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
20.2.329806836013751534092288.1	x^20 - x^19 - 5x^18 + 15x^17 - 3x^16 - 40x^15 + 72x^14 - 32x^13 - 62x^12 + 146x^11 - 174x^10 + 146x^9 - 62x^8 - 32x^7 + 72x^6 - 40x^5 - 3x^4 + 15x^3 - 5x^2 - x + 1	\( -\,2^{40}\cdot 17^{8}\cdot 43 \)	20T968	Trivial
20.2.1319227344055006136369152.1	x^20 - 2x^19 + 7x^18 - 6x^17 - 5x^16 + 52x^15 - 152x^14 + 288x^13 - 445x^12 + 522x^11 - 519x^10 + 410x^9 - 259x^8 + 144x^7 - 48x^6 + 28x^5 - 3x^4 + 2x^3 - x^2 - 2x - 1	\( -\,2^{42}\cdot 17^{8}\cdot 43 \)	20T968	Trivial
20.0.62832037223829129471721472.1	x^20 + 5x^18 + 11x^16 + 14x^14 + 12x^12 + 10x^10 + 6x^8 - 2x^4 + 2x^2 + 2	\( 2^{53}\cdot 17^{8} \)	20T968	Trivial (GRH)
20.4.62832037223829129471721472.1	x^20 + 2x^18 - x^16 + 8x^14 + 40x^12 + 40x^10 - 50x^8 - 100x^6 - 2x^4 - 4x^2 + 2	\( 2^{53}\cdot 17^{8} \)	20T968	Trivial (GRH)
20.0.62832037223829129471721472.2	x^20 + 6x^18 + 3x^16 - 8x^14 - 24x^12 - 12x^10 + 6x^8 + 36x^6 + 42x^4 + 12x^2 + 2	\( 2^{53}\cdot 17^{8} \)	20T968	Trivial (GRH)
20.4.62832037223829129471721472.2	x^20 + 5x^18 + 11x^16 + 10x^14 + 12x^12 + 10x^10 + 6x^8 + 20x^6 + 10x^4 - 14x^2 + 2	\( 2^{53}\cdot 17^{8} \)	20T968	Trivial (GRH)
20.6.7274060704988494997985326403.1	x^20 - 10x^19 + 44x^18 - 111x^17 + 144x^16 + 72x^15 - 769x^14 + 1777x^13 - 2480x^12 + 2569x^11 - 2363x^10 + 2074x^9 - 1341x^8 + 21x^7 + 1174x^6 - 1486x^5 + 1040x^4 - 470x^3 + 135x^2 - 21x + 1	\( -\,3^{9}\cdot 883^{8} \)	20T968	Trivial (GRH)
20.6.7274060704988494997985326403.2	x^20 - 5x^19 + 2x^18 + 18x^17 + 35x^16 - 337x^15 + 814x^14 - 911x^13 + 112x^12 + 1198x^11 - 1855x^10 + 1198x^9 + 112x^8 - 911x^7 + 814x^6 - 337x^5 + 35x^4 + 18x^3 + 2x^2 - 5x + 1	\( -\,3^{9}\cdot 883^{8} \)	20T968	Trivial (GRH)
20.2.1813343680342315665573096356608.1	x^20 - x^19 - x^18 + x^17 + 6x^16 + 31x^15 - 150x^14 - 30x^13 - 346x^12 + 144x^11 + 1346x^10 + 2792x^9 + 620x^8 - 5515x^7 + 2271x^6 - 6589x^5 - 6821x^4 + 8169x^3 - 7568x^2 - 730x - 625	\( -\,2^{8}\cdot 11^{9}\cdot 113^{9} \)	20T968	Trivial (GRH)
20.6.1926514210331674023159498080256.1	x^20 - 11x^18 + 65x^16 - 138x^14 - 211x^12 + 1031x^10 - 1021x^8 + 194x^6 + 147x^4 - 31x^2 - 9	\( -\,2^{16}\cdot 3^{4}\cdot 881^{8} \)	20T968	Trivial (GRH)
20.6.1926514210331674023159498080256.2	x^20 - 5x^19 + 22x^18 - 56x^17 + 104x^16 - 151x^15 + 114x^14 + 63x^13 - 337x^12 + 373x^11 - 148x^10 + 193x^9 - 258x^8 - 426x^7 + 1520x^6 - 941x^5 - 835x^4 + 1220x^3 - 272x^2 - 408x + 144	\( -\,2^{16}\cdot 3^{4}\cdot 881^{8} \)	20T968	Trivial (GRH)
