
# Number fields downloaded from the LMFDB on 11 June 2026.
# Search link: https://www.lmfdb.org/NumberField/?galois_group=20T1
# Query "{'degree': 20, 'galois_label': '20T1'}" returned 940 fields, sorted by degree.

# Each entry in the following data list has the form:
#    [Label, Polynomial, Discriminant, Galois group, Class group]
# For more details, see the definitions at the bottom of the file.



"20.0.2910383045673370361328125.1"	[1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1]	2910383045673370361328125	"20T1"	[]
"20.0.1402274470934209014892578125.1"	[1, -3, 12, -41, 146, 22, 199, 82, 334, -128, 260, -109, 179, -30, 59, -11, 20, -6, 5, -1, 1]	1402274470934209014892578125	"20T1"	[5]
"20.20.169675210983039290802001953125.1"	[1, 12, -108, -151, 951, 877, -2891, -2058, 4489, 2442, -4080, -1639, 2289, 650, -801, -151, 170, 19, -20, -1, 1]	169675210983039290802001953125	"20T1"	[]
"20.20.171855208463966846466064453125.1"	[1, 20, -100, -145, 825, 379, -2640, -450, 4290, 275, -4004, -90, 2275, 15, -800, -1, 170, 0, -20, 0, 1]	171855208463966846466064453125	"20T1"	[]
"20.20.3051757812500000000000000000000.1"	[5, 0, -125, 0, 875, 0, -2675, 0, 4300, 0, -4005, 0, 2275, 0, -800, 0, 170, 0, -20, 0, 1]	3051757812500000000000000000000	"20T1"	[]
"20.20.4394336169668803158610484050361.1"	[1, 10, -55, -165, 495, 792, -1716, -1716, 3003, 2002, -3003, -1365, 1820, 560, -680, -136, 153, 18, -19, -1, 1]	4394336169668803158610484050361	"20T1"	[]
"20.20.82802905234194108120391845703125.1"	[1, -21, -468, -978, 4671, 9222, -18180, -26929, 34487, 31502, -32674, -17268, 16062, 4764, -4199, -664, 579, 43, -39, -1, 1]	82802905234194108120391845703125	"20T1"	[]
"20.20.822111175511963665485382080078125.1"	[401, 8580, -15600, -92290, 175600, 132429, -325460, -79200, 272780, 24200, -128039, -3960, 36400, 330, -6400, -11, 680, 0, -40, 0, 1]	822111175511963665485382080078125	"20T1"	[]
"20.20.1470391355634309152000000000000000.1"	[1, -72, 787, -1814, -6419, 20748, 17949, -65992, -15516, 84688, -2270, -48836, 6764, 13960, -2696, -2044, 455, 146, -35, -4, 1]	1470391355634309152000000000000000	"20T1"	[]
"20.0.1655513490330868290261743826894848.1"	[32, 0, 960, 0, 6960, 0, 21280, 0, 32408, 0, 26944, 0, 12736, 0, 3416, 0, 498, 0, 36, 0, 1]	1655513490330868290261743826894848	"20T1"	[521]
"20.20.1655513490330868290261743826894848.1"	[32, 0, -960, 0, 6960, 0, -21280, 0, 32408, 0, -26944, 0, 12736, 0, -3416, 0, 498, 0, -36, 0, 1]	1655513490330868290261743826894848	"20T1"	[]
"20.0.2351977956823175708448011472615877.1"	[40283, -16471, 82138, 101736, -15945, -55350, 33622, 19061, 24675, 17042, 4614, 4302, 1680, 352, 189, -48, 55, 31, -9, -1, 1]	2351977956823175708448011472615877	"20T1"	[61]
"20.0.3125000000000000000000000000000000.1"	[5120, 0, 64000, 0, 224000, 0, 342400, 0, 275200, 0, 128160, 0, 36400, 0, 6400, 0, 680, 0, 40, 0, 1]	3125000000000000000000000000000000	"20T1"	[1202]
"20.20.3125000000000000000000000000000000.1"	[5120, 0, -64000, 0, 224000, 0, -342400, 0, 275200, 0, -128160, 0, 36400, 0, -6400, 0, 680, 0, -40, 0, 1]	3125000000000000000000000000000000	"20T1"	[]
"20.0.8341936223273428359616333847680741.1"	[611, -522, 2983, -439, -261, 1820, -1330, -541, 3278, 691, -745, 1778, 414, -267, 413, 51, -29, 36, 2, -1, 1]	8341936223273428359616333847680741	"20T1"	[41]
"20.0.10019151533337487082567413330078125.1"	[1197901, 173262, 1371042, -411001, 958226, -492583, 456689, -254178, 181094, -88253, 64285, -23144, 18734, -4410, 3874, -536, 500, -36, 35, -1, 1]	10019151533337487082567413330078125	"20T1"	[2, 2, 842]
