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 469)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.1744786769896095344492544.1	x^20 - 8x^19 + 35x^18 - 108x^17 + 273x^16 - 600x^15 + 1152x^14 - 1896x^13 + 2622x^12 - 2960x^11 + 2590x^10 - 1528x^9 + 222x^8 + 744x^7 - 1056x^6 + 792x^5 - 291x^4 - 72x^3 + 155x^2 - 76x + 13	\( 2^{52}\cdot 3^{18} \)	$C_2^2\times F_5$ (as 20T16)	Trivial
20.0.5904900000000000000000000.1	x^20 - 2x^15 + 5x^10 - 4x^5 + 1	\( 2^{20}\cdot 3^{10}\cdot 5^{20} \)	$C_2^2\times F_5$ (as 20T16)	Trivial (GRH)
20.0.634749729177600000000000000.1	x^20 - 14x^18 + 81x^16 - 240x^14 + 426x^12 - 120x^10 - 42x^8 - 72x^6 + 45x^4 - 2x^2 + 1	\( 2^{28}\cdot 3^{18}\cdot 5^{14} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$ (GRH)
20.0.634749729177600000000000000.2	x^20 + 5x^18 + 18x^16 + 42x^14 + 105x^12 + 189x^10 + 252x^8 + 228x^6 + 120x^4 + 32x^2 + 4	\( 2^{28}\cdot 3^{18}\cdot 5^{14} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$
20.4.2597002484341800960000000000.1	x^20 - 2x^18 - 19x^16 + 24x^14 + 148x^12 - 72x^10 - 536x^8 - 96x^6 + 716x^4 - 440x^2 + 100	\( 2^{52}\cdot 3^{10}\cdot 5^{10} \)	$C_2^2\times F_5$ (as 20T16)	Trivial (GRH)
20.4.10388009937367203840000000000.1	x^20 - 6x^18 + 33x^16 - 96x^14 + 162x^12 - 268x^10 + 162x^8 - 96x^6 + 33x^4 - 6x^2 + 1	\( 2^{54}\cdot 3^{10}\cdot 5^{10} \)	$C_2^2\times F_5$ (as 20T16)	Trivial (GRH)
20.0.37791360000000000000000000000.1	x^20 - 15x^18 + 90x^16 - 270x^14 + 405x^12 - 239x^10 + 120x^8 + 180x^6 + 4	\( 2^{28}\cdot 3^{10}\cdot 5^{22} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$ (GRH)
20.0.37791360000000000000000000000.2	x^20 - 10x^18 + 65x^16 - 400x^14 + 1750x^12 - 5772x^10 + 17350x^8 - 36160x^6 + 30425x^4 + 3350x^2 + 361	\( 2^{28}\cdot 3^{10}\cdot 5^{22} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$ (GRH)
20.0.649983722677862400000000000000.1	x^20 + 2x^18 - 24x^16 - 90x^14 + 96x^12 + 900x^10 + 1524x^8 + 600x^6 + 204x^4 + 32x^2 + 4	\( 2^{38}\cdot 3^{18}\cdot 5^{14} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$ (GRH)
20.0.649983722677862400000000000000.2	x^20 + 12x^18 + 48x^16 + 60x^14 + 12x^12 + 174x^10 + 612x^8 + 720x^6 + 288x^4 - 288x^2 + 576	\( 2^{38}\cdot 3^{18}\cdot 5^{14} \)	$C_2^2\times F_5$ (as 20T16)	$[4]$ (GRH)
20.0.649983722677862400000000000000.3	x^20 + 8x^18 + 60x^16 - 132x^14 - 696x^12 - 558x^10 + 6420x^8 + 4512x^6 + 2316x^4 + 560x^2 + 100	\( 2^{38}\cdot 3^{18}\cdot 5^{14} \)	$C_2^2\times F_5$ (as 20T16)	$[4]$ (GRH)
20.0.649983722677862400000000000000.4	x^20 - 2x^18 - 24x^16 + 90x^14 + 96x^12 - 900x^10 + 1524x^8 - 600x^6 + 204x^4 - 32x^2 + 4	\( 2^{38}\cdot 3^{18}\cdot 5^{14} \)	$C_2^2\times F_5$ (as 20T16)	$[4]$ (GRH)
