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 949)

Label	Polynomial	Discriminant	Galois group	Class group
20.10.3611383131888430543937259.1	x^20 - 3x^19 - 7x^18 + 25x^17 + 4x^16 - 27x^15 + 17x^14 - 191x^13 + 37x^12 + 613x^11 - 33x^10 - 796x^9 - 208x^8 + 490x^7 + 329x^6 - 71x^5 - 145x^4 - 46x^3 + 5x^2 + 6x + 1	\( -\,3^{10}\cdot 11^{19} \)	$C_5\times D_4$ (as 20T12)	Trivial
20.10.3933111925467505849609375.1	x^20 - x^19 - x^18 + 11x^17 - 53x^16 + 61x^15 - 54x^14 - 3x^13 + 266x^12 - 79x^11 - 167x^10 - 9x^9 - 215x^8 - 42x^7 + 305x^6 - 155x^5 + 17x^4 + 43x^3 - 30x^2 + 3x + 1	\( -\,5^{10}\cdot 3319^{5} \)	$D_5\wr C_2$ (as 20T48)	Trivial
20.10.4175899735297664052734375.1	x^20 - 2x^19 - 11x^18 + 23x^17 + 31x^16 - 111x^15 + 48x^14 + 275x^13 - 467x^12 - 341x^11 + 1168x^10 + 107x^9 - 1480x^8 + 268x^7 + 1065x^6 - 330x^5 - 456x^4 + 70x^3 + 45x^2 - 13x + 1	\( -\,5^{10}\cdot 3359^{5} \)	$D_5\wr C_2$ (as 20T48)	Trivial (GRH)
20.10.4936006137688415732421875.1	x^20 - 4x^19 - x^18 + 28x^17 - 60x^16 + 45x^15 + 65x^14 - 215x^13 + 233x^12 - x^11 - 318x^10 + 407x^9 - 158x^8 - 175x^7 + 270x^6 - 75x^5 - 110x^4 + 46x^3 + 24x^2 - 2x - 1	\( -\,5^{10}\cdot 11^{17} \)	$C_5\times D_4$ (as 20T12)	Trivial (GRH)
20.10.8978120457836040599985152.1	x^20 - 12x^18 + 63x^16 - 194x^14 + 385x^12 - 493x^10 + 371x^8 - 100x^6 - 80x^4 + 83x^2 - 23	\( -\,2^{10}\cdot 23\cdot 641^{2}\cdot 5519^{4} \)	20T1015	Trivial (GRH)
20.10.18546881403289244170576896.1	x^20 - 7x^18 + 18x^16 - 38x^14 + 84x^12 - 60x^10 - 128x^8 + 261x^6 - 186x^4 + 63x^2 - 9	\( -\,2^{10}\cdot 3^{6}\cdot 17^{4}\cdot 4153^{4} \)	20T992	Trivial (GRH)
20.10.24868623129665465017517056.1	x^20 - 2x^18 - 6x^16 + 19x^14 - 30x^12 - 28x^10 + 105x^8 - x^6 - 37x^4 + 12x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T846	Trivial (GRH)
20.10.24868623129665465017517056.2	x^20 + x^18 - 16x^16 - 17x^14 + 74x^12 + 90x^10 - 94x^8 - 112x^6 + 26x^4 + 5x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T846	Trivial (GRH)
20.10.24868623129665465017517056.3	x^20 - 3x^18 - 8x^16 + 27x^14 + 9x^12 - 71x^10 + 35x^8 + 49x^6 - 58x^4 + 19x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T846	Trivial (GRH)
20.10.24868623129665465017517056.4	x^20 + x^18 - 31x^16 + 59x^14 + 3x^12 - 86x^10 + 63x^8 + 15x^6 - 35x^4 + 12x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{2} \)	20T846	Trivial (GRH)
