^19 + 30x^18 + 15x^17 - 358x^16 + 1232x^15 - 2040x^14 + 370x^13 + 7119x^12 - 21082x^11 + 35938x^10 - 42295x^9 + 35562x^8 - 20872x^7 + 7729x^6 - 1125x^5 - 407x^4 + 223x^3 - 25x^2 - 5x + 1	\( 19^{8}\cdot 293^{9} \)	20T693	Trivial (GRH)
20.8.270294613348055239187250247211813.4	x^20 - 6x^19 - 3x^18 + 44x^17 - 28x^16 + 91x^15 + 310x^14 - 1212x^13 - 1403x^12 + 3661x^11 - 1549x^10 + 811x^9 + 10045x^8 - 16810x^7 - 8012x^6 + 41456x^5 - 39932x^4 + 7401x^3 + 2080x^2 + 15x - 7	\( 19^{8}\cdot 293^{9} \)	20T693	Trivial (GRH)
20.12.270294613348055239187250247211813.5	x^20 - 10x^19 + 36x^18 - 39x^17 - 183x^16 + 1056x^15 - 2439x^14 + 1959x^13 + 4202x^12 - 16333x^11 + 24370x^10 - 12901x^9 - 14419x^8 + 31813x^7 - 25243x^6 + 8239x^5 + 986x^4 - 1230x^3 + 88x^2 + 47x + 1	\( 19^{8}\cdot 293^{9} \)	20T693	Trivial (GRH)
20.8.270294613348055239187250247211813.5	x^20 - x^19 - 3x^18 + 4x^17 - 40x^16 + 35x^15 + 132x^14 + 374x^13 + 874x^12 - 3449x^11 - 6076x^10 + 8879x^9 - 11873x^8 + 10263x^7 + 44608x^6 - 3399x^5 - 7759x^4 + 914x^3 - 1977x^2 - 99x + 1	\( 19^{8}\cdot 293^{9} \)	20T693	Trivial (GRH)
20.10.5135597653613049544557754697024447.1	x^20 - x^19 - 12x^18 + 48x^17 + 134x^16 - 429x^15 - 1115x^14 + 2481x^13 + 5447x^12 - 15597x^11 - 17502x^10 + 66439x^9 + 26280x^8 - 199216x^7 - 81786x^6 + 263990x^5 + 141534x^4 - 137694x^3 - 114167x^2 - 23617x - 1301	\( -\,19^{9}\cdot 293^{9} \)	20T693	Trivial (GRH)
20.14.5135597653613049544557754697024447.1	x^20 - 3x^19 - 31x^18 + 99x^17 + 207x^16 - 1178x^15 + 515x^14 + 5394x^13 - 10447x^12 - 5778x^11 + 37163x^10 - 21481x^9 - 45045x^8 + 47768x^7 + 18061x^6 - 30663x^5 + 1425x^4 + 5641x^3 - 1810x^2 + 201x - 7	\( -\,19^{9}\cdot 293^{9} \)	20T693	Trivial (GRH)
20.6.5135597653613049544557754697024447.1	x^20 - 4x^19 + 5x^18 - x^17 - 93x^16 + 326x^15 - 480x^14 + 185x^13 + 2333x^12 - 4278x^11 + 4707x^10 - 13892x^9 + 13363x^8 - 6403x^7 + 9544x^6 + 4906x^5 + 4173x^4 + 6009x^3 - 19025x^2 + 19486x - 6551	\( -\,19^{9}\cdot 293^{9} \)	20T693	Trivial (GRH)
20.10.5135597653613049544557754697024447.2	x^20 - 3x^19 - 29x^18 + 89x^17 + 286x^16 - 847x^15 - 1392x^14 + 3002x^13 + 6134x^12 - 5102x^11 - 21492x^10 + 6359x^9 + 47689x^8 - 16744x^7 - 48617x^6 + 13733x^5 + 30458x^4 - 8949x^3 - 8132x^2 + 722x + 361	\( -\,19^{9}\cdot 293^{9} \)	20T693	Trivial (GRH)
20.14.5135597653613049544557754697024447.2	x^20 - 23x^18 - 32x^17 + 141x^16 + 647x^15 + 383x^14 - 3880x^13 - 7923x^12 + 5420x^11 + 35328x^10 + 30513x^9 - 65705x^8 - 157303x^7 + 58360x^6 + 291735x^5 - 41454x^4 - 222605x^3 + 18840x^2 + 59519x - 1943	\( -\,19^{9}\cdot 293^{9} \)	20T693	Trivial (GRH)
20.6.5135597653613049544557754697024447.2	x^20 - 7x^19 + 24x^18 - 55x^17 - 37x^16 + 565x^15 - 762x^14 + 329x^13 + 729x^12 - 4417x^11 + 4277x^10 + 579x^9 - 3082x^8 + 515x^7 - 11796x^6 - 20662x^5 - 23563x^4 - 16399x^3 - 6563x^2 - 1836x - 203	\( -\,19^{9}\cdot 293^{9} \)	20T693	$[2]$ (GRH)
20.10.5135597653613049544557754697024447.3	x^20 - 3x^19 - 30x^18 + 65x^17 + 265x^16 - 550x^15 - 438x^14 + 1998x^13 - 3671x^12 + 1781x^11 + 12608x^10 - 11281x^9 - 2282x^8 + 15211x^7 - 24505x^6 - 19483x^5 + 18981x^4 + 13934x^3 + 614x^2 - 327x - 31	\( -\,19^{9}\cdot 293^{9} \)	20T693	Trivial (GRH)
20.10.5135597653613049544557754697024447.4	x^20 + 23x^18 + 60x^16 - 1400x^14 - 4414x^12 + 26744x^10 - 140x^8 - 77337x^6 + 50938x^4 + 11951x^2 - 5567	\( -\,19^{9}\cdot 293^{9} \)	20T693	Trivial (GRH)
