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 105)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.1591368644495819328669.1	x^20 - 6x^19 + 11x^18 - 13x^16 - 19x^15 + 50x^14 + 8x^13 - 42x^12 - 38x^11 + 42x^10 + 31x^9 + 17x^8 - 59x^7 + 6x^6 + 2x^5 - x^4 + 15x^3 - 2x^2 - 3x + 1	\( 3^{10}\cdot 1609^{4}\cdot 4021 \)	20T887	Trivial (GRH)
20.0.67129997612651031322917.1	x^20 - 10x^19 + 54x^18 - 201x^17 + 570x^16 - 1296x^15 + 2439x^14 - 3879x^13 + 5293x^12 - 6265x^11 + 6486x^10 - 5904x^9 + 4736x^8 - 3341x^7 + 2060x^6 - 1097x^5 + 496x^4 - 185x^3 + 53x^2 - 10x + 1	\( 3^{10}\cdot 1777^{4}\cdot 114013 \)	20T887	Trivial (GRH)
20.2.527807503333353115234375.1	x^20 - 4x^19 + 5x^18 + 2x^17 - 6x^16 + 6x^15 - 16x^14 + 12x^13 + 33x^12 - 14x^11 - 17x^10 - 24x^9 + 23x^8 + 80x^7 - 17x^6 - 55x^5 + 9x^4 + 7x^3 + 5x^2 + 10x + 1	\( -\,5^{10}\cdot 13^{4}\cdot 41^{4}\cdot 669679 \)	20T887	Trivial (GRH)
20.0.562206990605729314922397.1	x^20 - 10x^19 + 56x^18 - 219x^17 + 662x^16 - 1624x^15 + 3336x^14 - 5846x^13 + 8849x^12 - 11650x^11 + 13383x^10 - 13406x^9 + 11659x^8 - 8726x^7 + 5535x^6 - 2905x^5 + 1210x^4 - 372x^3 + 72x^2 - 5x + 1	\( 3^{10}\cdot 103\cdot 1567^{4}\cdot 15331 \)	20T887	Trivial (GRH)
20.2.826435173591040000000000.2	x^20 - x^18 - x^16 - x^12 + 4x^10 + 2x^8 - 5x^6 - x^4 + 2x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 13^{4}\cdot 41^{4} \)	20T887	Trivial (GRH)
20.0.947500495953542851857093.1	x^20 - 10x^19 + 54x^18 - 201x^17 + 570x^16 - 1296x^15 + 2436x^14 - 3858x^13 + 5211x^12 - 6046x^11 + 6049x^10 - 5226x^9 + 3903x^8 - 2526x^7 + 1431x^6 - 723x^5 + 336x^4 - 144x^3 + 54x^2 - 15x + 3	\( 3^{18}\cdot 43\cdot 109\cdot 211\cdot 223^{4} \)	20T887	Trivial (GRH)
20.4.5399022361905183408203125.1	x^20 - 9x^19 + 45x^18 - 152x^17 + 383x^16 - 748x^15 + 1155x^14 - 1400x^13 + 1262x^12 - 642x^11 - 346x^10 + 1395x^9 - 2120x^8 + 2273x^7 - 1914x^6 + 1306x^5 - 714x^4 + 293x^3 - 82x^2 + 14x - 1	\( 5^{10}\cdot 11^{4}\cdot 131^{4}\cdot 128221 \)	20T887	Trivial (GRH)
20.4.6806565681538238525390625.1	x^20 - 10x^19 + 47x^18 - 138x^17 + 284x^16 - 436x^15 + 515x^14 - 463x^13 + 282x^12 - 41x^11 - 163x^10 + 270x^9 - 277x^8 + 213x^7 - 124x^6 + 54x^5 - 15x^4 - x^3 + 4x^2 - 2x + 1	\( 3^{4}\cdot 5^{16}\cdot 67^{4}\cdot 27329 \)	20T887	Trivial (GRH)
20.2.34494263992378240000000000.1	x^20 - 10x^19 + 56x^18 - 219x^17 + 655x^16 - 1568x^15 + 3078x^14 - 5020x^13 + 6838x^12 - 7774x^11 + 7338x^10 - 5698x^9 + 3601x^8 - 1842x^7 + 766x^6 - 259x^5 + 56x^4 + 12x^3 - 18x^2 + 7x - 1	\( -\,2^{16}\cdot 5^{10}\cdot 367^{4}\cdot 2971 \)	20T887	Trivial (GRH)