20.10.35032998206213016766645248.1	x^20 - 10x^18 + 42x^16 - 113x^14 + 236x^12 - 329x^10 + 191x^8 + 128x^6 - 249x^4 + 119x^2 - 17	\( -\,2^{10}\cdot 3^{4}\cdot 17^{5}\cdot 4153^{4} \)	20T992	Trivial (GRH)
20.10.36757053453857337692075119.1	x^20 - 10x^19 + 37x^18 - 48x^17 - 57x^16 + 252x^15 - 222x^14 - 204x^13 + 562x^12 - 304x^11 - 307x^10 + 517x^9 - 173x^8 - 184x^7 + 202x^6 - 49x^5 - 37x^4 + 34x^3 - 7x^2 - 3x + 1	\( -\,317\cdot 443\cdot 673^{2}\cdot 4903^{4} \)	20T1015	Trivial (GRH)
20.10.37939607261791361436851947.1	x^20 - x^19 - 7x^18 + 17x^17 + 5x^16 - 57x^15 + 55x^14 + 38x^13 - 176x^12 + 108x^11 + 241x^10 - 244x^9 - 92x^8 + 195x^7 - 120x^6 - 73x^5 + 130x^4 + 16x^3 - 34x^2 - 2x + 1	\( -\,7^{6}\cdot 43^{5}\cdot 1217^{4} \)	20T992	Trivial (GRH)
20.10.43406142794035599452422144.1	x^20 - 8x^18 + 23x^16 - 33x^14 + 25x^12 + 10x^10 - 40x^8 + 21x^6 + x^4 - 1	\( -\,2^{14}\cdot 307^{4}\cdot 739^{4} \)	20T1106	Trivial (GRH)
20.10.46465044146768981515042816.1	x^20 - 10x^19 + 37x^18 - 46x^17 - 81x^16 + 358x^15 - 434x^14 - 60x^13 + 775x^12 - 1046x^11 + 945x^10 - 638x^9 - 310x^8 + 1564x^7 - 1908x^6 + 1168x^5 - 339x^4 - 2x^3 + 34x^2 - 10x + 1	\( -\,2^{20}\cdot 83^{4}\cdot 983^{4} \)	20T992	Trivial (GRH)
20.10.46465044146768981515042816.2	x^20 - 6x^19 + 8x^18 + 26x^17 - 98x^16 + 82x^15 + 111x^14 - 194x^13 - 100x^12 + 70x^11 + 1277x^10 - 2956x^9 + 2439x^8 + 390x^7 - 2506x^6 + 2138x^5 - 732x^4 - 12x^3 + 74x^2 - 12x - 1	\( -\,2^{20}\cdot 83^{4}\cdot 983^{4} \)	20T992	Trivial (GRH)
20.10.74824300206301289262147419.1	x^20 - 3x^19 - 4x^18 + 23x^17 + 3x^16 - 108x^15 + 62x^14 + 353x^13 - 538x^12 - 333x^11 + 1385x^10 - 819x^9 - 865x^8 + 1401x^7 - 518x^6 - 210x^5 + 322x^4 - 267x^3 + 152x^2 - 37x + 1	\( -\,11^{17}\cdot 23^{6} \)	20T310	Trivial (GRH)
20.10.106562954951958175076204651.1	x^20 - 5x^19 + 16x^18 - 38x^17 + 36x^16 + 53x^15 - 225x^14 + 425x^13 - 559x^12 + 338x^11 + 384x^10 - 897x^9 + 449x^8 + 347x^7 - 442x^6 + 31x^5 + 132x^4 - 33x^3 - 17x^2 + 4x + 1	\( -\,251^{4}\cdot 1931^{5} \)	20T462	Trivial (GRH)
20.10.123694350305361166820442112.1	x^20 - 8x^19 + 24x^18 - 30x^17 - 18x^16 + 200x^15 - 584x^14 + 960x^13 - 937x^12 + 480x^11 + 328x^10 - 1274x^9 + 1384x^8 - 422x^7 - 322x^6 + 272x^5 - 60x^4 + 18x^3 - 20x^2 + 8x - 1	\( -\,2^{30}\cdot 103\cdot 5783^{4} \)	20T992	Trivial (GRH)