20.10.5135597653613049544557754697024447.5	x^20 - 4x^19 - 24x^18 + 95x^17 + 217x^16 - 938x^15 - 508x^14 + 5135x^13 - 3971x^12 - 17092x^11 + 25398x^10 + 29946x^9 - 53400x^8 - 19819x^7 + 53060x^6 - 9831x^5 - 26668x^4 + 23596x^3 - 1942x^2 - 5803x + 1891	\( -\,19^{9}\cdot 293^{9} \)	20T693	Trivial (GRH)
20.10.5135597653613049544557754697024447.6	x^20 - 2x^19 - 17x^18 + 49x^17 - 60x^16 - 441x^15 + 1163x^14 - 175x^13 - 2181x^12 + 5499x^11 + 1541x^10 - 1262x^9 - 1867x^8 - 5201x^7 - 4115x^6 + 8129x^5 + 2686x^4 - 4268x^3 - 240x^2 + 656x + 32	\( -\,19^{9}\cdot 293^{9} \)	20T693	Trivial (GRH)
20.10.6327476972540310189711090258108619.1	x^20 - 3x^19 + 4x^18 - 57x^17 + 106x^16 + 57x^15 + 539x^14 - 1294x^13 - 3995x^12 + 12227x^11 - 5039x^10 - 16190x^9 + 22921x^8 - 9603x^7 + 2305x^6 - 4483x^5 + 1441x^4 + 1356x^3 - 19x^2 - 274x + 1	\( -\,19^{11}\cdot 293^{8} \)	20T693	$[2]$ (GRH)
20.10.6327476972540310189711090258108619.2	x^20 - 7x^19 - 6x^18 + 168x^17 - 248x^16 - 1407x^15 + 3818x^14 + 3691x^13 - 21640x^12 + 10919x^11 + 45699x^10 - 49276x^9 - 47758x^8 + 69742x^7 + 32985x^6 - 51504x^5 - 21056x^4 + 16781x^3 + 11128x^2 + 2090x + 121	\( -\,19^{11}\cdot 293^{8} \)	20T693	$[2]$ (GRH)
20.14.17948300332081101479956111978679296.1	x^20 - 26x^18 + 195x^16 - 438x^14 - 147x^12 + 1189x^10 - 277x^8 - 1020x^6 + 226x^4 + 285x^2 - 19	\( -\,2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.18.17948300332081101479956111978679296.1	x^20 - 29x^18 + 233x^16 - 259x^14 - 2999x^12 + 11426x^10 - 16017x^8 + 10375x^6 - 3129x^4 + 418x^2 - 19	\( -\,2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.2.17948300332081101479956111978679296.1	x^20 + 32x^18 + 349x^16 + 1422x^14 + 735x^12 - 9446x^10 - 24185x^8 - 21944x^6 - 7330x^4 - 874x^2 - 19	\( -\,2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	$[4]$ (GRH)
20.6.17948300332081101479956111978679296.1	x^20 + 11x^18 - 14x^16 - 430x^14 - 728x^12 + 3218x^10 + 10717x^8 + 9883x^6 + 1890x^4 - 722x^2 - 19	\( -\,2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	$[2]$ (GRH)
20.14.17948300332081101479956111978679296.2	x^20 - 5x^19 - 13x^18 + 109x^17 - 107x^16 - 336x^15 + 753x^14 - 1981x^13 + 7164x^12 - 5259x^11 - 25133x^10 + 52830x^9 - 11998x^8 - 58724x^7 + 56360x^6 - 736x^5 - 21912x^4 + 10112x^3 - 944x^2 - 224x + 32	\( -\,2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.6.17948300332081101479956111978679296.2	x^20 - 8x^19 + 26x^18 + 19x^17 - 438x^16 + 1622x^15 - 3236x^14 + 3813x^13 - 4390x^12 + 6719x^11 - 13133x^10 + 21208x^9 - 25783x^8 + 22104x^7 - 10808x^6 - 2087x^5 + 5523x^4 - 2973x^3 + 311x^2 + 412x - 23	\( -\,2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.14.17948300332081101479956111978679296.3	x^20 - 8x^19 - 5x^18 + 175x^17 - 240x^16 - 1170x^15 + 2408x^14 + 2929x^13 - 6247x^12 - 6654x^11 + 3123x^10 + 27737x^9 - 18382x^8 - 27732x^7 + 57902x^6 - 44824x^5 - 13841x^4 + 2101x^3 + 42230x^2 - 8783x - 7091	\( -\,2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.6.17948300332081101479956111978679296.3	x^20 - 6x^19 + 12x^18 - 25x^17 + 59x^16 + 72x^15 - 150x^14 - 1362x^13 + 2836x^12 + 1691x^11 - 9138x^10 + 13507x^9 - 25198x^8 + 32182x^7 + 11567x^6 - 84293x^5 + 96414x^4 - 41364x^3 - 3136x^2 + 