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
20.0.98476246219039869763584.3	x^20 + 5x^18 + 8x^16 - 3x^14 - 23x^12 - 20x^10 + 11x^8 + 29x^6 + 21x^4 + 7x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 1123^{4} \)	20T794	Trivial (GRH)
20.0.98476246219039869763584.4	x^20 + 4x^18 + 12x^16 + 25x^14 + 40x^12 + 50x^10 + 49x^8 + 35x^6 + 18x^4 + 6x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 1123^{4} \)	20T794	Trivial (GRH)
20.0.373326179890223832367104.4	x^20 - 4x^18 + 12x^16 - 25x^14 + 41x^12 - 51x^10 + 48x^8 - 31x^6 + 13x^4 - 2x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 1567^{4} \)	20T794	Trivial (GRH)
20.0.826435173591040000000000.1	x^20 + 5x^18 + 12x^16 + 20x^14 + 26x^12 + 28x^10 + 25x^8 + 18x^6 + 10x^4 + 5x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 13^{4}\cdot 41^{4} \)	20T794	Trivial (GRH)
20.0.826435173591040000000000.2	x^20 + 4x^18 + 4x^16 - 5x^14 - 12x^12 - 2x^10 + 14x^8 + 15x^6 + 6x^4 + 3x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 13^{4}\cdot 41^{4} \)	20T794	Trivial (GRH)
20.0.1004620302040414446157824.3	x^20 + 4x^18 + 15x^16 + 39x^14 + 75x^12 + 99x^10 + 93x^8 + 60x^6 + 27x^4 + 7x^2 + 1	\( 2^{20}\cdot 3^{18}\cdot 223^{4} \)	20T794	Trivial (GRH)
20.4.18805933270743231481641721.2	x^20 - 2x^19 + 5x^18 - 6x^17 + 7x^16 + 2x^15 - 14x^14 + 24x^13 - 27x^12 + 20x^11 + 7x^10 - 13x^9 + 5x^8 + 12x^7 + 9x^6 - 67x^5 + 2x^4 + 29x^3 - 16x^2 - 2x + 1	\( 13^{10}\cdot 97^{2}\cdot 347^{4} \)	20T794	Trivial (GRH)
20.4.30022900559553681267097600.1	x^20 - 10x^19 + 43x^18 - 90x^17 + 23x^16 + 412x^15 - 1306x^14 + 2260x^13 - 2727x^12 + 2770x^11 - 2707x^10 + 1770x^9 + 1473x^8 - 6500x^7 + 10210x^6 - 10124x^5 + 7003x^4 - 3450x^3 + 1175x^2 - 250x + 25	\( 2^{30}\cdot 5^{2}\cdot 5783^{4} \)	20T794	Trivial (GRH)
20.4.94017070137600000000000000.1	x^20 + 3x^18 + 6x^16 + 12x^14 + 7x^12 - 25x^10 - 83x^8 - 141x^6 - 117x^4 - 27x^2 + 9	\( 2^{20}\cdot 3^{6}\cdot 5^{14}\cdot 67^{4} \)	20T794	Trivial (GRH)
20.4.94017070137600000000000000.2	x^20 - x^18 - 3x^16 - 2x^14 + 25x^12 - x^10 - 47x^8 - 21x^6 - 9x^4 + 9	\( 2^{20}\cdot 3^{6}\cdot 5^{14}\cdot 67^{4} \)	20T794	Trivial (GRH)
20.8.486911802025734669619140625.2	x^20 - 2x^19 - 4x^18 + 7x^17 + 3x^16 + 4x^15 - 13x^14 - 20x^13 + 93x^12 + 53x^11 - 407x^10 - 182x^9 + 942x^8 + 124x^7 - 826x^6 - 43x^5 + 239x^4 + 59x^3 - 17x^2 - 9x - 1	\( 5^{10}\cdot 13^{4}\cdot 347^{6} \)	20T794	Trivial (GRH)
