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 1898)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.328307557444402776721569.1	x^20 - x^19 + x^17 - x^16 + x^14 - x^13 + x^11 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1	\( 3^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	Trivial
20.0.5829995856912430117421056.1	x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1	\( 2^{20}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	Trivial
20.0.54296067514572573056640625.1	x^20 - x^19 + 2x^18 - 3x^17 + 5x^16 - 8x^15 + 13x^14 - 21x^13 + 34x^12 - 55x^11 + 89x^10 + 55x^9 + 34x^8 + 21x^7 + 13x^6 + 8x^5 + 5x^4 + 3x^3 + 2x^2 + x + 1	\( 5^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[2]$
20.0.1570539027548129147161113769.2	x^20 - x^19 - x^18 + 3x^17 - x^16 - 5x^15 + 7x^14 + 3x^13 - 17x^12 + 11x^11 + 23x^10 + 22x^9 - 68x^8 + 24x^7 + 112x^6 - 160x^5 - 64x^4 + 384x^3 - 256x^2 - 512x + 1024	\( 7^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[5]$
20.0.2845086159957207322343768064.1	x^20 - 9x^18 + 53x^16 - 182x^14 + 454x^12 - 711x^10 + 796x^8 - 469x^6 + 190x^4 - 15x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{16} \)	$C_2\times C_{10}$ (as 20T3)	Trivial
20.0.5969915757478328440239161344.5	x^20 - 2x^18 + 4x^16 - 8x^14 + 16x^12 - 32x^10 + 64x^8 - 128x^6 + 256x^4 - 512x^2 + 1024	\( 2^{30}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[5]$
20.0.5969915757478328440239161344.6	x^20 + 2x^18 + 4x^16 + 8x^14 + 16x^12 + 32x^10 + 64x^8 + 128x^6 + 256x^4 + 512x^2 + 1024	\( 2^{30}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[11]$
20.0.26496929674942114598525390625.1	x^20 - x^19 + 14x^18 - 3x^17 + 131x^16 - 23x^15 + 547x^14 + 141x^13 + 1496x^12 + 223x^11 + 1987x^10 + 109x^9 + 1892x^8 - 114x^7 + 860x^6 - 175x^5 + 293x^4 - 40x^3 + 27x^2 + 3x + 1	\( 3^{10}\cdot 5^{10}\cdot 11^{16} \)	$C_2\times C_{10}$ (as 20T3)	$[11]$
20.0.34371041692793369293212890625.1	x^20 + 10x^18 + 65x^16 - x^15 + 250x^14 - 15x^13 + 700x^12 - 75x^11 + 1252x^10 - 250x^9 + 1620x^8 - 375x^7 + 1200x^6 - 374x^5 + 600x^4 - 115x^3 + 50x^2 + 5x + 1	\( 3^{10}\cdot 5^{34} \)	$C_2\times C_{10}$ (as 20T3)	$[11]$
20.0.50522262278163705147147943936.1	x^20 + 25x^16 + 184x^12 + 403x^8 + 155x^4 + 1	\( 2^{40}\cdot 11^{16} \)	$C_2\times C_{10}$ (as 20T3)	$[5]$
20.0.344255425354822086003595935744.1	x^20 + 21x^18 + 188x^16 + 934x^14 + 2806x^12 + 5202x^10 + 5809x^8 + 3629x^6 + 1090x^4 + 120x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[22]$ (GRH)
20.20.344255425354822086003595935744.1	x^20 - 19x^18 + 152x^16 - 666x^14 + 1742x^12 - 2782x^10 + 2665x^8 - 1443x^6 + 390x^4 - 40x^2 + 1	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	Trivial (GRH)