20.10.144839477147925369006500864.1	x^20 - x^18 - 15x^16 + 14x^14 + 69x^12 - 133x^10 - 110x^8 + 517x^6 - 495x^4 + 165x^2 - 11	\( -\,2^{10}\cdot 11^{17}\cdot 23^{4} \)	20T749	Trivial (GRH)
20.10.144839477147925369006500864.2	x^20 + x^18 - 4x^16 - 36x^14 + 14x^12 + 254x^10 - 319x^8 - 33x^6 + 88x^4 + 44x^2 - 11	\( -\,2^{10}\cdot 11^{17}\cdot 23^{4} \)	20T749	Trivial (GRH)
20.10.160910726907504640000000000.1	x^20 - 2x^19 - 6x^18 + 22x^17 - 10x^16 - 88x^15 + 147x^14 + 84x^13 - 469x^12 + 240x^11 + 623x^10 - 708x^9 - 183x^8 + 732x^7 - 276x^6 - 262x^5 + 222x^4 - 10x^3 - 35x^2 + 6x + 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{4}\cdot 181^{4} \)	20T299	Trivial (GRH)
20.10.195532563918689056742899679.1	x^20 - x^19 - 13x^18 + 14x^17 + 70x^16 - 82x^15 - 203x^14 + 261x^13 + 351x^12 - 492x^11 - 397x^10 + 566x^9 + 346x^8 - 403x^7 - 262x^6 + 180x^5 + 142x^4 - 44x^3 - 36x^2 + 1	\( -\,16493^{2}\cdot 520151\cdot 1175561^{2} \)	20T1110	Trivial (GRH)
20.10.201484463662828739248046875.1	x^20 - 2x^19 - 11x^18 + 16x^17 + 40x^16 - 41x^15 - 71x^14 + 42x^13 + 39x^12 - 27x^11 + 159x^10 + 4x^9 - 369x^8 - 61x^7 + 444x^6 + 7x^5 - 200x^4 + 2x^3 + 29x^2 - x - 1	\( -\,5^{10}\cdot 19^{5}\cdot 1699^{4} \)	20T168	Trivial (GRH)
20.10.201484463662828739248046875.2	x^20 - 3x^19 - 10x^18 + 27x^17 + 45x^16 - 76x^15 - 145x^14 + 98x^13 + 274x^12 - 51x^11 - 339x^10 - 51x^9 + 274x^8 + 98x^7 - 145x^6 - 76x^5 + 45x^4 + 27x^3 - 10x^2 - 3x + 1	\( -\,5^{10}\cdot 19^{5}\cdot 1699^{4} \)	20T876	Trivial (GRH)
20.10.201484463662828739248046875.3	x^20 - 6x^19 + 13x^18 - 6x^17 - 42x^16 + 139x^15 - 198x^14 + 49x^13 + 354x^12 - 720x^11 + 620x^10 + 45x^9 - 811x^8 + 756x^7 - 133x^6 + 66x^5 - 177x^4 + 91x^3 + 8x^2 - 9x + 1	\( -\,5^{10}\cdot 19^{5}\cdot 1699^{4} \)	20T876	Trivial (GRH)
20.10.241050974838786899548191419.1	x^20 - 10x^19 + 34x^18 - 21x^17 - 135x^16 + 264x^15 + 122x^14 - 680x^13 + 158x^12 + 898x^11 - 439x^10 - 737x^9 + 429x^8 + 396x^7 - 229x^6 - 136x^5 + 74x^4 + 28x^3 - 15x^2 - 2x + 1	\( -\,11^{2}\cdot 41\cdot 3691\cdot 3628255063^{2} \)	20T1110	Trivial (GRH)
20.10.330675770864580911767512064.1	x^20 - x^19 - 3x^18 + 7x^17 - 6x^16 + 11x^15 - 31x^14 - 68x^13 + 269x^12 - 140x^11 - 496x^10 + 705x^9 + 157x^8 - 799x^7 + 490x^6 + 374x^5 - 387x^4 + 57x^3 + 127x^2 - 25x + 1	\( -\,2^{10}\cdot 11^{18}\cdot 241^{2} \)	20T846	Trivial (GRH)
