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 88)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.4818813138470041550848.1	x^20 - 2x^19 + 3x^18 - 8x^17 + 6x^16 - 2x^15 + 7x^14 - 6x^13 + 15x^12 - 4x^11 + 26x^10 + 6x^9 + 32x^8 + 20x^7 + 31x^6 + 4x^5 + 17x^4 + 6x^2 - 2x + 1	\( 2^{20}\cdot 47^{8}\cdot 193 \)	20T849	Trivial
20.0.11809837380809998204928.1	x^20 - 8x^19 + 31x^18 - 76x^17 + 133x^16 - 188x^15 + 268x^14 - 464x^13 + 852x^12 - 1328x^11 + 1580x^10 - 1372x^9 + 873x^8 - 498x^7 + 408x^6 - 392x^5 + 270x^4 - 110x^3 + 24x^2 - 4x + 1	\( 2^{20}\cdot 11\cdot 43\cdot 47^{8} \)	20T849	Trivial (GRH)
20.2.1335832802762267195251875.1	x^20 - 10x^19 + 52x^18 - 183x^17 + 481x^16 - 992x^15 + 1654x^14 - 2276x^13 + 2632x^12 - 2610x^11 + 2274x^10 - 1784x^9 + 1284x^8 - 854x^7 + 525x^6 - 296x^5 + 150x^4 - 65x^3 + 24x^2 - 7x + 1	\( -\,3^{4}\cdot 5^{4}\cdot 103^{8}\cdot 2083 \)	20T849	Trivial (GRH)
20.2.2122075472874848556941312.1	x^20 - 2x^19 + 4x^18 + 2x^17 + 14x^15 + 12x^14 + 26x^13 + 45x^12 + 78x^11 + 84x^10 + 166x^9 + 189x^8 + 210x^7 + 208x^6 + 252x^5 + 181x^4 + 108x^3 + 58x^2 + 54x + 19	\( -\,2^{30}\cdot 47^{8}\cdot 83 \)	20T849	Trivial (GRH)
20.4.4934464653793322548068352.1	x^20 - 6x^19 + 12x^18 + 4x^17 - 58x^16 + 80x^15 + 46x^14 - 260x^13 + 210x^12 + 254x^11 - 586x^10 + 118x^9 + 599x^8 - 390x^7 - 348x^6 + 246x^5 + 128x^4 - 54x^3 - 24x^2 + 2x + 1	\( 2^{30}\cdot 47^{8}\cdot 193 \)	20T849	Trivial (GRH)
20.4.4934464653793322548068352.2	x^20 - 4x^19 + 10x^18 - 4x^17 - 47x^16 + 154x^15 - 216x^14 + 4x^13 + 581x^12 - 1234x^11 + 1286x^10 - 356x^9 - 1154x^8 + 2352x^7 - 2660x^6 + 2268x^5 - 1623x^4 + 1024x^3 - 520x^2 + 182x - 31	\( 2^{30}\cdot 47^{8}\cdot 193 \)	20T849	Trivial (GRH)
20.2.55454903830612651150623744.1	x^20 + 4x^18 - x^16 - 35x^14 - 105x^12 - 140x^10 - 45x^8 + 33x^6 - 3x^4 - 7x^2 - 1	\( -\,2^{10}\cdot 3^{4}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.6.55454903830612651150623744.1	x^20 + x^18 - 8x^16 + 2x^14 - 6x^12 - 22x^10 + 48x^8 + 53x^6 + 26x^4 + 13x^2 - 1	\( -\,2^{10}\cdot 3^{4}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.2.55454903830612651150623744.2	x^20 - 9x^18 + 29x^16 - 31x^14 - 45x^12 + 120x^10 - 9x^8 - 89x^6 - 41x^4 - 6x^2 - 1	\( -\,2^{10}\cdot 3^{4}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.6.55454903830612651150623744.2	x^20 - x^18 - 6x^16 + 10x^14 - 11x^12 - 5x^10 + 39x^8 - 46x^6 + 15x^4 + 18x^2 - 1	\( -\,2^{10}\cdot 3^{4}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.6.55454903830612651150623744.3	x^20 + 8x^18 + 15x^16 - 5x^14 - 10x^12 + 33x^10 + 6x^8 - 57x^6 - 9x^4 + 10x^2 - 1	\( -\,2^{10}\cdot 3^{4}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.2.166364711491837953451871232.1	x^20 - 6x^18 + 15x^16 + x^14 - 46x^12 - 13x^10 + 78x^8 + 55x^6 + 7x^4 - 8x^2 - 3	\( -\,2^{10}\cdot 3^{5}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.0.166364711491837953451871232.1	x^20 - 4x^18 + 6x^16 + 17x^14 - 63x^12 + 94x^10 + 6x^8 - 2x^6 + 106x^4 + 35x^2 + 3	\( 2^{10}\cdot 3^{5}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.4.166364711491837953451871232.1	x^20 + x^18 + x^16 - 10x^14 + 25x^12 + 57x^10 - 78x^8 - 143x^6 + 293x^4 - 165x^2 + 27	\( 2^{10}\cdot 3^{5}\cdot 401^{8} \)	20T849	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)