20.0.649983722677862400000000000000.5	x^20 - 12x^18 + 48x^16 - 60x^14 + 12x^12 - 174x^10 + 612x^8 - 720x^6 + 288x^4 + 288x^2 + 576	\( 2^{38}\cdot 3^{18}\cdot 5^{14} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$ (GRH)
20.0.4622106472375910400000000000000.1	x^20 + 4x^18 + x^16 + 8x^14 + 134x^12 - 196x^10 + 594x^8 - 360x^6 + 585x^4 + 225	\( 2^{44}\cdot 3^{16}\cdot 5^{14} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$ (GRH)
20.0.4622106472375910400000000000000.2	x^20 - 16x^16 + 16x^12 + 304x^8 + 1376x^4 + 400	\( 2^{44}\cdot 3^{16}\cdot 5^{14} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$ (GRH)
20.0.7066437103077000852134120390656.1	x^20 - 8x^19 + 36x^18 - 140x^17 + 462x^16 - 1236x^15 + 2946x^14 - 6148x^13 + 9614x^12 - 9624x^11 - 8x^10 + 32620x^9 - 82312x^8 + 72952x^7 + 44046x^6 - 131568x^5 + 70862x^4 + 7172x^3 - 2294x^2 - 10388x + 4487	\( 2^{30}\cdot 7^{10}\cdot 13^{12} \)	$C_2^2\times F_5$ (as 20T16)	$[6]$ (GRH)
20.0.7231366374400000000000000000000.1	x^20 - 12x^15 + 72x^10 - 384x^5 + 1024	\( 2^{28}\cdot 5^{20}\cdot 7^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[5]$ (GRH)
20.0.38698352640000000000000000000000.2	x^20 + 10x^18 + 60x^16 + 160x^14 - 360x^12 - 4724x^10 - 10600x^8 + 9360x^6 + 70000x^4 + 113640x^2 + 79524	\( 2^{38}\cdot 3^{10}\cdot 5^{22} \)	$C_2^2\times F_5$ (as 20T16)	$[4]$ (GRH)
20.0.38698352640000000000000000000000.3	x^20 + 122x^10 + 4096	\( 2^{38}\cdot 3^{10}\cdot 5^{22} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$ (GRH)
20.0.38698352640000000000000000000000.4	x^20 - 122x^10 + 4096	\( 2^{38}\cdot 3^{10}\cdot 5^{22} \)	$C_2^2\times F_5$ (as 20T16)	$[4]$ (GRH)
20.0.38698352640000000000000000000000.5	x^20 - 10x^18 + 60x^16 - 160x^14 - 360x^12 + 4724x^10 - 10600x^8 - 9360x^6 + 70000x^4 - 113640x^2 + 79524	\( 2^{38}\cdot 3^{10}\cdot 5^{22} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$ (GRH)
20.4.41598958251383193600000000000000.1	x^20 + 8x^18 - 27x^16 - 480x^14 + 1962x^12 - 3024x^10 + 1962x^8 - 480x^6 - 27x^4 + 8x^2 + 1	\( 2^{44}\cdot 3^{18}\cdot 5^{14} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$ (GRH)
20.4.41598958251383193600000000000000.2	x^20 - 24x^18 + 285x^16 - 2016x^14 + 8994x^12 - 25116x^10 + 42750x^8 - 44064x^6 + 29781x^4 - 12060x^2 + 225	\( 2^{44}\cdot 3^{18}\cdot 5^{14} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$ (GRH)
20.0.43774679639190704400000000000000.1	x^20 - 3x^19 + 17x^18 - 60x^17 + 255x^16 - 423x^15 + 1269x^14 - 798x^13 + 3933x^12 + 2679x^11 + 8229x^10 + 6138x^9 + 6384x^8 + 4176x^7 + 3372x^6 + 1314x^5 + 708x^4 + 144x^3 + 80x^2 + 4	\( 2^{16}\cdot 3^{18}\cdot 5^{14}\cdot 7^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$ (GRH)