20.4.2095807236189058847283871744.1	x^20 + 9x^18 + 23x^16 - 9x^14 - 128x^12 - 186x^10 - 52x^8 + 77x^6 + 59x^4 + 14x^2 + 1	\( 2^{20}\cdot 13^{10}\cdot 347^{4} \)	20T794	Trivial (GRH)
20.4.2095807236189058847283871744.2	x^20 + 9x^18 + 30x^16 + 46x^14 + 34x^12 + 19x^10 + 13x^8 - 14x^6 - 29x^4 - 9x^2 + 1	\( 2^{20}\cdot 13^{10}\cdot 347^{4} \)	20T794	Trivial (GRH)
20.0.2141929924305725440000000000.1	x^20 + 9x^18 + 23x^16 + 9x^14 - 25x^12 + 7x^10 + 66x^8 + 61x^6 + 30x^4 + 9x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 3803^{4} \)	20T794	Trivial (GRH)
20.8.2141929924305725440000000000.1	x^20 + 3x^18 + 10x^16 - 6x^14 - 20x^12 - x^10 - 23x^8 + 30x^6 + 2x^4 - 6x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 3803^{4} \)	20T794	Trivial (GRH)
20.8.2141929924305725440000000000.2	x^20 - 4x^18 - x^16 + 27x^14 - 12x^12 - 47x^10 + 22x^8 + 27x^6 - 12x^4 - 3x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 3803^{4} \)	20T794	Trivial (GRH)
20.8.2141929924305725440000000000.3	x^20 + 3x^18 - x^16 - 19x^14 - 40x^12 - 34x^10 - 17x^8 + 38x^6 + 22x^4 - 13x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 3803^{4} \)	20T794	Trivial (GRH)
20.12.3178202722755606120397450849.1	x^20 - 6x^19 + 5x^18 + 25x^17 - 31x^16 - 36x^15 + 44x^14 - 38x^13 - 84x^12 + 483x^11 + 207x^10 - 1456x^9 + 92x^8 + 1993x^7 - 905x^6 - 1147x^5 + 871x^4 + 105x^3 - 125x^2 - 16x + 1	\( 13^{12}\cdot 97^{2}\cdot 347^{4} \)	20T794	Trivial (GRH)
20.0.4240248068839843840000000000.1	x^20 + 9x^18 + 29x^16 + 38x^14 + 20x^12 + 51x^10 + 157x^8 + 181x^6 + 86x^4 + 16x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 13^{4}\cdot 347^{4} \)	20T794	Trivial (GRH)
20.8.4591896834517011529541015625.1	x^20 - 3x^19 - 6x^18 + 32x^17 - 48x^16 + 39x^15 - 42x^14 + 168x^13 - 320x^12 + 269x^11 - 201x^10 - 46x^9 + 503x^8 - 601x^7 - 16x^6 + 353x^5 - 124x^4 - 64x^3 + 25x^2 + 3x - 1	\( 3^{4}\cdot 5^{14}\cdot 23^{6}\cdot 89^{4} \)	20T794	Trivial (GRH)
20.4.5397335908645724321531968521.1	x^20 - 2x^19 - 3x^18 - 2x^17 - x^16 + 6x^15 + 3x^14 + 4x^13 - x^12 - 4x^11 - 3x^10 - 4x^9 - x^8 + 4x^7 + 3x^6 + 6x^5 - x^4 - 2x^3 - 3x^2 - 2x + 1	\( 3^{2}\cdot 17^{10}\cdot 4153^{4} \)	20T794	Trivial (GRH)