20.2.499094134475513860355613696.2	x^20 + 4x^18 - 11x^16 - 49x^14 + 10x^12 + 97x^10 - 64x^8 - 423x^6 - 465x^4 - 144x^2 - 9	\( -\,2^{10}\cdot 3^{6}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.6.499094134475513860355613696.2	x^20 - 4x^19 + 7x^18 - 11x^17 + 14x^16 - 19x^15 + 27x^14 - 77x^13 + 266x^12 - 351x^11 - 56x^10 + 502x^9 - 100x^8 - 812x^7 + 984x^6 - 426x^5 + 40x^4 + 85x^3 - 97x^2 + 19x - 1	\( -\,2^{10}\cdot 3^{6}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.2.499094134475513860355613696.3	x^20 + 7x^18 + 27x^16 + 58x^14 + 65x^12 - 79x^10 - 460x^8 - 649x^6 - 385x^4 - 99x^2 - 9	\( -\,2^{10}\cdot 3^{6}\cdot 401^{8} \)	20T849	$[2]$ (GRH)
20.6.499094134475513860355613696.3	x^20 - 4x^19 + 2x^18 + 17x^17 - 24x^16 - 30x^15 + 53x^14 + 51x^13 - 84x^12 - 159x^11 + 89x^10 + 280x^9 + 17x^8 - 44x^7 + 186x^6 + 98x^5 - 61x^4 - 18x^3 + 11x^2 - x - 1	\( -\,2^{10}\cdot 3^{6}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.6.499094134475513860355613696.4	x^20 - 4x^19 + 9x^18 - 22x^17 + 52x^16 - 63x^15 - 35x^14 + 163x^13 - 34x^12 - 287x^11 + 312x^10 + 39x^9 - 234x^8 + 40x^7 + 54x^6 + 119x^5 - 148x^4 - 8x^3 + 70x^2 - 26x + 1	\( -\,2^{10}\cdot 3^{6}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.0.1497282403426541581066841088.1	x^20 - 2x^19 + 9x^18 - 13x^17 + 14x^16 + x^15 - 40x^14 + 89x^13 - 49x^12 + 42x^11 + 143x^10 + 11x^9 + 301x^8 + 416x^7 + 726x^6 + 691x^5 + 1131x^4 + 634x^3 + 1224x^2 + 241x + 19	\( 2^{10}\cdot 3^{7}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.4.1497282403426541581066841088.1	x^20 + x^18 + 16x^16 + 40x^14 + 81x^12 + 113x^10 + 327x^8 + 372x^6 + 171x^4 - 180x^2 + 27	\( 2^{10}\cdot 3^{7}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.10.4491847210279624743200523264.1	x^20 - x^19 - 5x^18 + 19x^17 - 19x^16 - 78x^15 + 124x^14 - 65x^13 - 199x^12 + 368x^11 - 117x^10 - 19x^9 + 36x^8 - 648x^7 - 1037x^6 - 583x^5 + 195x^4 + 368x^3 + 145x^2 + 21x + 1	\( -\,2^{10}\cdot 3^{8}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.2.4491847210279624743200523264.2	x^20 + 8x^18 + 16x^16 - 47x^14 - 325x^12 - 846x^10 - 1332x^8 - 1386x^6 - 954x^4 - 405x^2 - 81	\( -\,2^{10}\cdot 3^{8}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.6.4491847210279624743200523264.2	x^20 - 8x^19 + 27x^18 - 44x^17 + 24x^16 + 42x^15 - 156x^14 + 410x^13 - 770x^12 + 672x^11 + 174x^10 - 686x^9 + 559x^8 - 2084x^7 + 4631x^6 - 4458x^5 + 2370x^4 - 828x^3 + 206x^2 - 30x + 1	\( -\,2^{10}\cdot 3^{8}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.6.4491847210279624743200523264.3	x^20 - x^19 - 5x^18 - 4x^17 + 25x^16 + 31x^15 - 83x^14 - 92x^13 + 19x^12 + 103x^11 - 131x^10 - 227x^9 - 138x^8 + 74x^7 + 74x^6 - 13x^5 - 49x^4 - 3x^3 + 27x^2 - 10x + 1	\( -\,2^{10}\cdot 3^{8}\cdot 401^{8} \)	20T849	$[2]$ (GRH)