"20.0.22199191947851112787734405517578125.2"	[625, -125, 2650, 445, 10616, -14164, 47983, -44226, 174168, -104714, 68890, -36325, 19301, -4980, 2045, -481, 138, -4, 13, -1, 1]	22199191947851112787734405517578125	"20T1"	[2, 2, 10, 10]
"20.20.75487840807181783020496368408203125.1"	[51151, 354330, -514350, -2942985, 4443525, 2832749, -5547510, -1129950, 3105870, 230175, -972254, -25110, 184275, 1395, -21600, -31, 1530, 0, -60, 0, 1]	75487840807181783020496368408203125	"20T1"	[]
"20.20.131527565972137936816816034072938673.1"	[1033, -2449, -20309, 17397, 107725, -31515, -226443, 22455, 237299, -4409, -137522, -2629, 45828, 1660, -8765, -354, 926, 32, -49, -1, 1]	131527565972137936816816034072938673	"20T1"	[]
"20.0.177917354031751407392000000000000000.1"	[378125, 0, 1890625, 0, 3478750, 0, 3251875, 0, 1754500, 0, 581625, 0, 121550, 0, 15950, 0, 1265, 0, 55, 0, 1]	177917354031751407392000000000000000	"20T1"	[2, 2, 2762]
"20.0.180203247070312500000000000000000000.1"	[295245, 0, 2460375, 0, 5740875, 0, 5850225, 0, 3134700, 0, 973215, 0, 184275, 0, 21600, 0, 1530, 0, 60, 0, 1]	180203247070312500000000000000000000	"20T1"	[2, 4322]
"20.0.200317132330035063121671003054276608.1"	[3872, 0, 38720, 0, 129712, 0, 212960, 0, 196504, 0, 107712, 0, 35552, 0, 6952, 0, 770, 0, 44, 0, 1]	200317132330035063121671003054276608	"20T1"	[2050]
"20.20.200317132330035063121671003054276608.1"	[3872, 0, -38720, 0, 129712, 0, -212960, 0, 196504, 0, -107712, 0, 35552, 0, -6952, 0, 770, 0, -44, 0, 1]	200317132330035063121671003054276608	"20T1"	[]
"20.0.259481156482773157712790472689766689.1"	[51907, 37115, 50170, -82739, 74910, 10386, 2671, 16816, -8231, 5692, -1773, 316, -476, -506, 304, -177, 153, -23, 22, -1, 1]	259481156482773157712790472689766689	"20T1"	[2, 2, 2, 2, 34]
"20.20.284589332775604260722209388186521117.1"	[-43, -1316, -10254, 1845, 78872, 16639, -194675, -51088, 224814, 54957, -139547, -27812, 48842, 7010, -9572, -854, 998, 48, -51, -1, 1]	284589332775604260722209388186521117	"20T1"	[]
"20.20.396107830343483954099825714111328125.1"	[4621, -86946, 441152, -658628, -574064, 2013497, -355510, -2003579, 878982, 929822, -510719, -228288, 139797, 30774, -20399, -2224, 1609, 78, -64, -1, 1]	396107830343483954099825714111328125	"20T1"	[]
"20.0.401221017379430122673511505126953125.1"	[18662101, -13549320, 9995400, -10075065, 10764225, -5859721, 7022340, -2223450, 3246330, -452925, 976936, -49410, 184275, -2745, 21600, -61, 1530, 0, 60, 0, 1]	401221017379430122673511505126953125	"20T1"	[15362]
"20.0.1505680748169532571648000000000000000.1"	[90594151, -43101732, 92992732, -38741504, 47151361, -18262392, 15991074, -5429272, 3826719, -1188452, 710860, -198776, 101774, -24620, 10834, -2164, 815, -124, 40, -4, 1]	1505680748169532571648000000000000000	"20T1"	[22082]
"20.20.1505680748169532571648000000000000000.2"	[1451, 70588, -118608, -1007904, 614261, 2823768, -1203606, -3070872, 1047359, 1596028, -480740, -437336, 122474, 66220, -17726, -5524, 1435, 236, -60, -4, 1]	1505680748169532571648000000000000000	"20T1"	[5]
"20.0.1945771207112214793287128936767578125.1"	[6561, 15309, 39366, 88695, 202338, 82674, 153711, 59106, 108670, 44804, 73952, 27901, 45177, 6496, 3849, 679, 294, -38, 17, -1, 1]	1945771207112214793287128936767578125	"20T1"	[505]
"20.0.4607795443446634940843146923591335936.1"	[41, 0, 1517, 0, 13120, 0, 45141, 0, 71545, 0, 55801, 0, 23165, 0, 5289, 0, 656, 0, 41, 0, 1]	4607795443446634940843146923591335936	"20T1"	[2, 482]