20.10.2140998534168280361073681071283.1	x^20 - 10x^19 + 38x^18 - 50x^17 - 120x^16 + 654x^15 - 929x^14 - 1096x^13 + 4489x^12 - 881x^11 - 9037x^10 + 6360x^9 + 6691x^8 - 6756x^7 - 1475x^6 + 3117x^5 - 701x^4 - 749x^3 + 469x^2 + 85x - 75	\( -\,3^{8}\cdot 883^{9} \)	20T968	Trivial (GRH)
20.10.2482879387302739625978991412224.1	x^20 - 5x^19 - 2x^18 + 57x^17 - 92x^16 - 165x^15 + 594x^14 - 217x^13 - 1231x^12 + 1648x^11 + 331x^10 - 2636x^9 + 1977x^8 + 1988x^7 - 2472x^6 - 847x^5 + 866x^4 + 139x^3 - 6x^2 + 8x + 1	\( -\,2^{10}\cdot 3^{8}\cdot 883^{8} \)	20T968	Trivial (GRH)
20.2.2482879387302739625978991412224.1	x^20 + 21x^18 + 156x^16 + 459x^14 + 127x^12 - 2235x^10 - 4821x^8 - 4515x^6 - 2194x^4 - 531x^2 - 49	\( -\,2^{10}\cdot 3^{8}\cdot 883^{8} \)	20T968	$[2]$ (GRH)
20.0.2707615342490215507082596007936.1	x^20 - 4x^19 + 4x^18 + 12x^17 - 5x^16 - 140x^15 + 287x^14 - 38x^13 + 87x^12 - 2040x^11 + 4231x^10 - 2140x^9 - 2435x^8 + 1904x^7 + 3249x^6 - 5072x^5 + 2466x^4 - 312x^3 - 9x^2 - 58x + 20	\( 2^{14}\cdot 11^{8}\cdot 29\cdot 113^{8} \)	20T968	$[4]$ (GRH)
20.0.2707615342490215507082596007936.2	x^20 - x^19 - 4x^18 - 8x^17 + 13x^16 + 140x^15 - 222x^14 - 623x^13 + 1749x^12 + 330x^11 - 5984x^10 + 5236x^9 + 7780x^8 - 12368x^7 + 2044x^6 - 5232x^5 + 9896x^4 - 2028x^3 + 560x^2 + 724x + 212	\( 2^{14}\cdot 11^{8}\cdot 29\cdot 113^{8} \)	20T968	$[4]$ (GRH)
20.12.4500535989519743455685376800000.1	x^20 - 10x^18 - 27x^16 + 259x^14 + 324x^12 - 1190x^10 + 36x^8 + 532x^6 - 140x^4 - 17x^2 + 5	\( 2^{8}\cdot 5^{5}\cdot 17^{8}\cdot 73^{8} \)	20T968	Trivial (GRH)
20.8.4500535989519743455685376800000.1	x^20 - 2x^19 + x^18 + 28x^17 - 120x^16 + 14x^15 + 599x^14 - 964x^13 - 684x^12 + 3854x^11 - 2597x^10 - 6082x^9 + 10940x^8 + 1106x^7 - 17025x^6 + 9530x^5 + 9780x^4 - 10070x^3 + 829x^2 + 922x - 185	\( 2^{8}\cdot 5^{5}\cdot 17^{8}\cdot 73^{8} \)	20T968	Trivial (GRH)
20.4.5119085256895563693078033077504.1	x^20 - 6x^19 + 8x^18 + 28x^17 - 119x^16 + 144x^15 + 110x^14 - 549x^13 + 640x^12 - 162x^11 - 216x^10 - 214x^9 + 733x^8 + 323x^7 - 2947x^6 + 4777x^5 - 4261x^4 + 2425x^3 - 906x^2 + 209x - 23	\( 2^{8}\cdot 11^{10}\cdot 29\cdot 113^{8} \)	20T968	Trivial (GRH)
20.10.5975426962737027325975384293376.1	x^20 + x^18 - 46x^16 + 22x^14 + 337x^12 - 208x^10 - 629x^8 + 274x^6 + 274x^4 + 7x^2 - 1	\( -\,2^{20}\cdot 11^{8}\cdot 113^{8} \)	20T968	Trivial (GRH)