20.0.43774679639190704400000000000000.2	x^20 + 19x^18 - 12x^17 + 168x^16 - 84x^15 + 798x^14 - 324x^13 + 1953x^12 + 1776x^11 - 2283x^10 + 9534x^9 + 2250x^8 - 13752x^7 + 36366x^6 - 4530x^5 - 19272x^4 + 14640x^3 + 28696x^2 - 30600x + 21256	\( 2^{16}\cdot 3^{18}\cdot 5^{14}\cdot 7^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$ (GRH)
20.0.2606231402843906250000000000000000.1	x^20 + 25x^18 + 255x^16 + 1350x^14 + 3885x^12 + 15875x^10 + 14425x^8 + 5750x^6 + 1175x^4 + 125x^2 + 25	\( 2^{16}\cdot 3^{10}\cdot 5^{22}\cdot 7^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$ (GRH)
20.0.2606231402843906250000000000000000.2	x^20 + 35x^18 - 20x^17 + 500x^16 - 332x^15 + 3650x^14 - 2880x^13 + 13495x^12 - 15900x^11 + 25755x^10 - 49850x^9 + 29600x^8 - 70620x^7 + 31860x^6 - 13974x^5 + 29440x^4 + 38120x^3 + 19840x^2 + 19840x + 6304	\( 2^{16}\cdot 3^{10}\cdot 5^{22}\cdot 7^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$ (GRH)
20.0.4019475888928019955600000000000000.1	x^20 + 29x^18 - 12x^17 + 381x^16 - 132x^15 + 2790x^14 - 432x^13 + 11877x^12 + 5640x^11 + 22701x^10 + 42330x^9 + 57453x^8 + 18684x^7 + 254160x^6 + 5874x^5 + 94989x^4 + 364584x^3 + 13979x^2 + 87210x + 247285	\( 2^{16}\cdot 3^{18}\cdot 5^{14}\cdot 11^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[2, 2]$ (GRH)
20.0.4019475888928019955600000000000000.2	x^20 - 3x^19 + 22x^18 - 84x^17 + 429x^16 - 729x^15 + 2976x^14 - 1344x^13 + 14160x^12 + 14496x^11 + 54102x^10 + 61092x^9 + 114720x^8 + 110016x^7 + 151776x^6 + 91584x^5 + 89856x^4 + 27648x^3 + 28672x^2 + 4096	\( 2^{16}\cdot 3^{18}\cdot 5^{14}\cdot 11^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[4]$ (GRH)
20.20.7236031593550848872585339280031744.1	x^20 - 42x^18 - 4x^17 + 648x^16 - 48x^15 - 4960x^14 + 1484x^13 + 20259x^12 - 10008x^11 - 43824x^10 + 27916x^9 + 46614x^8 - 34168x^7 - 20754x^6 + 17048x^5 + 2795x^4 - 3136x^3 + 128x^2 + 100x + 1	\( 2^{40}\cdot 7^{10}\cdot 13^{12} \)	$C_2^2\times F_5$ (as 20T16)	Trivial (GRH)
20.0.10155995666841600000000000000000000.1	x^20 + 54x^10 + 2916	\( 2^{38}\cdot 3^{18}\cdot 5^{20} \)	$C_2^2\times F_5$ (as 20T16)	Trivial (GRH)
20.0.21363681729976837664400000000000000.1	x^20 - 3x^19 - 8x^18 + 60x^17 - 75x^16 + 27x^15 - 66x^14 - 2748x^13 + 11928x^12 + 4704x^11 - 44106x^10 - 108792x^9 + 127104x^8 + 861696x^7 - 741888x^6 - 2820096x^5 + 3391488x^4 + 3538944x^3 - 5242880x^2 + 4194304	\( 2^{16}\cdot 3^{18}\cdot 5^{14}\cdot 13^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[8]$ (GRH)
20.0.21363681729976837664400000000000000.2	x^20 - 31x^18 - 12x^17 + 453x^16 + 156x^15 - 3762x^14 + 216x^13 + 19293x^12 - 20064x^11 - 51423x^10 + 122754x^9 + 139785x^8 - 363852x^7 - 398664x^6 + 319290x^5 + 557193x^4 + 229440x^3 + 689231x^2 + 951210x + 452761	\( 2^{16}\cdot 3^{18}\cdot 5^{14}\cdot 13^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[2, 2]$ (GRH)