20.4.30743450172982969617507942400.1	x^20 + 10x^18 - 20x^17 + 29x^16 - 160x^15 + 160x^14 - 352x^13 + 516x^12 - 608x^11 + 442x^10 - 288x^9 + 617x^8 - 1200x^7 + 820x^6 - 168x^5 + 27x^4 - 48x^3 - 16x^2 + 20x + 1	\( 2^{40}\cdot 5^{2}\cdot 5783^{4} \)	20T794	$[2]$ (GRH)
20.8.30743450172982969617507942400.1	x^20 - 10x^18 + 21x^16 + 88x^14 - 104x^13 - 287x^12 - 16x^11 + 810x^10 + 1232x^9 - 3411x^8 - 832x^7 + 4388x^6 - 276x^5 - 1856x^4 + 232x^3 + 120x^2 - 188x - 49	\( 2^{40}\cdot 5^{2}\cdot 5783^{4} \)	20T794	Trivial (GRH)
20.8.30743450172982969617507942400.2	x^20 - 12x^18 - 4x^17 + 49x^16 - 144x^14 + 88x^13 + 79x^12 - 432x^11 + 334x^10 + 288x^9 - 519x^8 + 248x^7 - 94x^6 - 60x^5 + 336x^4 - 160x^3 - 92x^2 + 84x + 17	\( 2^{40}\cdot 5^{2}\cdot 5783^{4} \)	20T794	Trivial (GRH)
20.4.41327071510653103765869140625.1	x^20 - 11x^18 - 14x^17 + 47x^16 + 99x^15 - 25x^14 - 286x^13 - 179x^12 + 672x^11 + 283x^10 - 1030x^9 - 430x^8 + 650x^7 + 650x^6 - 312x^5 - 320x^4 + 52x^3 + 418x^2 + 281x + 79	\( 3^{6}\cdot 5^{14}\cdot 23^{6}\cdot 89^{4} \)	20T794	Trivial (GRH)
20.12.104954566290980546560000000000.1	x^20 - 19x^18 + 157x^16 - 740x^14 + 2191x^12 - 4226x^10 + 5324x^8 - 4268x^6 + 2043x^4 - 511x^2 + 49	\( 2^{20}\cdot 5^{10}\cdot 7^{2}\cdot 3803^{4} \)	20T794	Trivial (GRH)
20.12.114797420862925288238525390625.1	x^20 - x^19 - 14x^18 + 29x^17 + 71x^16 - 278x^15 - 62x^14 + 1312x^13 - 872x^12 - 3358x^11 + 4146x^10 + 4394x^9 - 8419x^8 - 1676x^7 + 8471x^6 - 2250x^5 - 3770x^4 + 2230x^3 + 500x^2 - 250x - 25	\( 3^{4}\cdot 5^{16}\cdot 23^{6}\cdot 89^{4} \)	20T794	Trivial (GRH)
20.4.716601923633933608960000000000.1	x^20 + 10x^18 + 21x^16 - 45x^14 - 111x^12 + 196x^10 - 290x^8 - 3042x^6 - 3445x^4 - 845x^2 + 169	\( 2^{20}\cdot 5^{10}\cdot 13^{6}\cdot 347^{4} \)	20T794	Trivial (GRH)
20.0.786993757275194005675029037056.3	x^20 + x^18 + 30x^16 + 121x^14 + 196x^12 + 51x^10 - 165x^8 - 147x^6 + 183x^4 - 63x^2 + 9	\( 2^{20}\cdot 3^{16}\cdot 11491^{4} \)	20T794	Trivial (GRH)
20.0.786993757275194005675029037056.4	x^20 - 14x^18 + 90x^16 - 356x^14 + 958x^12 - 1824x^10 + 2517x^8 - 2619x^6 + 2145x^4 - 1062x^2 + 441	\( 2^{20}\cdot 3^{16}\cdot 11491^{4} \)	20T794	Trivial (GRH)