"20.0.5867314468047698028385639190673828125.1"	[161532401, -123793680, 98054400, -82660420, 89987200, -40331421, 49539760, -11635200, 18020840, -1777600, 4111321, -145440, 582400, -6060, 51200, -101, 2720, 0, 80, 0, 1]	5867314468047698028385639190673828125	"20T1"	[11, 5302]
"20.0.15914835482628690354834740122825579433.1"	[83519437, 20544384, 26015925, 9962701, 8994354, 2390937, 2845143, -32881, 700706, -168519, 130294, -40054, 20558, -4874, 2986, -472, 348, -31, 27, -1, 1]	15914835482628690354834740122825579433	"20T1"	[8194]
"20.20.17843751288604107685387134552001953125.1"	[-6502099, 68478000, -84750000, -210961225, 278040625, 118907199, -200058500, -28406250, 66677450, 3471875, -12505424, -227250, 1421875, 7575, -100000, -101, 4250, 0, -100, 0, 1]	17843751288604107685387134552001953125	"20T1"	[]
"20.20.21333423461884919389012763702392578125.1"	[-4645, 8405, 63070, -137680, -146594, 478381, -12337, -586336, 205983, 341431, -174550, -104480, 64636, 17240, -12200, -1526, 1198, 66, -57, -1, 1]	21333423461884919389012763702392578125	"20T1"	[]
"20.20.42913439156921905845805508304306640625.1"	[-4099, 129857, -352368, -656657, 1584530, 1291062, -2320717, -1138974, 1631687, 509336, -630959, -125226, 142122, 17616, -18966, -1407, 1465, 59, -60, -1, 1]	42913439156921905845805508304306640625	"20T1"	[2]
"20.0.47929047471561558446078911407470703125.1"	[1102456301, -219225038, 863744092, -382542201, 410339451, -176867903, 141833529, -45394658, 36820719, -7799638, 6805360, -921679, 849729, -71950, 68499, -3451, 3360, -91, 90, -1, 1]	47929047471561558446078911407470703125	"20T1"	[2, 2, 64564]
"20.0.48544842802805942483246326446533203125.1"	[924979351, -725290750, 600406250, -439980025, 484303125, -182755451, 228935250, -42468750, 68327550, -5190625, 12538426, -339750, 1421875, -11325, 100000, -151, 4250, 0, 100, 0, 1]	48544842802805942483246326446533203125	"20T1"	[2, 2, 2, 2, 122, 122]
"20.0.86825139158850321116448000000000000000.3"	[2065660201, -786154512, 1764047967, -597365054, 733497061, -224863132, 196375269, -53466672, 36960084, -9006872, 5168310, -1102236, 534824, -96080, 39824, -5724, 2035, -214, 65, -4, 1]	86825139158850321116448000000000000000	"20T1"	[10, 31810]
"20.0.97756416090547441671665711234313879552.1"	[95829823, -47685756, 95586810, -38829056, 47163703, -21370648, 17951094, -5786136, 4088499, -1402508, 886308, -282888, 149216, -38000, 16682, -3204, 1183, -160, 50, -4, 1]	97756416090547441671665711234313879552	"20T1"	[131042]
"20.20.97756416090547441671665711234313879552.1"	[6247, 391236, -111054, -3602816, 1920559, 7942856, -3351642, -7029912, 2504547, 3078868, -977916, -732552, 215144, 97888, -27190, -7236, 1927, 272, -70, -4, 1]	97756416090547441671665711234313879552	"20T1"	[]
"20.20.120567015877601807005703449249267578125.1"	[-64286399, 437027220, -520959600, -953469870, 1223413200, 442743929, -720099540, -88063200, 199252740, 8969400, -31120079, -489240, 2948400, 13590, -172800, -151, 6120, 0, -120, 0, 1]	120567015877601807005703449249267578125	"20T1"	[]
"20.0.120810895044353150938886048668570711901.1"	[120577, 197892, 125333, -21866, -16152, 144019, 112662, -6930, -31618, 7237, 24000, 1958, -80, -1991, 316, 300, 44, -11, 3, -1, 1]	120810895044353150938886048668570711901	"20T1"	[5, 25]
"20.20.138881946372451702408146629446494920973.1"	[529, 17940, 2500, -1007476, -3020232, -1687071, 3433304, 4213355, -343368, -2291342, -537473, 517750, 205169, -53182, -30387, 2188, 2161, -8, -74, -1, 1]	138881946372451702408146629446494920973	"20T1"	[]