20.0.71311236675536751140274176.1	x^20 - 4x^19 + 6x^18 - 8x^17 + 19x^16 - 24x^15 + 36x^14 - 40x^13 + 34x^12 - 48x^11 + 48x^10 - 200x^9 - 58x^8 + 376x^7 + 652x^6 - 216x^5 - 963x^4 - 492x^3 + 442x^2 + 528x + 167	\( 2^{42}\cdot 359\cdot 461^{4} \)	20T887	Trivial (GRH)
20.0.96736970086313085808672768.1	x^20 + 20x^18 + 178x^16 + 928x^14 + 3134x^12 + 7146x^10 + 11102x^8 + 11552x^6 + 7666x^4 + 2920x^2 + 487	\( 2^{42}\cdot 461^{4}\cdot 487 \)	20T887	Trivial (GRH)
20.4.116615248953870513916015625.1	x^20 - 10x^19 + 53x^18 - 192x^17 + 521x^16 - 1108x^15 + 1883x^14 - 2563x^13 + 2739x^12 - 2147x^11 + 929x^10 + 387x^9 - 1233x^8 + 1385x^7 - 1043x^6 + 578x^5 - 237x^4 + 68x^3 - 8x^2 - 3x + 1	\( 5^{15}\cdot 7^{4}\cdot 149^{4}\cdot 3229 \)	20T887	Trivial (GRH)
20.4.480522573253793529189453125.1	x^20 - 10x^19 + 54x^18 - 201x^17 + 563x^16 - 1240x^15 + 2194x^14 - 3144x^13 + 3649x^12 - 3408x^11 + 2575x^10 - 1694x^9 + 1262x^8 - 1296x^7 + 1398x^6 - 1222x^5 + 786x^4 - 353x^3 + 102x^2 - 16x + 1	\( 5^{10}\cdot 13^{4}\cdot 331\cdot 347^{4}\cdot 359 \)	20T887	Trivial (GRH)
20.6.692417267200313623544921875.1	x^20 - 10x^19 + 56x^18 - 219x^17 + 655x^16 - 1568x^15 + 3080x^14 - 5034x^13 + 6884x^12 - 7868x^11 + 7445x^10 - 5705x^9 + 3365x^8 - 1318x^7 + 97x^6 + 318x^5 - 274x^4 + 122x^3 - 25x^2 - 2x + 1	\( -\,5^{10}\cdot 419\cdot 809\cdot 3803^{4} \)	20T887	Trivial (GRH)
20.12.772549750986794000244140625.1	x^20 - x^19 - 9x^18 + 19x^17 - 12x^16 - 31x^15 + 93x^14 - 138x^13 + 121x^12 - 8x^11 - 126x^10 + 216x^9 - 151x^8 - 26x^7 + 158x^6 - 93x^5 - 68x^4 + 38x^3 + 16x^2 - 3x - 1	\( 3^{4}\cdot 5^{14}\cdot 23^{4}\cdot 89^{5} \)	20T887	Trivial (GRH)
20.2.2095807236189058847283871744.1	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)
20.10.2095807236189058847283871744.1	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)
20.10.2141929924305725440000000000.1	x^20 - 2x^18 - 6x^16 + 9x^14 + 11x^12 - 20x^8 - 7x^6 + 10x^4 + 4x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3803^{4} \)	20T887	Trivial (GRH)
20.6.2141929924305725440000000000.3	x^20 + 8x^18 + 21x^16 + 9x^14 - 52x^12 - 81x^10 - 2x^8 + 64x^6 + 28x^4 - 4x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3803^{4} \)	20T887	Trivial (GRH)
20.6.2141929924305725440000000000.4	x^20 - 7x^18 + 7x^16 + 47x^14 - 135x^12 + 144x^10 - 81x^8 + 13x^6 + 10x^4 - 7x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3803^{4} \)	20T887	Trivial (GRH)
20.6.2141929924305725440000000000.5	x^20 - x^18 + 8x^14 - 30x^12 + 37x^10 - 97x^8 + 10x^6 + 27x^4 - 3x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3803^{4} \)	20T887	Trivial (GRH)
20.6.2141929924305725440000000000.6	x^20 + 7x^18 + 7x^16 - 47x^14 - 135x^12 - 144x^10 - 81x^8 - 13x^6 + 10x^4 + 7x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3803^{4} \)	20T887	Trivial (GRH)