20.10.499094134475513860355613696.1	x^20 - 10x^18 + 18x^16 - 42x^14 + 23x^12 + 100x^10 - 52x^8 - 120x^6 + 72x^4 + 18x^2 - 9	\( -\,2^{10}\cdot 3^{6}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.10.658618684118710741619590144.1	x^20 - 9x^18 + 18x^16 + 26x^14 - 80x^12 + 22x^10 - 93x^8 - 105x^6 + 780x^4 - 210x^2 - 241	\( -\,2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T846	Trivial (GRH)
20.10.658618684118710741619590144.2	x^20 - 3x^19 - 7x^18 + 4x^17 + 59x^16 + 41x^15 - 155x^14 - 151x^13 + 146x^12 - 149x^11 - 667x^10 + 273x^9 + 1109x^8 + 143x^7 - 550x^6 - 211x^5 + 94x^4 + 83x^3 - 7x^2 - 9x - 1	\( -\,2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T846	Trivial (GRH)
20.10.658618684118710741619590144.3	x^20 - 2x^19 - 10x^18 + 30x^17 + 2x^16 - 119x^15 + 241x^14 - 159x^13 - 305x^12 + 1042x^11 - 1683x^10 + 1548x^9 - 250x^8 - 1523x^7 + 2507x^6 - 1857x^5 + 376x^4 + 492x^3 - 472x^2 + 75x + 67	\( -\,2^{10}\cdot 11^{16}\cdot 241^{3} \)	20T846	Trivial (GRH)
20.10.806877848402725521973046875.1	x^20 - 2x^19 - 11x^18 + 29x^17 + 11x^16 - 122x^15 + 184x^14 + 47x^13 - 342x^12 + 569x^11 - 536x^10 - 1288x^9 + 403x^8 + 3536x^7 + 167x^6 - 3112x^5 - 1429x^4 + 1221x^3 + 772x^2 - 92x - 1	\( -\,5^{8}\cdot 151^{4}\cdot 331^{5} \)	20T462	Trivial (GRH)
20.10.909556369822141985336351744.1	x^20 - 9x^19 + 30x^18 - 26x^17 - 92x^16 + 235x^15 - 38x^14 - 277x^13 - 443x^12 + 1550x^11 + 245x^10 - 4064x^9 + 3041x^8 + 2955x^7 - 4618x^6 + 302x^5 + 2054x^4 - 768x^3 - 178x^2 + 108x - 9	\( -\,2^{10}\cdot 71^{5}\cdot 281^{6} \)	20T993	Trivial (GRH)
20.10.909556369822141985336351744.2	x^20 + 6x^18 + 8x^16 - 89x^14 - 80x^12 + 257x^10 + 245x^8 - 512x^6 + 23x^4 + 213x^2 - 71	\( -\,2^{10}\cdot 71^{5}\cdot 281^{6} \)	20T993	Trivial (GRH)
20.10.976514400368289676505645056.1	x^20 - 2x^18 - 4x^16 + 7x^14 + x^12 + 3x^10 + 3x^8 - 11x^6 + 4x^2 - 1	\( -\,2^{20}\cdot 30516826559^{2} \)	20T1110	Trivial (GRH)
20.10.1082081291410568717705150464.1	x^20 - 10x^18 + 36x^16 - 48x^14 - 13x^12 + 78x^10 - 21x^8 - 52x^6 + 24x^4 + 8x^2 - 4	\( -\,2^{38}\cdot 89^{8} \)	20T965	Trivial (GRH)
20.10.1242593181789399040000000000.1	x^20 - 7x^18 + 20x^16 - 8x^14 - 145x^12 + 486x^10 - 688x^8 + 468x^6 - 146x^4 + 21x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T168	Trivial (GRH)
20.10.1242593181789399040000000000.2	x^20 - 7x^18 + 16x^16 - 18x^14 + 29x^12 - 40x^10 + 31x^6 - 15x^4 + 3x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T876	Trivial (GRH)