"20.0.182187370528513441169408000000000000000.1"	[387200000, 0, 968000000, 0, 890560000, 0, 416240000, 0, 112288000, 0, 18612000, 0, 1944800, 0, 127600, 0, 5060, 0, 110, 0, 1]	182187370528513441169408000000000000000	"20T1"	[2, 2, 62564]
"20.20.182187370528513441169408000000000000000.1"	[387200000, 0, -968000000, 0, 890560000, 0, -416240000, 0, 112288000, 0, -18612000, 0, 1944800, 0, -127600, 0, 5060, 0, -110, 0, 1]	182187370528513441169408000000000000000	"20T1"	[2]
"20.0.184528125000000000000000000000000000000.1"	[302330880, 0, 1259712000, 0, 1469664000, 0, 748828800, 0, 200620800, 0, 31142880, 0, 2948400, 0, 172800, 0, 6120, 0, 120, 0, 1]	184528125000000000000000000000000000000	"20T1"	[2, 152842]
"20.20.184528125000000000000000000000000000000.1"	[302330880, 0, -1259712000, 0, 1469664000, 0, -748828800, 0, 200620800, 0, -31142880, 0, 2948400, 0, -172800, 0, 6120, 0, -120, 0, 1]	184528125000000000000000000000000000000	"20T1"	[2]
"20.0.193315443721344440894830801055908203125.1"	[4751163121, -1149290321, 3808215652, -973042478, 1487095911, -374838878, 364805340, -85243529, 61958107, -12647278, 7455206, -1272388, 651922, -86676, 42001, -3824, 1959, -97, 61, -1, 1]	193315443721344440894830801055908203125	"20T1"	[331922]
"20.0.396508891893913150393870750167904820789.1"	[1575113, -2576267, 5906450, -7158636, 16658019, -23433182, 16223240, -7453323, 3730667, -1486634, 461402, -186410, 52672, -12556, 4981, -800, 209, -93, 1, -1, 1]	396508891893913150393870750167904820789	"20T1"	[8221]
"20.20.492582992048072671206984897371700075309.1"	[-7319, 52670, 49587, -514303, -860605, 432663, 1713746, 670703, -940697, -803106, 88864, 284208, 55314, -39429, -14471, 2186, 1374, -25, -59, -1, 1]	492582992048072671206984897371700075309	"20T1"	[]
"20.20.838860800000000000000000000000000000000.1"	[-751, -18880, 13380, 226520, 151010, -550316, -517500, 542820, 586485, -269900, -320518, 72540, 94440, -10520, -15450, 756, 1370, -20, -60, 0, 1]	838860800000000000000000000000000000000	"20T1"	[]
"20.0.838860800000000000000000000000000000000.2"	[1714657, -572320, 2998100, 904440, 606610, 1582468, 1274900, 575140, 396045, 139300, 12570, -4900, -2560, -3240, -1050, 436, 250, -20, -20, 0, 1]	838860800000000000000000000000000000000	"20T1"	[46381]
"20.0.862046047973632812500000000000000000000.1"	[1412376245, 0, 5044200875, 0, 5044200875, 0, 2202977525, 0, 505890700, 0, 67312035, 0, 5462275, 0, 274400, 0, 8330, 0, 140, 0, 1]	862046047973632812500000000000000000000	"20T1"	[2, 2, 2, 2, 2, 18362]
"20.0.1121572688496016376706341337921142578125.1"	[28561, 90077, 246740, 607659, 1429704, 1676096, 2320613, 2553308, 2080482, -822722, 687626, -221439, 277729, -7224, 12451, -257, 574, -32, 25, -1, 1]	1121572688496016376706341337921142578125	"20T1"	[41, 205]
"20.0.1191764441646885988302528858184814453125.1"	[615143, 868210, 2661560, 3691080, 3875560, -52767, -210670, -6275, 73090, 70190, -33419, -23470, 4515, 5160, -415, -1110, 155, 130, -20, -5, 1]	1191764441646885988302528858184814453125	"20T1"	[2141]
"20.0.1224419198989056167192757129669189453125.1"	[14282703401, -11221459620, 9783834900, -5735486785, 6398382025, -1816839501, 2338395640, -303606450, 511417970, -26505325, 67390996, -1239210, 5462275, -29505, 274400, -281, 8330, 0, 140, 0, 1]	1224419198989056167192757129669189453125	"20T1"	[2, 319762]