20.10.5975426962737027325975384293376.2	x^20 - x^18 - 78x^16 + 120x^14 + 1153x^12 - 2368x^10 - 1072x^8 + 3472x^6 - 464x^4 - 752x^2 - 16	\( -\,2^{20}\cdot 11^{8}\cdot 113^{8} \)	20T968	Trivial (GRH)
20.4.7448638161908218877936974236672.1	x^20 + 3x^18 - 30x^16 + 5x^14 + 163x^12 - 641x^10 + 2959x^8 - 3837x^6 - 1922x^4 + 1475x^2 + 27	\( 2^{10}\cdot 3^{9}\cdot 883^{8} \)	20T968	$[2]$ (GRH)
20.8.7448638161908218877936974236672.1	x^20 + 6x^18 - 40x^16 - 282x^14 + 311x^12 + 2208x^10 - 2099x^8 - 3846x^6 + 5071x^4 - 2076x^2 + 243	\( 2^{10}\cdot 3^{9}\cdot 883^{8} \)	20T968	Trivial (GRH)
20.4.7448638161908218877936974236672.2	x^20 + 3x^18 - 36x^16 - 38x^14 + 715x^12 + 1619x^10 - 479x^8 - 12744x^6 - 17231x^4 + 5464x^2 + 3	\( 2^{10}\cdot 3^{9}\cdot 883^{8} \)	20T968	Trivial (GRH)
20.8.7448638161908218877936974236672.2	x^20 + 3x^18 - 18x^16 + 92x^14 + 574x^12 - 266x^10 - 3326x^8 - 1827x^6 + 1840x^4 - 301x^2 + 3	\( 2^{10}\cdot 3^{9}\cdot 883^{8} \)	20T968	Trivial (GRH)
20.4.7448638161908218877936974236672.3	x^20 + 21x^18 + 140x^16 + 405x^14 + 333x^12 - 1073x^10 - 3119x^8 - 2941x^6 - 420x^4 + 47x^2 + 3	\( 2^{10}\cdot 3^{9}\cdot 883^{8} \)	20T968	$[2]$ (GRH)
20.8.7448638161908218877936974236672.3	x^20 - 4x^18 + 10x^16 + 15x^14 - 1145x^12 + 1198x^10 + 2424x^8 - 5052x^6 + 3784x^4 - 1473x^2 + 243	\( 2^{10}\cdot 3^{9}\cdot 883^{8} \)	20T968	Trivial (GRH)
20.4.7448638161908218877936974236672.4	x^20 + 11x^18 + 42x^16 + 246x^14 + 514x^12 - 894x^10 - 4335x^8 - 971x^6 + 7796x^4 + 2458x^2 + 3	\( 2^{10}\cdot 3^{9}\cdot 883^{8} \)	20T968	Trivial (GRH)
20.8.7448638161908218877936974236672.4	x^20 + 4x^18 + 5x^16 - 176x^14 + 135x^12 + 1131x^10 - 1143x^8 - 1406x^6 + 1834x^4 - 543x^2 + 27	\( 2^{10}\cdot 3^{9}\cdot 883^{8} \)	20T968	Trivial (GRH)
20.2.19268986807514523249663129641547.1	x^20 - 8x^19 + 40x^18 - 144x^17 + 364x^16 - 817x^15 + 1248x^14 - 2606x^13 + 3734x^12 - 10791x^11 + 15328x^10 - 33835x^9 + 26950x^8 - 41267x^7 + 25x^6 - 16655x^5 - 20149x^4 - 14095x^3 - 9869x^2 - 2082x - 1047	\( -\,3^{10}\cdot 883^{9} \)	20T968	$[2]$ (GRH)
20.2.26913925303086389023951462924288.1	x^20 + 14x^18 - 12x^17 + 91x^16 - 196x^15 + 419x^14 - 1298x^13 + 1780x^12 - 4428x^11 + 6245x^10 - 8358x^9 + 13878x^8 - 9068x^7 + 14821x^6 - 6142x^5 + 423x^4 - 3668x^3 - 15899x^2 - 3406x - 11581	\( -\,2^{16}\cdot 17^{8}\cdot 73^{9} \)	20T968	Trivial (GRH)