8272x - 1952	\( -\,2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.14.17948300332081101479956111978679296.4	x^20 - x^19 - 31x^18 + 59x^17 + 201x^16 - 855x^15 + 1521x^14 + 2515x^13 - 19576x^12 + 19706x^11 + 52183x^10 - 122364x^9 + 18003x^8 + 226722x^7 - 232556x^6 - 164055x^5 + 310257x^4 + 43833x^3 - 150537x^2 - 8740x + 20767	\( -\,2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.6.17948300332081101479956111978679296.4	x^20 - 176x^16 + 606x^14 + 1683x^12 + 180x^10 - 2252x^8 - 2376x^6 - 1066x^4 - 228x^2 - 19	\( -\,2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.12.17948300332081101479956111978679296.1	x^20 - 9x^18 - 25x^16 + 251x^14 + 105x^12 - 1872x^10 + 597x^8 + 3987x^6 - 2255x^4 - 722x^2 + 19	\( 2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.16.17948300332081101479956111978679296.1	x^20 - 30x^18 + 174x^16 + 161x^14 - 4261x^12 + 14404x^10 - 20796x^8 + 12846x^6 - 2100x^4 - 285x^2 + 19	\( 2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.4.17948300332081101479956111978679296.1	x^20 + 12x^18 - 8x^16 - 596x^14 - 2490x^12 - 2596x^10 + 4119x^8 + 9674x^6 + 4926x^4 + 570x^2 + 19	\( 2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.8.17948300332081101479956111978679296.1	x^20 - 4x^18 - 154x^16 - 25x^14 + 5000x^12 + 11079x^10 - 4895x^8 - 19428x^6 - 5503x^4 + 817x^2 + 19	\( 2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.12.17948300332081101479956111978679296.2	x^20 + 4x^18 - 272x^16 + 1336x^14 + 1207x^12 - 16211x^10 + 20889x^8 + 4342x^6 - 9142x^4 + 1444x^2 + 19	\( 2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.16.17948300332081101479956111978679296.2	x^20 - 36x^18 + 378x^16 - 1599x^14 + 2553x^12 - 82x^10 - 3070x^8 + 1282x^6 + 942x^4 - 285x^2 + 19	\( 2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.4.17948300332081101479956111978679296.2	x^20 - 9x^19 + 24x^18 + 2x^17 - 159x^16 + 850x^15 - 3296x^14 + 6620x^13 - 3263x^12 - 5879x^11 - 994x^10 + 6919x^9 + 10803x^8 + 15688x^7 + 13037x^6 + 9195x^5 + 5200x^4 + 1030x^3 + 191x^2 - 90x + 1	\( 2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.8.17948300332081101479956111978679296.2	x^20 + 23x^18 + 169x^16 + 334x^14 - 1177x^12 - 5019x^10 - 1118x^8 + 12545x^6 + 6898x^4 - 6878x^2 + 931	\( 2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.12.17948300332081101479956111978679296.3	x^20 - 35x^18 - 8x^17 + 362x^16 + 455x^15 - 1517x^14 - 3712x^13 + 1163x^12 + 9602x^11 + 3821x^10 - 11787x^9 - 7557x^8 + 12328x^7 + 9885x^6 - 6716x^5 - 5864x^4 - 309x^3 - 1107x^2 - 821x - 127	\( 2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.16.17948300332081101479956111978679296.3	x^20 - 6x^19 - 3x^18 + 109x^17 - 319x^16 - 93x^15 + 2796x^14 - 5438x^13 - 4145x^12 + 25256x^11 - 16741x^10 - 35263x^9 + 51562x^8 + 4969x^7 - 42730x^6 + 17494x^5 + 7806x^4 - 5769x^3 + 286x^2 + 236x - 7	\( 2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.4.17948300332081101479956111978679296.3	x^20 + 11x^18 - 46x^16 - 1014x^14 - 3730x^12 + 2030x^10 + 36785x^8 + 74161x^6 + 57828x^4 + 19342x^2 + 2299	\( 2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)
20.8.17948300332081101479956111978679296.3	x^20 - 5x^18 - 147x^16 - 5x^14 + 4540x^12 + 6441x^10 - 23449x^8 - 10634x^6 + 1925x^4 + 513x^2 + 19	\( 2^{10}\cdot 19^{9}\cdot 293^{8} \)	20T693	Trivial (GRH)