"20.0.1241291203716901419760482976136252014889.1"	[14455289, 4749614, 12238773, -5615279, 5117951, 4291524, -1932652, 1252884, -353041, -50314, 143941, -87711, 77916, -17316, 15720, -1530, 1465, -64, 63, -1, 1]	1241291203716901419760482976136252014889	"20T1"	[26050]
"20.20.1310840085328660359002928911407470703125.1"	[-9305, -24485, 156880, 498410, -116069, -1425462, -603922, 1476993, 966689, -710592, -571208, 169492, 165468, -18668, -24953, 634, 1925, 19, -71, -1, 1]	1310840085328660359002928911407470703125	"20T1"	[]
"20.20.2385432270183230866678059101104736328125.1"	[-1333421599, 7632319680, -8691609600, -10161847960, 12658662400, 3476778999, -5433008960, -517939200, 1120902320, 39564800, -131156879, -1618560, 9318400, 33720, -409600, -281, 10880, 0, -160, 0, 1]	2385432270183230866678059101104736328125	"20T1"	[]
"20.20.2466227638053818291661582077909665841152.1"	[-115127, 813944, -326245, -5445606, 2338293, 10963772, -4178291, -9159896, 3139284, 3847072, -1212022, -884788, 261316, 114360, -32088, -8124, 2183, 290, -75, -4, 1]	2466227638053818291661582077909665841152	"20T1"	[]
"20.0.2826976780158713912797906502960205078125.1"	[43048528051, -10396170396, 29810100332, -7175480378, 9866835796, -2240309653, 2023763270, -411643979, 282578412, -49003348, 27789601, -3903468, 1971087, -206886, 101401, -6964, 3679, -132, 86, -1, 1]	2826976780158713912797906502960205078125	"20T1"	[1040722]
"20.0.3270841399155633067515663742706298828125.1"	[302581, 537364, 1368636, 6289470, 13331898, -272386, 7371921, 1421186, 1921570, 549364, 326967, 108601, 39432, 5751, 1444, -756, 139, -48, 27, -1, 1]	3270841399155633067515663742706298828125	"20T1"	[2, 2644]
"20.0.4457481511823277105577290058135986328125.1"	[43704064801, -33981478720, 30122086400, -16076932840, 18016281600, -4542160121, 5901800640, -665395200, 1137644880, -50828800, 131366161, -2079360, 9318400, -43320, 409600, -361, 10880, 0, 160, 0, 1]	4457481511823277105577290058135986328125	"20T1"	[2, 2, 341722]
"20.0.4718382534089354179423382449757527998464.1"	[41984, 0, 776704, 0, 3358720, 0, 5778048, 0, 4578880, 0, 1785632, 0, 370640, 0, 42312, 0, 2624, 0, 82, 0, 1]	4718382534089354179423382449757527998464	"20T1"	[2, 26050]
"20.20.4718382534089354179423382449757527998464.1"	[41984, 0, -776704, 0, 3358720, 0, -5778048, 0, 4578880, 0, -1785632, 0, 370640, 0, -42312, 0, 2624, 0, -82, 0, 1]	4718382534089354179423382449757527998464	"20T1"	[2, 2]
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"20.20.1388324138164578851489360085874891008707429616424477801774628460407257080078125.1"	[160137350317402218087250852951, -74731107110899123565063629015, 12662997371147244028698053560, -806499357787283659778984485, -15284983434141687252911210, 4260562261636921655646298, -103329879907061835615890, -8127578910285451642040, 358645611645687119440, 8103965547348856465, -535373462150581076, -4692217029889705, 460799384082545, 1673683294155, -242528341295, -389778998, 76853405, 60605, -13455, -5, 1]	1388324138164578851489360085874891008707429616424477801774628460407257080078125	"20T1"	NULL
"20.0.5277282514816237610219827136784299666165496003125000000000000000000000000000000.1"	[195047562515048797866547252601, -82946268284238792306444164990, 13318420102627110139308576725, -831573937148321718225908660, -13762482558289046706603325, 4209137216443993773380452, -111654812031542208734735, -7561401791483013544400, 368266857921479408460, 6862112351986821050, -537504261513988751, -3335534288174880, 457571674459775, 826053962030, -239895100800, -81903602, 76072370, 0, -13370, 0, 1]	5277282514816237610219827136784299666165496003125000000000000000000000000000000	"20T1"	NULL