20.0.344255425354822086003595935744.2	x^20 + 11x^18 + 77x^16 + 330x^14 + 1034x^12 + 2189x^10 + 3388x^8 + 3267x^6 + 2178x^4 + 605x^2 + 121	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[22]$ (GRH)
20.0.344255425354822086003595935744.3	x^20 + 3x^18 + 9x^16 + 27x^14 + 81x^12 + 243x^10 + 729x^8 + 2187x^6 + 6561x^4 + 19683x^2 + 59049	\( 2^{20}\cdot 3^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[22]$ (GRH)
20.0.470525233802978928640000000000.1	x^20 + 27x^18 + 277x^16 + 1386x^14 + 3694x^12 + 5493x^10 + 4588x^8 + 2079x^6 + 470x^4 + 45x^2 + 1	\( 2^{20}\cdot 5^{10}\cdot 11^{16} \)	$C_2\times C_{10}$ (as 20T3)	$[31]$ (GRH)
20.0.610351562500000000000000000000.1	x^20 + 20x^18 + 170x^16 + 800x^14 + 2275x^12 + 4003x^10 + 4280x^8 + 2605x^6 + 775x^4 + 75x^2 + 1	\( 2^{20}\cdot 5^{34} \)	$C_2\times C_{10}$ (as 20T3)	$[55]$ (GRH)
20.0.766436025104871719096831462361.1	x^20 - x^19 - 13x^18 + 104x^16 + 43x^15 - 734x^14 - 9x^13 + 3770x^12 + 355x^11 - 11777x^10 - 7082x^9 + 29156x^8 + 6480x^7 - 42976x^6 + 18272x^5 + 39296x^4 - 9856x^3 - 4608x^2 - 1536x + 1024	\( 3^{10}\cdot 7^{10}\cdot 11^{16} \)	$C_2\times C_{10}$ (as 20T3)	$[5]$ (GRH)
20.0.766481815643182771348259698369.1	x^20 - x^19 + 4x^18 - 7x^17 + 19x^16 - 40x^15 + 97x^14 - 217x^13 + 508x^12 - 1159x^11 + 2683x^10 + 3477x^9 + 4572x^8 + 5859x^7 + 7857x^6 + 9720x^5 + 13851x^4 + 15309x^3 + 26244x^2 + 19683x + 59049	\( 11^{18}\cdot 13^{10} \)	$C_2\times C_{10}$ (as 20T3)	$[25]$ (GRH)
20.0.2913368227796180298080018497536.2	x^20 - 18x^18 + 212x^16 - 1456x^14 + 7264x^12 - 22752x^10 + 50944x^8 - 60032x^6 + 48640x^4 - 7680x^2 + 1024	\( 2^{30}\cdot 3^{10}\cdot 11^{16} \)	$C_2\times C_{10}$ (as 20T3)	$[5]$ (GRH)
20.0.2913368227796180298080018497536.4	x^20 + 18x^18 + 212x^16 + 1456x^14 + 7264x^12 + 22752x^10 + 50944x^8 + 60032x^6 + 48640x^4 + 7680x^2 + 1024	\( 2^{30}\cdot 3^{10}\cdot 11^{16} \)	$C_2\times C_{10}$ (as 20T3)	$[5, 5]$ (GRH)
20.0.3206128490667995866421572265625.1	x^20 - x^19 + 19x^18 - 15x^17 + 148x^16 - 88x^15 + 618x^14 - 266x^13 + 1534x^12 - 470x^11 + 2342x^10 - 263x^9 + 1906x^8 + 1335x^7 + 479x^6 + 2937x^5 - 134x^4 + 3709x^3 - 1963x^2 - 1928x + 9901	\( 3^{10}\cdot 5^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[44]$ (GRH)
20.20.3206128490667995866421572265625.1	x^20 - x^19 - 31x^18 + 30x^17 + 368x^16 - 338x^15 - 2132x^14 + 1794x^13 + 6524x^12 - 4730x^11 - 11153x^10 + 6622x^9 + 10781x^8 - 4995x^7 - 5641x^6 + 1922x^5 + 1391x^4 - 316x^3 - 108x^2 + 12x + 1	\( 3^{10}\cdot 5^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	Trivial (GRH)