20.4.26913925303086389023951462924288.1	x^20 - x^19 - 3x^18 - 9x^17 - 71x^16 - 102x^15 + 558x^14 + 2171x^13 + 869x^12 - 6959x^11 - 12462x^10 - 6555x^9 + 3087x^8 + 6372x^7 + 2094x^6 - 2391x^5 - 1477x^4 + 455x^3 + 307x^2 - 72x - 37	\( 2^{16}\cdot 17^{8}\cdot 73^{9} \)	20T968	Trivial (GRH)
20.12.52015883678955198625306448166912.1	x^20 - 15x^18 + 140x^16 - 870x^14 + 3404x^12 - 8334x^10 + 12810x^8 - 12195x^6 + 6867x^4 - 2052x^2 + 243	\( 2^{16}\cdot 3^{7}\cdot 881^{8} \)	20T968	Trivial (GRH)
20.12.72008575832315895290966028800000.1	x^20 + 18x^18 + 65x^16 - 357x^14 - 1844x^12 + 1017x^10 + 4254x^8 - 4467x^6 + 1375x^4 - 147x^2 + 5	\( 2^{12}\cdot 5^{5}\cdot 17^{8}\cdot 73^{8} \)	20T968	Trivial (GRH)
20.8.72008575832315895290966028800000.1	x^20 + 17x^18 + 9x^16 - 447x^14 - 467x^12 + 1528x^10 + 1356x^8 - 1544x^6 - 928x^4 + 256x^2 + 80	\( 2^{12}\cdot 5^{5}\cdot 17^{8}\cdot 73^{8} \)	20T968	Trivial (GRH)
20.0.79452140393687668031327725191168.1	x^20 - 3x^19 + 11x^18 - 12x^17 + 28x^16 - 14x^15 + 108x^14 - 193x^13 + 711x^12 - 1456x^11 + 1243x^10 + 1745x^9 - 6160x^8 + 194x^7 + 16675x^6 - 34604x^5 + 47607x^4 - 18031x^3 + 30273x^2 - 689x + 147	\( 2^{15}\cdot 3^{8}\cdot 883^{8} \)	20T968	$[2]$ (GRH)
20.12.79452140393687668031327725191168.2	x^20 - 23x^18 + 178x^16 - 675x^14 + 2205x^12 - 7723x^10 + 16638x^8 - 18828x^6 + 15008x^4 - 5296x^2 + 288	\( 2^{15}\cdot 3^{8}\cdot 883^{8} \)	20T968	Trivial (GRH)
20.0.92472682095920353111655907852288.1	x^20 + 5x^18 + 52x^16 + 178x^14 + 616x^12 + 1246x^10 + 1334x^8 + 789x^6 + 259x^4 + 44x^2 + 3	\( 2^{20}\cdot 3^{5}\cdot 881^{8} \)	20T968	Trivial (GRH)
20.14.95606831403792437215606148694016.1	x^20 - 17x^18 + 63x^16 + 31x^14 - 545x^12 + 878x^10 - 104x^8 - 712x^6 + 464x^4 - 48x^2 - 16	\( -\,2^{24}\cdot 11^{8}\cdot 113^{8} \)	20T968	Trivial (GRH)
20.6.95606831403792437215606148694016.1	x^20 + x^18 - 66x^16 - 48x^14 + 939x^12 + 1376x^10 - 1973x^8 - 4188x^6 - 1924x^4 - 265x^2 - 1	\( -\,2^{24}\cdot 11^{8}\cdot 113^{8} \)	20T968	Trivial (GRH)
20.14.95606831403792437215606148694016.2	x^20 - 20x^18 + 136x^16 - 316x^14 - 167x^12 + 1110x^10 + 105x^8 - 340x^6 + 70x^4 + 2x^2 - 1	\( -\,2^{24}\cdot 11^{8}\cdot 113^{8} \)	20T968	Trivial (GRH)
20.6.95606831403792437215606148694016.2	x^20 + 25x^18 + 216x^16 + 696x^14 + 93x^12 - 3108x^10 - 3039x^8 + 972x^6 + 1442x^4 + 167x^2 - 25	\( -\,2^{24}\cdot 11^{8}\cdot 113^{8} \)	20T968	Trivial (GRH)