"20.20.5277282514816237610219827136784299666165496003125000000000000000000000000000000.1"	[146921933215910498165740017601, -69465476082339387341408366590, 12057208642946807675162280225, -810499376754534017827327260, -10481657292420915367839325, 4078992543430193105278452, -115704367709033083012735, -7381243001493543175400, 373990263465890083460, 6746833396934131050, -545714432489327251, -3302122713998680, 464822452147775, 822665546230, -243497056800, -81903602, 77011770, 0, -13470, 0, 1]	5277282514816237610219827136784299666165496003125000000000000000000000000000000	"20T1"	NULL
"20.0.18316493246359846919108213646728048590034142156851196289062500000000000000000000.1"	[1077790729783474588064576, 363192334408832457447040, 224132695576557172677520, 2445927594676144989760, -99709347703181174800, -141557030597673294496, -27333668399133276280, 1408358534028770960, 254195816667237180, -6880989167579600, -1167195614488719, 19101116800320, 3249167478485, -29670761920, -5670368550, 24109104, 6087390, -8080, -3715, 0, 1]	18316493246359846919108213646728048590034142156851196289062500000000000000000000	"20T1"	NULL
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"20.0.304314702360726576802607981054664170886139036609890747070312500000000000000000000.1"	[208330694134656583917335195101, -86546413072302088828961669840, 13645580605337067999582787100, -836722490050330469743904010, -14603137118741371927297450, 4241728665414340647232202, -110635537877568006699985, -7606266857390727901650, 366849881821351674085, 6890761268859152300, -535475007270316626, -3343832345418180, 455778869360275, 826901065980, -239002973050, -81903602, 75838895, 0, -13345, 0, 1]	304314702360726576802607981054664170886139036609890747070312500000000000000000000	"20T1"	NULL
"20.0.677554131069839479700976310702569208665983240894833478171494789421558380126953125.1"	[193022259518169002103496273651, 81332702675548524035580693845, 13102680329623056401349264095, 844045252486595650826742405, -9945370303275068627305020, -4062190438399831111677719, -122071457076201664041935, 6859630095280789538140, 379356921600614103635, -5545931869155648315, -541734109158446864, 1976054685812435, 456639805691035, 8551279915, -238601771285, -220950294, 75682405, 59980, -13330, -5, 1]	677554131069839479700976310702569208665983240894833478171494789421558380126953125	"20T1"	NULL
"20.0.2067585682514728660624940482215256472929804323597186849781428463757038116455078125.1"	[96460493901783548590094375, 102056661064671265319359375, 49736425840648902117381250, 14784885773595859071506250, 2990008492222742278944375, 433862647324587919084500, 46326225189803932716250, 3658963280612034398125, 210134219032355015625, 8271258487466329000, 181563664164460650, -607332217220250, -179440933119750, -4860425443000, -9790052175, 2149544280, 35233525, -261775, -9975, -5, 1]	2067585682514728660624940482215256472929804323597186849781428463757038116455078125	"20T1"	NULL
"20.0.2067585682514728660624940482215256472929804323597186849781428463757038116455078125.2"	[127142809602874079920375625, 126038215290320939528253125, 58242553489914388259456250, 16585843748660333303787500, 3241397423282931453881875, 457870762171983402145750, 47885190105749664630000, 3722865180810132218125, 211274120041841589375, 8238717458443537750, 178988004146512150, -666756024146750, -179538369278500, -4842224146500, -9647277675, 2146173180, 35230125, -260925, -9975, -5, 1]	2067585682514728660624940482215256472929804323597186849781428463757038116455078125	"20T1"	NULL