20.0.3206128490667995866421572265625.2	x^20 - x^19 - 11x^18 + 12x^17 + 76x^16 - 88x^15 - 318x^14 + 406x^13 + 946x^12 - 1352x^11 - 1783x^10 + 3334x^9 + 1837x^8 - 9549x^7 + 4445x^6 + 13860x^5 - 16127x^4 + 17590x^3 - 2068x^2 - 37412x + 39601	\( 3^{10}\cdot 5^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[4]$ (GRH)
20.0.3206128490667995866421572265625.3	x^20 - x^19 - 3x^18 + 7x^17 + 5x^16 - 33x^15 + 13x^14 + 119x^13 - 171x^12 - 305x^11 + 989x^10 - 1220x^9 - 2736x^8 + 7616x^7 + 3328x^6 - 33792x^5 + 20480x^4 + 114688x^3 - 196608x^2 - 262144x + 1048576	\( 3^{10}\cdot 5^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[2, 22]$ (GRH)
20.20.6113193735657808322804901216256.1	x^20 - 20x^18 + 169x^16 - 784x^14 + 2172x^12 - 3664x^10 + 3683x^8 - 2072x^6 + 575x^4 - 60x^2 + 1	\( 2^{40}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	Trivial (GRH)
20.0.6113193735657808322804901216256.3	x^20 + 20x^18 + 169x^16 + 784x^14 + 2172x^12 + 3664x^10 + 3683x^8 + 2072x^6 + 575x^4 + 60x^2 + 1	\( 2^{40}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[110]$ (GRH)
20.0.6113193735657808322804901216256.4	x^20 + 33x^16 + 352x^12 + 1331x^8 + 1331x^4 + 121	\( 2^{40}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[22]$ (GRH)
20.0.11208759391001129236841977834969.1	x^20 - x^19 + 5x^18 - 9x^17 + 29x^16 - 65x^15 + 181x^14 - 441x^13 + 1165x^12 - 2929x^11 + 7589x^10 + 11716x^9 + 18640x^8 + 28224x^7 + 46336x^6 + 66560x^5 + 118784x^4 + 147456x^3 + 327680x^2 + 262144x + 1048576	\( 11^{18}\cdot 17^{10} \)	$C_2\times C_{10}$ (as 20T3)	$[41]$ (GRH)
20.0.13610161416118240236476132491264.1	x^20 - 27x^18 + 352x^16 - 2709x^14 + 13339x^12 - 42123x^10 + 84004x^8 - 96768x^6 + 59840x^4 - 11520x^2 + 1024	\( 2^{20}\cdot 7^{10}\cdot 11^{16} \)	$C_2\times C_{10}$ (as 20T3)	$[5]$ (GRH)
20.0.34088221436915805032899514033281.2	x^20 - x^19 - 4x^18 + 9x^17 + 11x^16 - 56x^15 + x^14 + 279x^13 - 284x^12 - 1111x^11 + 2531x^10 - 5555x^9 - 7100x^8 + 34875x^7 + 625x^6 - 175000x^5 + 171875x^4 + 703125x^3 - 1562500x^2 - 1953125x + 9765625	\( 11^{18}\cdot 19^{10} \)	$C_2\times C_{10}$ (as 20T3)	$[55]$ (GRH)
20.0.41278417207323610480699463560809.1	x^20 - x^19 - x^18 - 34x^17 + 29x^16 + 25x^15 + 371x^14 - 237x^13 - 232x^12 - 1510x^11 + 811x^10 + 1383x^9 + 1792x^8 - 1064x^7 - 2903x^6 + 1617x^5 + 2774x^4 - 960x^3 - 1175x^2 - 500x + 625	\( 3^{10}\cdot 31^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[15]$ (GRH)
20.0.56933553290160450365440000000000.1	x^20 + 17x^18 + 124x^16 + 502x^14 + 1230x^12 + 1858x^10 + 1721x^8 + 833x^6 + 554x^4 - 1560x^2 + 7921	\( 2^{20}\cdot 5^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[124]$ (GRH)