20.10.1242593181789399040000000000.3	x^20 - 11x^18 + 45x^16 - 92x^14 + 96x^12 - 36x^10 - 19x^8 + 38x^6 - 37x^4 + 15x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T876	Trivial (GRH)
20.10.1242593181789399040000000000.4	x^20 - 3x^18 + 11x^14 - 31x^12 + 46x^10 - 44x^8 + 51x^6 - 45x^4 + 16x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T876	Trivial (GRH)
20.10.1242593181789399040000000000.5	x^20 - 4x^18 - 4x^16 + 26x^14 - 26x^12 + 8x^10 - 20x^8 + 49x^6 - 39x^4 + 11x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3319^{4} \)	20T876	Trivial (GRH)
20.10.1254027648371107840000000000.1	x^20 - 6x^18 + 10x^16 - 4x^14 + 7x^12 - 12x^10 - 14x^8 + 18x^6 + 7x^4 - 5x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11066329^{2} \)	20T1045	Trivial (GRH)
20.10.1287675250344566243662109375.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 107x^16 + 244x^15 + 49x^14 - 533x^13 + 171x^12 + 651x^11 - 306x^10 - 544x^9 + 218x^8 + 329x^7 - 53x^6 - 142x^5 - 12x^4 + 39x^3 + 5x^2 - 5x - 1	\( -\,5^{10}\cdot 19\cdot 61\cdot 929\cdot 11066329^{2} \)	20T1045	Trivial (GRH)
20.10.1303586853480048640000000000.1	x^20 - 8x^18 + 14x^16 + 29x^14 - 105x^12 + 88x^10 - 13x^8 + 8x^6 - 21x^4 + 9x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3359^{4} \)	20T168	Trivial (GRH)
20.10.1818446924078203240000000000.1	x^20 - 10x^18 + 37x^16 - 57x^14 + 11x^12 + 67x^10 - 59x^8 - 6x^6 + 16x^4 - 1	\( -\,2^{12}\cdot 5^{10}\cdot 491^{2}\cdot 434249^{2} \)	20T1045	Trivial (GRH)
20.10.1991862385339271699798949888.1	x^20 - 4x^18 - 6x^16 - 86x^14 + 107x^12 + 380x^10 - 117x^8 - 436x^6 + 23x^4 + 66x^2 - 7	\( -\,2^{30}\cdot 3^{8}\cdot 7\cdot 2521^{4} \)	20T1106	Trivial (GRH)
20.10.2095807236189058847283871744.1	x^20 - 11x^18 + 48x^16 - 98x^14 + 62x^12 + 115x^10 - 265x^8 + 226x^6 - 97x^4 + 19x^2 - 1	\( -\,2^{20}\cdot 13^{10}\cdot 347^{4} \)	20T887	Trivial (GRH)
20.10.2136345869968048790230393423.1	x^20 - x^19 - 14x^18 + 18x^17 + 49x^16 - 88x^15 + 24x^14 + 196x^13 - 468x^12 - 239x^11 + 956x^10 + 78x^9 - 767x^8 + 202x^7 + 314x^6 - 22x^5 + 119x^4 + 35x^3 - 38x^2 - 3x + 1	\( -\,11^{18}\cdot 727^{3} \)	20T303	Trivial (GRH)
20.10.2136345869968048790230393423.2	x^20 - 9x^19 + 42x^18 - 137x^17 + 332x^16 - 637x^15 + 947x^14 - 961x^13 + 382x^12 + 920x^11 - 2641x^10 + 3848x^9 - 3738x^8 + 2337x^7 - 607x^6 - 353x^5 + 406x^4 - 117x^3 - 30x^2 + 15x + 1	\( -\,11^{18}\cdot 727^{3} \)	20T303	Trivial (GRH)