20.6.2141929924305725440000000000.7	x^20 + 3x^18 - 7x^16 - 3x^14 + 85x^12 + 65x^10 - 117x^8 - 105x^6 + 14x^4 + 16x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 3803^{4} \)	20T887	Trivial (GRH)
20.0.2302725561923832607497256960.1	x^20 - 10x^19 + 52x^18 - 174x^17 + 419x^16 - 758x^15 + 1008x^14 - 858x^13 + 97x^12 + 1088x^11 - 1977x^10 + 1752x^9 - 383x^8 - 1068x^7 + 1470x^6 - 744x^5 - 122x^4 + 220x^3 + 73x^2 + 10x + 1	\( 2^{20}\cdot 5\cdot 61^{4}\cdot 397^{4}\cdot 1277 \)	20T887	$[3]$ (GRH)
20.4.3239225449408145366103515625.1	x^20 - 10x^19 + 57x^18 - 228x^17 + 697x^16 - 1700x^15 + 3376x^14 - 5510x^13 + 7369x^12 - 7944x^11 + 6595x^10 - 3666x^9 + 422x^8 + 1778x^7 - 2383x^6 + 1835x^5 - 972x^4 + 357x^3 - 82x^2 + 8x + 1	\( 3^{4}\cdot 5^{10}\cdot 11^{4}\cdot 139^{4}\cdot 749249 \)	20T887	Trivial (GRH)
20.8.3411129053084802306923828125.1	x^20 - 10x^19 + 36x^18 - 39x^17 - 83x^16 + 256x^15 - 104x^14 - 386x^13 + 472x^12 + 132x^11 - 547x^10 + 199x^9 + 275x^8 - 238x^7 - 35x^6 + 98x^5 - 18x^4 - 14x^3 + 3x^2 + 2x + 1	\( 5^{10}\cdot 151\cdot 3803^{4}\cdot 11059 \)	20T887	Trivial (GRH)
20.4.3551123440117203753498174869.1	x^20 - 10x^19 + 54x^18 - 201x^17 + 564x^16 - 1248x^15 + 2230x^14 - 3256x^13 + 3901x^12 - 3828x^11 + 3061x^10 - 1990x^9 + 1065x^8 - 492x^7 + 193x^6 - 29x^5 - 58x^4 + 72x^3 - 38x^2 + 9x + 1	\( 13^{10}\cdot 347^{4}\cdot 1776701 \)	20T887	Trivial (GRH)
20.8.3862748754933970001220703125.1	x^20 - 5x^19 + 18x^18 - 46x^17 + 73x^16 - 84x^15 - 23x^14 + 342x^13 - 575x^12 + 624x^11 - 495x^10 - 416x^9 + 1570x^8 - 1347x^7 + 254x^6 + 86x^5 + 107x^4 - 84x^3 - 8x^2 + 8x + 1	\( 3^{4}\cdot 5^{15}\cdot 23^{4}\cdot 89^{5} \)	20T887	Trivial (GRH)
20.8.6952947758881146002197265625.1	x^20 - 6x^18 - 17x^17 - 6x^16 + 58x^15 + 135x^14 + 120x^13 - 38x^12 - 256x^11 - 294x^10 - 135x^9 - 68x^8 - 86x^7 + 12x^6 + 124x^5 + 90x^4 + 5x^3 - 19x^2 - 8x - 1	\( 3^{6}\cdot 5^{14}\cdot 23^{4}\cdot 89^{5} \)	20T887	Trivial (GRH)
20.8.9090804088496766732900390625.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 114x^16 + 300x^15 - 86x^14 - 568x^13 + 747x^12 + 198x^11 - 1205x^10 + 596x^9 + 918x^8 - 852x^7 - 369x^6 + 469x^5 + 85x^4 - 115x^3 - 12x^2 + 12x + 1	\( 5^{10}\cdot 5519^{4}\cdot 1003369 \)	20T887	Trivial (GRH)
20.12.15383083333031826560000000000.1	x^20 - 10x^19 + 36x^18 - 39x^17 - 83x^16 + 256x^15 - 106x^14 - 372x^13 + 454x^12 + 58x^11 - 354x^10 + 246x^9 - 179x^8 - 90x^7 + 402x^6 - 119x^5 - 202x^4 + 84x^3 + 30x^2 - 13x + 1	\( 2^{16}\cdot 5^{10}\cdot 367^{4}\cdot 1324949 \)	20T887	Trivial (GRH)