20.10.19553672942050962092752651264.1	x^20 - 3x^18 - 7x^16 + 8x^14 + 31x^12 + 49x^10 - 28x^8 - 101x^6 - 122x^4 + 92x^2 - 1	\( -\,2^{10}\cdot 13^{4}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.10.22237416436075673111400121344.1	x^20 - 3x^19 - 2x^18 + x^17 + 43x^16 - 54x^15 - 50x^14 + 24x^13 + 273x^12 + 582x^11 - 3852x^10 + 2343x^9 + 9858x^8 - 12486x^7 - 6362x^6 + 14982x^5 - 2465x^4 - 4550x^3 + 1952x^2 - 211x - 1	\( -\,2^{10}\cdot 3^{4}\cdot 401^{9} \)	20T849	Trivial (GRH)
20.8.122826167518443894461242018521.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 112x^16 + 284x^15 - 50x^14 - 540x^13 + 538x^12 + 360x^11 - 888x^10 + 100x^9 + 847x^8 - 386x^7 - 537x^6 + 318x^5 + 204x^4 - 124x^3 - 38x^2 + 28x - 1	\( 3^{4}\cdot 61\cdot 401^{8}\cdot 37181 \)	20T849	Trivial (GRH)
20.4.254197748246662507205784466432.1	x^20 + 3x^18 - 46x^16 - 23x^14 + 120x^12 + 294x^10 - 173x^8 - 491x^6 - 75x^4 + 89x^2 + 13	\( 2^{10}\cdot 13^{5}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.8.254197748246662507205784466432.1	x^20 - 8x^18 + 18x^16 - 145x^14 + 787x^12 - 1644x^10 - 2092x^8 + 1716x^6 + 516x^4 - 315x^2 + 13	\( 2^{10}\cdot 13^{5}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.4.254197748246662507205784466432.2	x^20 - 2x^19 - 9x^18 + 17x^17 + 33x^16 - 37x^15 - 97x^14 - 26x^13 + 319x^12 + 298x^11 - 1002x^10 - 1696x^9 + 305x^8 + 3115x^7 + 3279x^6 - 1011x^5 - 5047x^4 - 2579x^3 + 1860x^2 + 2013x + 487	\( 2^{10}\cdot 13^{5}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.4.254197748246662507205784466432.3	x^20 + 15x^18 + 74x^16 + 149x^14 + 88x^12 - 290x^10 - 605x^8 + 273x^6 + 77x^4 - 83x^2 + 13	\( 2^{10}\cdot 13^{5}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.4.254197748246662507205784466432.4	x^20 - 2x^19 - 9x^18 + 20x^17 + 2x^16 - 99x^15 + 46x^14 + 65x^13 - 43x^12 + 57x^11 - 485x^10 + 388x^9 + 396x^8 - 785x^7 + 993x^6 - 759x^5 + 33x^4 + 1000x^3 - 1409x^2 + 880x - 281	\( 2^{10}\cdot 13^{5}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.12.569780740478705161127649640448.1	x^20 - 8x^18 + 13x^16 + 43x^14 - 132x^12 - 13x^10 + 285x^8 - 141x^6 - 97x^4 + 18x^2 + 8	\( 2^{15}\cdot 1429^{8} \)	20T849	Trivial (GRH)
20.16.3236791826785199222359606689792.1	x^20 - 2x^19 - 25x^18 + 28x^17 + 289x^16 - 60x^15 - 1892x^14 - 1002x^13 + 6924x^12 + 7606x^11 - 12322x^10 - 21148x^9 + 5602x^8 + 23324x^7 + 7045x^6 - 5926x^5 - 2533x^4 + 508x^3 + 229x^2 - 12x - 3	\( 2^{20}\cdot 3^{5}\cdot 19\cdot 401^{8} \)	20T849	Trivial (GRH)
20.8.3236791826785199222359606689792.1	x^20 - 8x^19 + 16x^18 + 4x^17 - 50x^16 + 116x^15 - 143x^14 + 84x^13 + 44x^12 - 194x^11 + 241x^10 - 194x^9 + 44x^8 + 84x^7 - 143x^6 + 116x^5 - 50x^4 + 4x^3 + 16x^2 - 8x + 1	\( 2^{20}\cdot 3^{5}\cdot 19\cdot 401^{8} \)	20T849	Trivial (GRH)
20.8.3236791826785199222359606689792.2	x^20 - 10x^19 + 45x^18 - 102x^17 + 5x^16 + 856x^15 - 3612x^14 + 9120x^13 - 15713x^12 + 17788x^11 - 9643x^10 - 7082x^9 + 20338x^8 - 17322x^7 + 2773x^6 + 5010x^5 - 1960x^4 - 1146x^3 + 678x^2 + 16x - 31	\( 2^{20}\cdot 3^{5}\cdot 19\cdot 401^{8} \)	20T849	Trivial (GRH)