20.0.40623982667366400000000000000000000.1	x^20 + 9	\( 2^{40}\cdot 3^{18}\cdot 5^{20} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$ (GRH)
20.0.72220413630873600000000000000000000.1	x^20 - 36x^15 + 2124x^10 - 2160x^5 + 648	\( 2^{44}\cdot 3^{16}\cdot 5^{20} \)	$C_2^2\times F_5$ (as 20T16)	Trivial (GRH)
20.0.179301087802125125222400000000000000.1	x^20 - 10x^19 + 49x^18 - 156x^17 + 486x^16 - 1644x^15 + 4596x^14 - 9318x^13 + 5145x^12 + 36236x^11 - 83405x^10 + 2264x^9 + 140118x^8 - 45090x^7 - 2028876x^6 + 5720946x^5 + 32556156x^4 - 74437464x^3 - 110117546x^2 + 148257512x + 174972106	\( 2^{28}\cdot 3^{18}\cdot 5^{14}\cdot 7^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[2, 4]$ (GRH)
20.0.179301087802125125222400000000000000.2	x^20 - 2x^19 + 13x^18 - 48x^17 - 144x^16 + 1104x^15 - 3102x^14 + 9012x^13 - 513x^12 - 94802x^11 + 376063x^10 - 1108412x^9 + 2141184x^8 + 812556x^7 - 15950598x^6 + 42851868x^5 - 57380232x^4 - 22835628x^3 + 286416976x^2 - 524324336x + 358394404	\( 2^{28}\cdot 3^{18}\cdot 5^{14}\cdot 7^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[2, 4]$ (GRH)
20.0.239309216447570156250000000000000000.1	x^20 + 35x^18 + 510x^16 + 3990x^14 + 18045x^12 + 89635x^10 + 204100x^8 + 229600x^6 + 137600x^4 + 44800x^2 + 25600	\( 2^{16}\cdot 3^{10}\cdot 5^{22}\cdot 11^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[4]$ (GRH)
20.0.239309216447570156250000000000000000.2	x^20 + 45x^18 - 20x^17 + 825x^16 - 412x^15 + 7690x^14 - 4020x^13 + 36615x^12 - 25260x^11 + 83607x^10 - 105290x^9 + 81705x^8 - 248640x^7 + 77610x^6 - 221386x^5 + 195565x^4 + 93660x^3 + 237545x^2 + 181770x + 88159	\( 2^{16}\cdot 3^{10}\cdot 5^{22}\cdot 11^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[2, 2]$ (GRH)
20.0.253899891671040000000000000000000000.1	x^20 + 120x^16 + 450x^14 + 1020x^12 - 276x^10 + 1080x^8 + 10080x^6 + 22500x^4 + 22320x^2 + 10404	\( 2^{38}\cdot 3^{18}\cdot 5^{22} \)	$C_2^2\times F_5$ (as 20T16)	$[10]$ (GRH)
20.0.312414937093187559824400000000000000.1	x^20 - 3x^19 - 13x^18 + 84x^17 - 33x^16 - 99x^15 - 657x^14 - 5334x^13 + 31653x^12 + 24135x^11 - 188889x^10 - 436230x^9 + 910200x^8 + 4014000x^7 - 5542500x^6 - 15243750x^5 + 24562500x^4 + 22500000x^3 - 43750000x^2 + 39062500	\( 2^{16}\cdot 3^{18}\cdot 5^{14}\cdot 17^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[4]$ (GRH)
20.0.312414937093187559824400000000000000.2	x^20 - 41x^18 - 12x^17 + 780x^16 + 204x^15 - 8634x^14 + 324x^13 + 60849x^12 - 39048x^11 - 269871x^10 + 344478x^9 + 914778x^8 - 1408896x^7 - 2510994x^6 + 2515542x^5 + 4162668x^4 - 1873344x^3 - 550760x^2 + 6029496x + 4345624	\( 2^{16}\cdot 3^{18}\cdot 5^{14}\cdot 17^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[12]$ (GRH)