20.12.19313743774669850006103515625.1	x^20 - 3x^19 - 16x^18 + 52x^17 + 85x^16 - 320x^15 - 148x^14 + 820x^13 - 109x^12 - 646x^11 + 602x^10 - 571x^9 - 449x^8 + 851x^7 - 313x^6 - 235x^5 + 213x^4 + 94x^3 + 60x^2 - 38x - 1	\( 3^{4}\cdot 5^{16}\cdot 23^{4}\cdot 89^{5} \)	20T887	Trivial (GRH)
20.0.30001577521140590722279644573.1	x^20 - 2x^19 + 7x^18 - 7x^17 + 7x^16 - 12x^15 + 52x^14 - 36x^13 + 57x^12 - 29x^11 + 93x^10 - 265x^9 + 334x^8 - 293x^7 + 171x^6 - 33x^5 + 27x^4 - 57x^3 + 37x^2 - 10x + 1	\( 3^{10}\cdot 61^{6}\cdot 397^{5} \)	20T887	Trivial (GRH)
20.12.34764738794405730010986328125.1	x^20 - 8x^19 + 14x^18 + 57x^17 - 271x^16 + 290x^15 + 472x^14 - 1402x^13 + 779x^12 + 1004x^11 - 1352x^10 - 52x^9 + 844x^8 + 232x^7 - 1889x^6 + 2195x^5 - 1167x^4 + 245x^3 + 20x^2 - 14x + 1	\( 3^{6}\cdot 5^{15}\cdot 23^{4}\cdot 89^{5} \)	20T887	Trivial (GRH)
20.8.39202479476297295788759765625.1	x^20 - 10x^19 + 37x^18 - 48x^17 - 59x^16 + 268x^15 - 264x^14 - 190x^13 + 677x^12 - 448x^11 - 413x^10 + 794x^9 - 202x^8 - 454x^7 + 373x^6 + 91x^5 - 190x^4 - 15x^3 + 40x^2 + 12x + 1	\( 3^{4}\cdot 5^{10}\cdot 11^{5}\cdot 139^{4}\cdot 824339 \)	20T887	Trivial (GRH)
20.14.75744139454672614891787109375.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 120x^16 + 348x^15 - 218x^14 - 484x^13 + 1049x^12 - 522x^11 - 762x^10 + 1263x^9 - 440x^8 - 478x^7 + 515x^6 - 87x^5 - 115x^4 + 62x^3 - 7x + 1	\( -\,3^{4}\cdot 5^{10}\cdot 439\cdot 21611^{4} \)	20T887	Trivial (GRH)
20.8.82060022357794878562001953125.1	x^20 - 10x^19 + 34x^18 - 21x^17 - 138x^16 + 288x^15 + 71x^14 - 743x^13 + 501x^12 + 751x^11 - 1180x^10 - 46x^9 + 1151x^8 - 533x^7 - 545x^6 + 420x^5 + 111x^4 - 118x^3 - 7x^2 + 13x + 1	\( 3^{12}\cdot 5^{10}\cdot 293^{4}\cdot 2145389 \)	20T887	Trivial (GRH)
20.8.90186244283743294466494140625.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 117x^16 + 324x^15 - 146x^14 - 568x^13 + 971x^12 - 54x^11 - 1416x^10 + 1101x^9 + 853x^8 - 1246x^7 - 143x^6 + 603x^5 - 62x^4 - 136x^3 + 25x^2 + 15x - 1	\( 5^{10}\cdot 53^{4}\cdot 71\cdot 139^{4}\cdot 44159 \)	20T887	Trivial (GRH)
20.8.96568718873349250030517578125.1	x^20 - 5x^19 + 8x^18 + 15x^17 - 101x^16 + 220x^15 - 308x^14 + 250x^13 + 501x^12 - 2665x^11 + 5325x^10 - 5215x^9 + 1635x^8 + 1720x^7 - 2725x^6 + 1740x^5 + 930x^4 - 510x^3 - 160x^2 + 50x + 5	\( 3^{4}\cdot 5^{17}\cdot 23^{4}\cdot 89^{5} \)	20T887	Trivial (GRH)
20.4.125981104337726781440000000000.1	x^20 + 9x^18 + 26x^16 - 3x^14 - 183x^12 - 439x^10 - 463x^8 - 207x^6 + 7x^4 + 40x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 11\cdot 5783^{4} \)	20T887	Trivial (GRH)
20.0.211676530855094943575671046144.1	x^20 + 19x^18 + 156x^16 + 730x^14 + 2162x^12 + 4255x^10 + 5672x^8 + 5074x^6 + 2882x^4 + 895x^2 + 101	\( 2^{20}\cdot 13^{10}\cdot 101\cdot 347^{4} \)	20T887	$[3]$ (GRH)