20.8.3236791826785199222359606689792.3	x^20 - 2x^18 - 10x^17 - 25x^16 + 154x^15 - 225x^14 - 318x^13 + 742x^12 - 8x^11 - 347x^10 - 1118x^9 + 1722x^8 + 1832x^7 - 241x^6 - 4372x^5 + 701x^4 + 1764x^3 - 90x^2 - 142x + 9	\( 2^{20}\cdot 3^{5}\cdot 19\cdot 401^{8} \)	20T849	Trivial (GRH)
20.0.6404375933589793856083234947072.1	x^20 - 6x^19 + 35x^18 - 131x^17 + 416x^16 - 956x^15 + 1818x^14 - 2532x^13 + 2766x^12 - 1767x^11 + 1430x^10 - 4484x^9 + 16426x^8 - 35456x^7 + 56025x^6 - 64930x^5 + 59463x^4 - 41430x^3 + 22913x^2 - 8681x + 2267	\( 2^{15}\cdot 3^{6}\cdot 401^{9} \)	20T849	$[2, 2]$ (GRH)
20.12.7235635357212484551434589700096.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 97x^16 + 164x^15 + 250x^14 - 540x^13 - 537x^12 + 1350x^11 + 567x^10 - 1950x^9 - 288x^8 + 1604x^7 + 98x^6 - 752x^5 - 32x^4 + 178x^3 + 3x^2 - 14x + 1	\( 2^{20}\cdot 401^{8}\cdot 10321 \)	20T849	Trivial (GRH)
20.12.9116491847659282578042394247168.1	x^20 - x^19 - 22x^18 + 6x^17 + 251x^16 + 28x^15 - 1959x^14 + 425x^13 + 9196x^12 - 7255x^11 - 21388x^10 + 29222x^9 + 20580x^8 - 51308x^7 + 1364x^6 + 43476x^5 - 15824x^4 - 16900x^3 + 9200x^2 + 2408x - 1504	\( 2^{19}\cdot 1429^{8} \)	20T849	Trivial (GRH)
20.6.13796030581901716511938373960704.1	x^20 + 8x^18 + 13x^16 - 38x^14 - 106x^12 + 24x^10 + 183x^8 + 48x^6 - 35x^4 - 14x^2 - 1	\( -\,2^{10}\cdot 67^{4}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.12.16354316598493638176132749590528.1	x^20 - 15x^18 + 97x^16 - 406x^14 + 1199x^12 - 2431x^10 + 3716x^8 - 4536x^6 + 3816x^4 - 1728x^2 + 288	\( 2^{25}\cdot 3^{6}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.0.16354316598493638176132749590528.2	x^20 + 29x^18 + 333x^16 + 2020x^14 + 7265x^12 + 16351x^10 + 23222x^8 + 20316x^6 + 10320x^4 + 2736x^2 + 288	\( 2^{25}\cdot 3^{6}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.4.16354316598493638176132749590528.2	x^20 - 50x^16 + 59x^14 + 332x^12 - 799x^10 - 952x^8 - 3156x^6 - 1944x^4 + 1584x^2 + 288	\( 2^{25}\cdot 3^{6}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.4.16354316598493638176132749590528.3	x^20 + 4x^18 - 45x^16 - 130x^14 - 296x^12 - 2395x^10 - 5518x^8 - 6408x^6 - 6480x^4 + 4176x^2 + 288	\( 2^{25}\cdot 3^{6}\cdot 401^{8} \)	20T849	$[2]$ (GRH)
20.8.16354316598493638176132749590528.3	x^20 - 12x^18 + 23x^16 + 128x^14 - 484x^12 + 405x^10 + 206x^8 - 660x^6 + 816x^4 - 720x^2 + 288	\( 2^{25}\cdot 3^{6}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.8.16354316598493638176132749590528.4	x^20 - 16x^18 + 43x^16 + 215x^14 - 535x^12 - 609x^10 + 638x^8 + 516x^6 + 384x^4 - 1008x^2 + 288	\( 2^{25}\cdot 3^{6}\cdot 401^{8} \)	20T849	Trivial (GRH)
20.8.23498082529503866065777048066957.1	x^20 - 4x^19 - 13x^18 + 70x^17 + 20x^16 - 453x^15 + 576x^14 + 577x^13 - 2382x^12 + 2054x^11 + 944x^10 - 213x^9 - 3806x^8 + 2487x^7 + 1785x^6 - 3094x^5 - 1769x^4 + 986x^3 + 767x^2 - 49x - 71	\( 97^{4}\cdot 397\cdot 401^{8} \)	20T849	Trivial (GRH)