20.20.56933553290160450365440000000000.1	x^20 - 33x^18 + 429x^16 - 2838x^14 + 10450x^12 - 22407x^10 + 28556x^8 - 21417x^6 + 8954x^4 - 1815x^2 + 121	\( 2^{20}\cdot 5^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	Trivial (GRH)
20.0.56933553290160450365440000000000.2	x^20 - 23x^18 + 232x^16 - 1354x^14 + 5094x^12 - 13102x^10 + 24113x^8 - 33551x^6 + 38270x^4 - 39480x^2 + 39601	\( 2^{20}\cdot 5^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[4]$ (GRH)
20.0.56933553290160450365440000000000.3	x^20 - 5x^18 + 25x^16 - 125x^14 + 625x^12 - 3125x^10 + 15625x^8 - 78125x^6 + 390625x^4 - 1953125x^2 + 9765625	\( 2^{20}\cdot 5^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[2, 62]$ (GRH)
20.0.92738759037689478010716606945681.1	x^20 - x^19 + 22x^18 - 21x^17 + 307x^16 - 286x^15 + 2619x^14 - 2333x^13 + 16258x^12 - 13925x^11 + 67715x^10 - 53723x^9 + 202840x^8 - 146169x^7 + 361505x^6 - 203544x^5 + 399607x^4 - 237335x^3 + 147488x^2 - 28073x + 4489	\( 3^{10}\cdot 7^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[66]$ (GRH)
20.20.92738759037689478010716606945681.1	x^20 - x^19 - 38x^18 + 33x^17 + 613x^16 - 448x^15 - 5463x^14 + 3223x^13 + 29302x^12 - 13187x^11 - 96559x^10 + 30691x^9 + 191218x^8 - 39237x^7 - 212737x^6 + 28344x^5 + 116035x^4 - 15587x^3 - 23758x^2 + 4783x + 331	\( 3^{10}\cdot 7^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	Trivial (GRH)
20.0.92738759037689478010716606945681.3	x^20 - 8x^19 + 27x^18 - 52x^17 + 132x^16 - 452x^15 + 1108x^14 - 1974x^13 + 4254x^12 - 9042x^11 + 17084x^10 - 27764x^9 + 50255x^8 - 71930x^7 + 123807x^6 - 139074x^5 + 238062x^4 - 158880x^3 + 351000x^2 - 96318x + 278653	\( 3^{10}\cdot 7^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[330]$ (GRH)
20.0.92738759037689478010716606945681.4	x^20 - x^19 + 6x^18 - 11x^17 + 41x^16 - 96x^15 + 301x^14 - 781x^13 + 2286x^12 - 6191x^11 + 17621x^10 + 30955x^9 + 57150x^8 + 97625x^7 + 188125x^6 + 300000x^5 + 640625x^4 + 859375x^3 + 2343750x^2 + 1953125x + 9765625	\( 3^{10}\cdot 7^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[66]$ (GRH)
20.0.126754505709914865311944228515625.3	x^20 - 8x^19 + 21x^18 - 57x^16 - 166x^15 + 1385x^14 - 3815x^13 + 8065x^12 - 16253x^11 + 38496x^10 - 88398x^9 + 203504x^8 - 392889x^7 + 695944x^6 - 1005043x^5 + 1343738x^4 - 1372952x^3 + 1330894x^2 - 768615x + 512579	\( 5^{10}\cdot 7^{10}\cdot 11^{16} \)	$C_2\times C_{10}$ (as 20T3)	$[5, 55]$ (GRH)
