-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -1, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 6, 'dirichlet_group': [], 'disc_abs': 49781, 'disc_rad': 49781, 'disc_sign': 1, 'frobs': [[2, [[6, 1]]], [3, [[6, 1]]], [5, [[5, 1], [1, 1]]], [7, [[4, 1], [2, 1]]], [11, [[6, 1]]], [13, [[5, 1], [1, 1]]], [17, [[3, 1], [2, 1], [1, 1]]], [19, [[5, 1], [1, 1]]], [23, [[4, 1], [2, 1]]], [29, [[4, 1], [1, 2]]], [31, [[3, 1], [2, 1], [1, 1]]], [37, [[5, 1], [1, 1]]], [41, [[2, 3]]], [43, [[3, 1], [2, 1], [1, 1]]], [47, [[2, 2], [1, 2]]], [53, [[3, 1], [2, 1], [1, 1]]], [59, [[3, 1], [2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [360, 360], 'galois_label': '6T16', 'galt': 16, 'grd': 223.11656146507815, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '6.2.49781.1', 'local_algs': ['67.2.1.2', '67.4.0.1', 'm743.1.1.0', 'm743.2.1.1', 'm743.1.3.0'], 'monogenic': 1, 'num_ram': 2, 'r2': 2, 'ramps': [67, 743], 'rd': 6.06518337778, 'regulator': {'__RealLiteral__': 0, 'data': '0.740631472629', 'prec': 47}, 'res': {'sex': ['-468,1099,-872,246,-10,-1,1'], 'sib': ['-1,0,0,1,-1,1,2,-1,0,-2,2,0,-1,0,0,1', '-27386346041201,3191165010510,8762420286648,-2240221750452,-338911187157,194053651173,20834562054,-22973823923,2335321129,229129925,717721,-24277482,1345305,942533,-49826,-29546,3177,54,16,-8,1', '-468,1099,-872,246,-10,-1,1', '1,-8,0,-9,27,-2,27,0,9,0,1', '1,0,-1,0,0,2,-3,-1,3,1,1,-1,3,1,-3,-2,0,0,-1,0,1', '1495529578102729,26106877642102,-2352435172999,-39411482547,-11231969438,-99568901,-74578954,-756263,78899,-38,270,0,1', '1619157161064936,289040475558815,-270424073735824,-36495383308666,16431368715448,2104149742543,-578037571118,-101010246113,19478019989,3667939038,-557072802,-89714047,9632713,2292681,-213933,-43164,4044,420,-15,-10,1', '48,197,-412,-1898,-10,737,-1248,22,-149,453,-3,8,-42,0,0,1', '6400,0,-23381,0,22425,0,-9740,0,1230,0,-60,0,1', '-1160455815621,-4950910694628,-9411258136872,-9588818670314,-3993786882720,2431610270841,4278384658017,1956042241173,-492874884230,-953706163571,-318393062846,107275547813,112636928464,18669898888,-13481784138,-6887228720,-1545544,876086994,199951016,-52317676,-28320176,290746,2182157,184715,-110029,-13664,3816,448,-87,-6,1', '-17702825497435615363,6720675428319098773,-4197146608008787785,-1275077903446033637,736554837276295513,-323680153271567193,-5434835561047891,10494325636744376,-6839894342781909,1675920327977032,-728929428640764,148854934127350,-30884462880915,3829828800004,-913900634049,-18670719300,-6843039207,5619518478,-2069736619,175941121,-29244575,5479525,-983441,166129,2395,-3023,720,-160,40,-5,1', '-18,-39,-2695,12220,-12907,-22381,31168,-3536,-30093,39274,18256,-16588,13716,-13252,-14090,4497,-6421,414,-1424,-4132,1980,-2150,2376,-370,996,-33,189,0,18,0,1', '-229,6160,-58308,336702,-1239605,2915177,-3808647,2869510,-3374942,-7141004,7879769,-14551545,12844801,-5500286,-4829047,4298162,-752180,1585433,-3746158,-1446195,2775512,-1701723,-356148,-428887,429863,120335,50406,-198843,16474,-16456,40241,1200,-946,-2742,-550,563,189,115,-119,36,-6,11,-15,0,0,1', '-439255269,-39035691,1890201793,-61571202,-3273618250,-101000238,3012674684,-29101898,-1894859820,91581798,836614998,-63455952,-257086781,21789656,52638971,-2582810,-5382704,-500647,-305361,192269,178739,-25480,-13440,1645,-2828,-42,609,0,-42,0,1', '-690914276488480307953303,95852384021531370502820,-112499510294331541177418,10251981533911048647614,-5327604467998260305649,337453580379481055180,195869344060557421402,-6384234903106596231,31464295214961760481,-399991128037296870,1025726094565562759,1378692828935109,-11898125950813714,220585678406989,-1274441263032849,9227092775867,-3991617748106,204134331548,677652892732,-4878629409,1334193812,-20774299,-213244211,229763,855763,5903,28603,-36,-324,0,1', '1,-6,21,-56,126,-253,461,-771,1196,-1736,2368,-3041,3686,-4226,4586,-4713,4586,-4226,3686,-3041,2368,-1736,1196,-771,461,-253,126,-56,21,-6,1', '10290186013630118341351824,0,-16960039340461901103112205,0,9386976157112342894634354,0,-2141384749300098514220633,0,291485600435216203167434,0,-32026799301260206100056,0,2032033684604698506542,0,-232099085422609051131,0,16216526493436902173,0,-811731412836035755,0,55739800815746811,0,-2025796980667784,0,84882948771180,0,-1815009981311,0,64272418039,0,-1246163984,0,24678733,0,-315710,0,7906,0,0,0,1', '19854500836,0,772962485967,0,2116519752889,0,2406419730564,0,1700201783541,0,1191473737311,0,773392645431,0,292064321781,0,43825947393,0,-6771769242,0,-4690083714,0,-453371013,0,229630626,0,31292028,0,-6068238,0,-482997,0,67068,0,5184,0,-648,0,0,0,1', '23647402783,-133554607742,448696839084,-1115474596850,2251481441028,-3870568065236,5836852482855,-7874018778715,9634274077272,-10801041245496,11180396566310,-10749060058520,9643030561465,-8101745959105,6393319850930,-4749581645592,3327741644008,-2201960128394,1377469757646,-815212509801,456621754230,-242099597631,121485949022,-57672776906,25883856032,-10971409292,4386230684,-1651061655,583892877,-193470344,59859282,-17219806,4581106,-1119261,248887,-49748,8788,-1336,168,-16,1', '36871977614451449,-111704974383566971,155092742031131887,-139181116780554623,114571972463121789,-89846707117295869,58208906418480066,-31307558895001901,16271157196534558,-7125275528839269,2164930906255146,-958319195503053,219282445614857,-54676653351382,21302716143760,-5894932851983,558592588455,-532338394102,126907726667,22784156681,12309714955,106095053,-832971778,-435253780,-80314763,-8113100,5447731,1775870,514866,52278,7753,-2865,-126,-272,20,-4,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{5} - a^{4} - a - 1 \\)', '\\( a^{5} + a^{3} - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5']}
Number field data - 6.2.49781.1