"20.0.9908312336370064404146969182230826585719200673403859737238963134586811065673828125.1"	[205497890627389663191310419601, 84807912695020072231539373445, 13431775670002829006645383320, 850449283907831479993605955, -10733837104574347684652270, -4096821490554080884401294, -121177646962078380813060, 6907085486209023596690, 378063392528596476310, -5579218709853478815, -539766981142754064, 1989641661981135, 454867434553885, 4490807165, -237715369785, -219954094, 75449855, 59855, -13305, -5, 1]	9908312336370064404146969182230826585719200673403859737238963134586811065673828125	"20T1"	NULL
"20.0.311618255217384014645870572599976110987406373488528125000000000000000000000000000000.1"	[251418384773687125766819163601, -97925353171011459599185196990, 14656292119219292087665829225, -851871004272256051553970060, -17174751153991406437347325, 4339643821750813876290452, -107560782066604290319135, -7740442605440092673400, 362631866146058373460, 6976303933175583050, -529442340190450251, -3368594910026280, 450447614847775, 829442377830, -236346488800, -81903602, 75141770, 0, -13270, 0, 1]	311618255217384014645870572599976110987406373488528125000000000000000000000000000000	"20T1"	NULL
"20.20.311618255217384014645870572599976110987406373488528125000000000000000000000000000000.1"	[106147843681588803423900258601, -57379255289892764243912521790, 10869644389849987162522539725, -788682887964233106240145860, -7329952495109498089215325, 3949177932988274158800452, -119711055157698575473135, -7199966900589298334400, 379803677864708478460, 6630443523067689050, -554076073537697751, -3268360187497680, 472202266887775, 819277130430, -247153028800, -81903602, 77959970, 0, -13570, 0, 1]	311618255217384014645870572599976110987406373488528125000000000000000000000000000000	"20T1"	NULL
"20.0.556477898863588120781159895111390825057253639487765102382752229459583759307861328125.1"	[11244395313609212997910045954586431201, 0, 0, 0, 0, -21567871246088265118347164849, 0, 0, 0, 0, 16982111008542128251, 0, 0, 0, 0, -6431899199, 0, 0, 0, 0, 1]	556477898863588120781159895111390825057253639487765102382752229459583759307861328125	"20T1"	NULL
"20.0.2809276271957340184582677482209319982093743977687530560365880955941975116729736328125.1"	[30931621486729361923185382900195320601, 0, 0, 0, 0, -14406085412296720451189209201, 0, 0, 0, 0, 5946555933708864601, 0, 0, 0, 0, -2590267651, 0, 0, 0, 0, 1]	2809276271957340184582677482209319982093743977687530560365880955941975116729736328125	"20T1"	NULL
"20.0.313366222202336889787417988197115802157534825706138776725349870685057717491872608661651611328125.1"	[248349773866653963886793573412379130583699601, 0, 0, 0, 0, -7767374568768626164509839869134751, 0, 0, 0, 0, 92234742714289603826101, 0, 0, 0, 0, -492881326201, 0, 0, 0, 0, 1]	313366222202336889787417988197115802157534825706138776725349870685057717491872608661651611328125	"20T1"	NULL


# Label --
#    Each (global) number field has a unique label of the form d.r.D.i where
#    <ul>
#    <li>\(d\) is the degree;
#    <li>\(r\) is the real signature;  the full signature is therefore \([r,(d-r)/2]\);
#    <li>\(D\) is the absolute value of the discriminant;
#    <li>\(i\) is the index, counting from 1.  This is in case there is more than one
#      field with the same signature and absolute value of the
#      discriminant: for example <a href="/NumberField/4.0.1008.1">4.0.1008.1</a> and <a href="/NumberField/4.0.1008.2">4.0.1008.2</a>.