20.0.164422235102392733097076416015625.1	x^20 + 30x^18 + 435x^16 - 11x^15 + 3750x^14 - 265x^13 + 20825x^12 - 2735x^11 + 74975x^10 - 15000x^9 + 173240x^8 - 42800x^7 + 238320x^6 - 63648x^5 + 172800x^4 - 28800x^3 + 32000x^2 + 2560x + 1024	\( 5^{34}\cdot 7^{10} \)	$C_2\times C_{10}$ (as 20T3)	$[4, 4, 4, 4]$ (GRH)
20.0.230327976934347149972494554684169.1	x^20 - x^19 - 5x^18 + 11x^17 + 19x^16 - 85x^15 - 29x^14 + 539x^13 - 365x^12 - 2869x^11 + 5059x^10 - 17214x^9 - 13140x^8 + 116424x^7 - 37584x^6 - 660960x^5 + 886464x^4 + 3079296x^3 - 8398080x^2 - 10077696x + 60466176	\( 11^{18}\cdot 23^{10} \)	$C_2\times C_{10}$ (as 20T3)	$[2, 2, 2, 6]$ (GRH)
20.20.352517555563337816067682238201856.1	x^20 - 2x^19 - 39x^18 + 76x^17 + 590x^16 - 1104x^15 - 4374x^14 + 7644x^13 + 16726x^12 - 25808x^11 - 33034x^10 + 40262x^9 + 33501x^8 - 26542x^7 - 16067x^6 + 6736x^5 + 3516x^4 - 450x^3 - 292x^2 - 20x + 1	\( 2^{30}\cdot 3^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	Trivial (GRH)
20.0.352517555563337816067682238201856.2	x^20 + 38x^18 + 608x^16 + 5328x^14 + 27872x^12 + 89024x^10 + 170560x^8 + 184704x^6 + 99840x^4 + 20480x^2 + 1024	\( 2^{30}\cdot 3^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[5, 110]$ (GRH)
20.20.352517555563337816067682238201856.2	x^20 - 38x^18 + 608x^16 - 5328x^14 + 27872x^12 - 89024x^10 + 170560x^8 - 184704x^6 + 99840x^4 - 20480x^2 + 1024	\( 2^{30}\cdot 3^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	Trivial (GRH)
20.0.352517555563337816067682238201856.4	x^20 - 22x^18 + 308x^16 - 2640x^14 + 16544x^12 - 70048x^10 + 216832x^8 - 418176x^6 + 557568x^4 - 309760x^2 + 123904	\( 2^{30}\cdot 3^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[22]$ (GRH)
20.0.352517555563337816067682238201856.5	x^20 + 22x^18 + 308x^16 + 2640x^14 + 16544x^12 + 70048x^10 + 216832x^8 + 418176x^6 + 557568x^4 + 309760x^2 + 123904	\( 2^{30}\cdot 3^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[124]$ (GRH)
20.0.352517555563337816067682238201856.7	x^20 - 2x^19 + x^18 + 4x^17 + 66x^16 - 144x^15 + 266x^14 - 100x^13 + 1822x^12 - 3344x^11 + 10198x^10 - 10362x^9 + 36517x^8 - 42190x^7 + 138157x^6 - 145432x^5 + 383064x^4 - 352162x^3 + 765484x^2 - 438908x + 652081	\( 2^{30}\cdot 3^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[2, 310]$ (GRH)
20.0.352517555563337816067682238201856.8	x^20 - 6x^18 + 36x^16 - 216x^14 + 1296x^12 - 7776x^10 + 46656x^8 - 279936x^6 + 1679616x^4 - 10077696x^2 + 60466176	\( 2^{30}\cdot 3^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[5, 10]$ (GRH)
20.0.352517555563337816067682238201856.9	x^20 + 6x^18 + 36x^16 + 216x^14 + 1296x^12 + 7776x^10 + 46656x^8 + 279936x^6 + 1679616x^4 + 10077696x^2 + 60466176	\( 2^{30}\cdot 3^{10}\cdot 11^{18} \)	$C_2\times C_{10}$ (as 20T3)	$[124]$ (GRH)