20.20.427004953041945600000000000000000000.1	x^20 - 40x^18 + 680x^16 - 12x^15 - 6400x^14 + 360x^13 + 36400x^12 - 4320x^11 - 128056x^10 + 26400x^9 + 273120x^8 - 86400x^7 - 327840x^6 + 145056x^5 + 182400x^4 - 106560x^3 - 22400x^2 + 21120x - 3008	\( 2^{28}\cdot 3^{10}\cdot 5^{20}\cdot 7^{10} \)	$C_2^2\times F_5$ (as 20T16)	Trivial (GRH)
20.0.649983722677862400000000000000000000.1	x^20 + 8688x^10 + 144	\( 2^{44}\cdot 3^{18}\cdot 5^{20} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$ (GRH)
20.0.950120275075465393875600000000000000.1	x^20 - 3x^19 + 32x^18 - 132x^17 + 885x^16 - 1557x^15 + 9846x^14 - 1932x^13 + 84600x^12 + 111264x^11 + 637014x^10 + 929592x^9 + 3174528x^8 + 4041216x^7 + 9604608x^6 + 7981056x^5 + 14401536x^4 + 5898240x^3 + 11534336x^2 + 4194304	\( 2^{16}\cdot 3^{18}\cdot 5^{14}\cdot 19^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[8]$ (GRH)
20.0.950120275075465393875600000000000000.2	x^20 + 49x^18 - 12x^17 + 1077x^16 - 228x^15 + 13614x^14 - 648x^13 + 107613x^12 + 28992x^11 + 543153x^10 + 362082x^9 + 1997289x^8 + 1568340x^7 + 6060696x^6 + 4501338x^5 + 10244121x^4 + 13098912x^3 + 8853151x^2 + 13635882x + 11335609	\( 2^{16}\cdot 3^{18}\cdot 5^{14}\cdot 19^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[2, 10]$ (GRH)
20.0.1271938450811187656250000000000000000.1	x^20 - 35x^18 + 555x^16 - 88x^15 - 4550x^14 - 1520x^13 + 28315x^12 + 19180x^11 - 98105x^10 - 166250x^9 + 257955x^8 + 450680x^7 - 87670x^6 - 1164726x^5 - 1070835x^4 + 2020440x^3 + 4384705x^2 + 3238350x + 1118589	\( 2^{16}\cdot 3^{10}\cdot 5^{22}\cdot 13^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[2, 10]$ (GRH)
20.0.1271938450811187656250000000000000000.3	x^20 - 25x^18 + 330x^16 - 2850x^14 + 17685x^12 - 79625x^10 + 134800x^8 + 448000x^6 + 204800x^4 - 8192000x^2 + 26214400	\( 2^{16}\cdot 3^{10}\cdot 5^{22}\cdot 13^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[8]$ (GRH)
20.0.1805510340771840000000000000000000000.1	x^20 - 20x^18 + 265x^16 - 2560x^14 + 18470x^12 - 102244x^10 + 429690x^8 - 1310400x^6 + 2727945x^4 - 3547800x^2 + 2259009	\( 2^{44}\cdot 3^{16}\cdot 5^{22} \)	$C_2^2\times F_5$ (as 20T16)	$[2]$ (GRH)
20.0.6419791692782351621744400000000000000.1	x^20 + 59x^18 - 12x^17 + 1560x^16 - 276x^15 + 23886x^14 - 756x^13 + 231729x^12 + 52512x^11 + 1474509x^10 + 789438x^9 + 6623538x^8 + 4667544x^7 + 22362606x^6 + 17022462x^5 + 47245728x^4 + 49085616x^3 + 55936280x^2 + 59948856x + 56607784	\( 2^{16}\cdot 3^{18}\cdot 5^{14}\cdot 23^{10} \)	$C_2^2\times F_5$ (as 20T16)	$[6]$ (GRH)