20.12.211676530855094943575671046144.1	x^20 - 19x^18 + 156x^16 - 730x^14 + 2162x^12 - 4255x^10 + 5672x^8 - 5074x^6 + 2882x^4 - 895x^2 + 101	\( 2^{20}\cdot 13^{10}\cdot 101\cdot 347^{4} \)	20T887	Trivial (GRH)
20.12.408678818272014026129150390625.1	x^20 - 6x^19 + 4x^18 + 38x^17 - 77x^16 - 77x^15 + 492x^14 - 289x^13 - 1733x^12 + 2866x^11 + 1148x^10 - 8154x^9 + 7563x^8 + 10081x^7 - 14437x^6 - 7578x^5 + 4345x^4 + 4696x^3 + 1812x^2 - 1517x + 191	\( 3^{4}\cdot 5^{14}\cdot 23^{6}\cdot 89^{5} \)	20T887	Trivial (GRH)
20.12.408678818272014026129150390625.2	x^20 - 5x^19 - 3x^18 + 41x^17 - 43x^16 + 25x^15 - 29x^14 - 176x^13 - 73x^12 + 714x^11 - 125x^10 + 20x^9 - 9x^8 - 1012x^7 - 329x^6 + 575x^5 + 548x^4 + 132x^3 - 99x^2 - 63x - 9	\( 3^{4}\cdot 5^{14}\cdot 23^{6}\cdot 89^{5} \)	20T887	Trivial (GRH)
20.6.437673968523300805364990234375.1	x^20 - 7x^19 + 15x^18 + 12x^17 - 147x^16 + 450x^15 - 904x^14 + 1407x^13 - 1828x^12 + 2086x^11 - 2169x^10 + 2086x^9 - 1828x^8 + 1407x^7 - 904x^6 + 450x^5 - 147x^4 + 12x^3 + 15x^2 - 7x + 1	\( -\,5^{14}\cdot 8209^{4}\cdot 15791 \)	20T887	Trivial (GRH)
20.0.490501952666011125760000000000.1	x^20 + 21x^18 + 193x^16 + 1020x^14 + 3423x^12 + 7590x^10 + 11188x^8 + 10708x^6 + 6251x^4 + 1945x^2 + 229	\( 2^{20}\cdot 5^{10}\cdot 229\cdot 3803^{4} \)	20T887	Trivial (GRH)
20.8.563188768469372826177978515625.1	x^20 - 7x^19 + 19x^18 - 34x^17 + 101x^16 - 280x^15 + 550x^14 - 895x^13 + 712x^12 + 201x^11 - 736x^10 - 35x^9 + 5640x^8 - 8368x^7 - 8204x^6 + 24258x^5 - 12953x^4 - 6669x^3 + 11861x^2 - 6740x + 1579	\( 3^{10}\cdot 5^{14}\cdot 23^{4}\cdot 89^{5} \)	20T887	Trivial (GRH)
20.16.1082828299852220422027587890625.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 116x^16 + 316x^15 - 130x^14 - 540x^13 + 854x^12 - 80x^11 - 1012x^10 + 940x^9 + 195x^8 - 794x^7 + 347x^6 + 182x^5 - 200x^4 + 20x^3 + 26x^2 - 4x - 1	\( 3^{4}\cdot 5^{15}\cdot 23^{4}\cdot 61\cdot 89^{4}\cdot 409 \)	20T887	Trivial (GRH)
20.16.1853001347776081251704775390625.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 120x^16 + 348x^15 - 214x^14 - 512x^13 + 1085x^12 - 374x^11 - 1185x^10 + 1354x^9 + 266x^8 - 1076x^7 + 255x^6 + 339x^5 - 149x^4 - 39x^3 + 24x^2 + 2x - 1	\( 5^{10}\cdot 61^{4}\cdot 397^{4}\cdot 551689 \)	20T887	Trivial (GRH)
20.8.2028205157601753313537587890625.1	x^20 - 10x^19 + 55x^18 - 210x^17 + 596x^16 - 1300x^15 + 2175x^14 - 2675x^13 + 2035x^12 + 101x^11 - 3033x^10 + 5215x^9 - 5402x^8 + 3733x^7 - 1544x^6 + 95x^5 + 339x^4 - 237x^3 + 80x^2 - 14x + 1	\( 3^{4}\cdot 5^{10}\cdot 17^{4}\cdot 29\cdot 461\cdot 1231^{4} \)	20T887	Trivial (GRH)