20.12.112513399737993586392134420000000.1	x^20 - 10x^19 + 60x^18 - 255x^17 + 724x^16 - 1304x^15 + 634x^14 + 4612x^13 - 15282x^12 + 22350x^11 - 7523x^10 - 38599x^9 + 80863x^8 - 65988x^7 - 7603x^6 + 76578x^5 - 61914x^4 + 2808x^3 + 15212x^2 - 5364x + 500	\( 2^{8}\cdot 5^{7}\cdot 17^{8}\cdot 73^{8} \)	20T968	Trivial (GRH)
20.8.112513399737993586392134420000000.1	x^20 - 6x^19 + 9x^18 + 14x^17 - 73x^16 + 34x^15 + 269x^14 - 138x^13 - 501x^12 + 275x^11 + 595x^10 - 1600x^9 - 4530x^8 - 1591x^7 + 11085x^6 + 17691x^5 + 11506x^4 - 2932x^3 - 10138x^2 - 1523x + 53	\( 2^{8}\cdot 5^{7}\cdot 17^{8}\cdot 73^{8} \)	20T968	Trivial (GRH)
20.12.327621456441316076356994116960256.1	x^20 - 9x^19 + 19x^18 + 62x^17 - 456x^16 + 1169x^15 - 789x^14 - 4736x^13 + 19679x^12 - 38905x^11 + 37211x^10 + 15536x^9 - 110601x^8 + 186715x^7 - 174859x^6 + 80352x^5 + 2712x^4 - 20490x^3 + 8434x^2 - 1198x + 25	\( 2^{14}\cdot 11^{10}\cdot 29\cdot 113^{8} \)	20T968	Trivial (GRH)
20.4.327621456441316076356994116960256.1	x^20 - x^19 - 6x^18 + 42x^17 - 21x^16 - 74x^15 + 904x^14 - 1188x^13 - 2678x^12 + 5786x^11 - 2892x^10 - 10762x^9 + 9384x^8 + 14404x^7 - 18552x^6 + 11056x^5 - 674x^4 + 3196x^3 - 4848x^2 + 2784x - 928	\( 2^{14}\cdot 11^{10}\cdot 29\cdot 113^{8} \)	20T968	Trivial (GRH)
20.16.1051325207151812071248104020480000.1	x^20 - 38x^18 - 24x^17 + 561x^16 + 660x^15 - 3915x^14 - 6634x^13 + 12304x^12 + 29630x^11 - 11072x^10 - 59052x^9 - 14368x^8 + 54078x^7 + 31086x^6 - 22804x^5 - 17526x^4 + 4942x^3 + 3029x^2 - 816x + 1	\( 2^{12}\cdot 5^{4}\cdot 17^{8}\cdot 73^{9} \)	20T968	Trivial (GRH)
20.8.1051325207151812071248104020480000.1	x^20 - 8x^19 + 10x^18 + 70x^17 - 201x^16 + 136x^15 - 485x^14 + 736x^13 + 4694x^12 - 9596x^11 - 12522x^10 + 42466x^9 + 3246x^8 - 99112x^7 + 63808x^6 + 75818x^5 - 82996x^4 + 6460x^3 + 22929x^2 - 6400x - 3329	\( 2^{12}\cdot 5^{4}\cdot 17^{8}\cdot 73^{9} \)	20T968	Trivial (GRH)
20.16.1051325207151812071248104020480000.2	x^20 - 7x^19 - 7x^18 + 118x^17 - 94x^16 - 397x^15 + 325x^14 - 969x^13 + 4901x^12 + 684x^11 - 19372x^10 + 14770x^9 + 15490x^8 - 21672x^7 + 3396x^6 + 4176x^5 - 1036x^4 - 448x^3 + 132x^2 + 12x - 4	\( 2^{12}\cdot 5^{4}\cdot 17^{8}\cdot 73^{9} \)	20T968	Trivial (GRH)
20.10.1152137213317054324655456460800000.1	x^20 - 10x^19 + 31x^18 - 16x^17 - 78x^16 + 186x^15 - 228x^14 - 104x^13 - 288x^12 + 114x^11 + 4494x^10 - 1290x^9 + 4882x^8 - 124x^7 - 45911x^6 - 9876x^5 + 41577x^4 + 16654x^3 + 1106x^2 - 92x + 1	\( -\,2^{16}\cdot 5^{5}\cdot 17^{8}\cdot 73^{8} \)	20T968	Trivial (GRH)