20.8.1033176787766327594146728515625.1	x^20 - x^18 - 25x^17 - 57x^16 - 30x^15 - 44x^14 + 135x^13 - 213x^12 - 460x^11 + 734x^10 - 100x^9 - 752x^8 + 550x^7 + 96x^6 - 150x^5 + 2x^4 + 35x^3 + 4x^2 - 5x - 1	\( 3^{6}\cdot 5^{16}\cdot 23^{6}\cdot 89^{4} \)	20T794	Trivial (GRH)
20.16.1559830077598614328922738902569.1	x^20 - 8x^19 + 12x^18 + 80x^17 - 356x^16 + 264x^15 + 1611x^14 - 4707x^13 + 2564x^12 + 10710x^11 - 23211x^10 + 11312x^9 + 19341x^8 - 30287x^7 + 10859x^6 + 7044x^5 - 6587x^4 + 1077x^3 + 399x^2 - 126x + 9	\( 3^{2}\cdot 17^{12}\cdot 4153^{4} \)	20T794	Trivial (GRH)
20.12.3347492792362901405035400390625.1	x^20 - x^19 - 19x^18 + 13x^17 + 129x^16 - 37x^15 - 430x^14 - 160x^13 + 805x^12 + 971x^11 - 660x^10 - 1743x^9 - 172x^8 + 1754x^7 + 90x^6 - 741x^5 + 151x^4 + 94x^3 - 48x^2 + 3x + 1	\( 3^{10}\cdot 5^{14}\cdot 23^{6}\cdot 89^{4} \)	20T794	Trivial (GRH)
20.12.3521934896736480471040000000000.1	x^20 - 5x^18 - 5x^16 + 52x^14 - 36x^12 - 108x^10 + 111x^8 + 39x^6 - 39x^4 - 6x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 61^{4}\cdot 397^{4} \)	20T794	Trivial (GRH)
20.8.7100265268622819943040000000000.1	x^20 + 6x^18 + 3x^16 - 35x^14 - 41x^12 + 61x^10 + 89x^8 - 27x^6 - 53x^4 - 4x^2 + 1	\( 2^{16}\cdot 5^{10}\cdot 57713^{4} \)	20T794	Trivial (GRH)
20.8.7100265268622819943040000000000.2	x^20 + 5x^18 - 3x^16 - 39x^14 - 18x^12 + 78x^10 + 50x^8 - 40x^6 - 35x^4 - 4x^2 + 1	\( 2^{16}\cdot 5^{10}\cdot 57713^{4} \)	20T794	Trivial (GRH)
20.8.7811260074827935595953369140625.1	x^20 - 2x^19 + 4x^18 - 4x^17 - 43x^16 - 5x^15 + 116x^14 + 31x^13 - 613x^12 - 802x^11 + 3810x^10 + 4203x^9 - 2956x^8 + 4241x^7 - 22877x^6 - 12197x^5 + 28752x^4 - 8262x^3 + 10040x^2 - 6533x + 1091	\( 5^{14}\cdot 61^{6}\cdot 397^{4} \)	20T794	Trivial (GRH)
20.12.7811260074827935595953369140625.2	x^20 - x^19 - 7x^18 + 32x^17 - 103x^16 + 5x^15 + 494x^14 - 1836x^13 + 3791x^12 - 2543x^11 - 2169x^10 + 13464x^9 - 18233x^8 + 3706x^7 + 14589x^6 - 33067x^5 + 11265x^4 + 20878x^3 - 10588x^2 - 1238x + 499	\( 5^{14}\cdot 61^{6}\cdot 397^{4} \)	20T794	Trivial (GRH)
20.8.8455924749076998400000000000000.2	x^20 - 34x^16 - 54x^14 + 226x^12 + 580x^10 + 175x^8 - 343x^6 - 158x^4 + 27x^2 + 1	\( 2^{20}\cdot 5^{14}\cdot 6029^{4} \)	20T794	Trivial (GRH)
20.12.8455924749076998400000000000000.3	x^20 - 3x^18 - 20x^16 + 89x^14 - 51x^12 - 190x^10 + 220x^8 + 80x^6 - 150x^4 + 25	\( 2^{20}\cdot 5^{14}\cdot 6029^{4} \)	20T794	Trivial (GRH)