#    </ul>
#    The discriminant portion of the label can take the form \(a_1\) e \(\epsilon_1\) _ \(a_2\) e \(\epsilon_2\) _ \(\cdots\) _ \(a_k\) e \(\epsilon_k\) to mean the absolute value of the
#    discriminant equals \(a_1^{\epsilon_1}a_2^{\epsilon_2}\cdots a_k^{\epsilon_k}\).  The separators are the letter e and the underscore symbol.


#Polynomial (coeffs) --
#    A **defining polynomial** of a number field $K$ is an irreducible polynomial $f\in\Q[x]$ such that $K\cong \mathbb{Q}(a)$, where $a$ is a root of $f(x)$. Equivalently, it is a polynomial $f\in \Q[x]$ such that $K \cong \Q[x]/(f)$.

#    A root \(a \in K\) of the defining polynomial is a generator of \(K\).




#Discriminant (disc) --
#    The **discriminant** of a number field $K$ is the square of the determinant of the matrix
#    \[
#    \left( \begin{array}{ccc}
#     \sigma_1(\beta_1) & \cdots & \sigma_1(\beta_n) \\
#    \vdots & & \vdots \\
#    \sigma_n(\beta_1) & \cdots & \sigma_n(\beta_n) \\
#    \end{array} \right)
#    \]
#    where $\sigma_1,..., \sigma_n$ are the embeddings of $K$ into the complex numbers $\mathbb{C}$, and $\{\beta_1, \ldots, \beta_n\}$ is an integral basis for the ring of integers of $K$.

#    The discriminant of $K$ is a non-zero integer divisible exactly by the primes which ramify in $K$.



#Galois group (galois_label) --
#    Let $K$ be a finite degree $n$ separable extension of a field $F$, and $K^{gal}$ be its
#    Galois (or normal) closure.
#    The **Galois group** for $K/F$ is the automorphism group $\Aut(K^{gal}/F)$.

#    This automorphism group acts on the $n$ embeddings $K\hookrightarrow K^{gal}$ via composition.  As a result, we get an injection $\Aut(K^{gal}/F)\hookrightarrow S_n$, which is well-defined up to the labelling of the $n$ embeddings, which corresponds to being well-defined up to conjugation in $S_n$.

#    We use the notation $\Gal(K/F)$ for $\Aut(K/F)$ when $K=K^{gal}$.

#    There is a naming convention for Galois groups up to degree $47$.





#Class group (class_group) --
#    The **ideal class group** of a number field $K$ with ring of integers $O_K$ is the group of equivalence classes of ideals, given by the quotient of the multiplicative group of all fractional ideals of $O_K$ by the subgroup of principal fractional ideals.

#    Since $K$ is a number field, the ideal class group of $K$ is a finite abelian group, and so has the structure of a product of cyclic groups encoded by a finite list $[a_1,\dots,a_n]$, where the $a_i$ are positive integers with $a_i\mid a_{i+1}$ for $1\leq i < n$.