20.16.8455924749076998400000000000000.3	x^20 - 18x^18 + 121x^16 - 388x^14 + 599x^12 - 335x^10 - 116x^8 + 157x^6 - 16x^4 - 7x^2 + 1	\( 2^{20}\cdot 5^{14}\cdot 6029^{4} \)	20T794	Trivial (GRH)
20.4.8455924749076998400000000000000.3	x^20 + 12x^18 + 50x^16 + 70x^14 - 52x^12 - 212x^10 - 137x^8 + 35x^6 + 60x^4 + 17x^2 + 1	\( 2^{20}\cdot 5^{14}\cdot 6029^{4} \)	20T794	Trivial (GRH)
20.8.8455924749076998400000000000000.3	x^20 + 3x^18 - 19x^16 - 52x^14 + 114x^12 + 275x^10 - 196x^8 - 442x^6 - 46x^4 + 12x^2 + 1	\( 2^{20}\cdot 5^{14}\cdot 6029^{4} \)	20T794	Trivial (GRH)
20.12.8455924749076998400000000000000.4	x^20 - 3x^18 - 21x^16 + 38x^14 + 149x^12 - 105x^10 - 341x^8 - 7x^6 + 76x^4 - 17x^2 + 1	\( 2^{20}\cdot 5^{14}\cdot 6029^{4} \)	20T794	Trivial (GRH)
20.8.8455924749076998400000000000000.4	x^20 + 5x^18 - 14x^16 - 77x^14 - 23x^12 + 142x^10 + 75x^8 - 54x^6 - 22x^4 + 7x^2 + 1	\( 2^{20}\cdot 5^{14}\cdot 6029^{4} \)	20T794	Trivial (GRH)
20.12.19751718904610600919732666015625.1	x^20 - 6x^19 - 13x^18 + 177x^17 - 419x^16 - 245x^15 + 3241x^14 - 7954x^13 + 10072x^12 - 2795x^11 - 17856x^10 + 45194x^9 - 63642x^8 + 62739x^7 - 45713x^6 + 24597x^5 - 9526x^4 + 2532x^3 - 420x^2 + 36x - 1	\( 5^{14}\cdot 61^{4}\cdot 97^{2}\cdot 397^{4} \)	20T794	Trivial (GRH)
20.8.19751718904610600919732666015625.1	x^20 - x^19 - 4x^18 + 35x^17 - 71x^16 + 31x^15 + 311x^14 - 1084x^13 + 1545x^12 - 1050x^11 - 1690x^10 + 7139x^9 - 13045x^8 + 19708x^7 - 27658x^6 + 31442x^5 - 24879x^4 + 11997x^3 - 2946x^2 + 183x + 41	\( 5^{14}\cdot 61^{4}\cdot 97^{2}\cdot 397^{4} \)	20T794	Trivial (GRH)
20.12.46505117981495597364067978515625.1	x^20 - 10x^19 + 32x^18 + 7x^17 - 375x^16 + 1385x^15 - 2091x^14 - 2209x^13 + 17271x^12 - 35975x^11 + 30586x^10 + 18705x^9 - 82621x^8 + 103558x^7 - 60836x^6 - 351x^5 + 26338x^4 - 15889x^3 - 1986x^2 + 764x - 29	\( 5^{10}\cdot 61^{8}\cdot 397^{4} \)	20T794	Trivial (GRH)
20.12.81917911788950073600000000000000.1	x^20 - 14x^18 + 40x^16 + 150x^14 - 637x^12 - 136x^10 + 967x^8 - 30x^6 - 240x^4 - 9x^2 + 9	\( 2^{20}\cdot 3^{6}\cdot 5^{14}\cdot 23^{4}\cdot 89^{4} \)	20T794	Trivial (GRH)
20.16.81917911788950073600000000000000.1	x^20 - 9x^18 - 9x^16 + 321x^14 - 1286x^12 + 2210x^10 - 1604x^8 + 81x^6 + 411x^4 - 126x^2 + 9	\( 2^{20}\cdot 3^{6}\cdot 5^{14}\cdot 23^{4}\cdot 89^{4} \)	20T794	Trivial (GRH)