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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -2, 5, -7, 12, -19, 33, -56, 79, -104, 116, -121, 114, -97, 77, -53, 34, -18, 9, -3, 1], 'conductor': 0, 'degree': 20, 'dirichlet_group': [], 'disc_abs': 2392595214874267578125, 'disc_rad': 1400005, 'disc_sign': 1, 'frobs': [[2, [[20, 1]]], [3, [[12, 1], [4, 2]]], [5, [0]], [7, [[4, 5]]], [11, [[5, 2], [3, 2], [2, 2]]], [13, [[8, 2], [4, 1]]], [17, [[8, 2], [4, 1]]], [19, [[6, 1], [4, 2], [2, 3]]], [23, [[8, 2], [4, 1]]], [29, [[6, 1], [4, 2], [2, 3]]], [31, [[4, 4], [1, 4]]], [37, [[12, 1], [4, 2]]], [41, [[4, 2], [3, 2], [1, 6]]], [43, [[4, 5]]], [47, [[8, 2], [4, 1]]], [53, [[8, 2], [4, 1]]], [59, [[6, 2], [2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [43200, 28800], 'galois_label': '20T654', 'galt': 654, 'grd': 1769.3236981512437, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '20.0.2392595214874267578125.1', 'local_algs': ['m5.4.5.15', 'm280001.1.1.0', 'm280001.1.1.0', 'm280001.1.1.0', 'm280001.1.1.0', 'm280001.2.1.1', 'm280001.2.1.1', 'm280001.1.3.0', 'm280001.1.3.0', 'm280001.1.3.0', 'm280001.1.3.0'], 'monogenic': 0, 'num_ram': 2, 'r2': 10, 'ramps': [5, 280001], 'rd': 11.7204277355, 'regulator': {'__RealLiteral__': 0, 'data': '858.376938924', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-1.-1.1', '1.-1.1.-1.1', '1.1.-3.-1.5.-1.-3.3.-1.-1.1'], 'torsion_gen': '\\( -\\frac{19365}{45787} a^{19} + \\frac{80529}{45787} a^{18} - \\frac{197650}{45787} a^{17} + \\frac{13336}{1477} a^{16} - \\frac{699485}{45787} a^{15} + \\frac{1068754}{45787} a^{14} - \\frac{1430312}{45787} a^{13} + \\frac{242521}{6541} a^{12} - \\frac{1799985}{45787} a^{11} + \\frac{56946}{1477} a^{10} - \\frac{1543911}{45787} a^{9} + \\frac{1089651}{45787} a^{8} - \\frac{765314}{45787} a^{7} + \\frac{248604}{45787} a^{6} - \\frac{74953}{45787} a^{5} + \\frac{65525}{45787} a^{4} - \\frac{25694}{45787} a^{3} + \\frac{93824}{45787} a^{2} + \\frac{19872}{45787} a + \\frac{15355}{45787} \\)', 'torsion_order': 10, 'units': ['\\( \\frac{22434}{45787} a^{19} - \\frac{23365}{45787} a^{18} + \\frac{64846}{45787} a^{17} - \\frac{1325}{1477} a^{16} + \\frac{42409}{45787} a^{15} + \\frac{60793}{45787} a^{14} - \\frac{180758}{45787} a^{13} + \\frac{407625}{45787} a^{12} - \\frac{577839}{45787} a^{11} + \\frac{3237}{211} a^{10} - \\frac{924309}{45787} a^{9} + \\frac{764521}{45787} a^{8} - \\frac{835836}{45787} a^{7} + \\frac{564092}{45787} a^{6} - \\frac{302410}{45787} a^{5} + \\frac{206686}{45787} a^{4} - \\frac{41731}{45787} a^{3} + \\frac{16671}{6541} a^{2} - \\frac{23375}{45787} a + \\frac{19365}{45787} \\)', '\\( \\frac{6862}{45787} a^{19} - \\frac{63408}{45787} a^{18} + \\frac{137876}{45787} a^{17} - \\frac{11868}{1477} a^{16} + \\frac{594210}{45787} a^{15} - \\frac{1045719}{45787} a^{14} + \\frac{1373492}{45787} a^{13} - \\frac{1838195}{45787} a^{12} + \\frac{1922157}{45787} a^{11} - \\frac{9664}{211} a^{10} + \\frac{1827765}{45787} a^{9} - \\frac{1465496}{45787} a^{8} + \\frac{1121304}{45787} a^{7} - \\frac{471199}{45787} a^{6} + \\frac{285438}{45787} a^{5} - \\frac{75839}{45787} a^{4} + \\frac{79381}{45787} a^{3} - \\frac{18180}{6541} a^{2} + \\frac{76444}{45787} a - \\frac{39080}{45787} \\)', '\\( \\frac{72505}{45787} a^{19} - \\frac{34514}{6541} a^{18} + \\frac{660837}{45787} a^{17} - \\frac{43444}{1477} a^{16} + \\frac{2411602}{45787} a^{15} - \\frac{3739430}{45787} a^{14} + \\frac{5217171}{45787} a^{13} - \\frac{6443980}{45787} a^{12} + \\frac{7253399}{45787} a^{11} - \\frac{243099}{1477} a^{10} + \\frac{6936809}{45787} a^{9} - \\frac{5889089}{45787} a^{8} + \\frac{4365650}{45787} a^{7} - \\frac{2693627}{45787} a^{6} + \\frac{1565777}{45787} a^{5} - \\frac{870061}{45787} a^{4} + \\frac{85945}{6541} a^{3} - \\frac{435241}{45787} a^{2} + \\frac{180184}{45787} a - \\frac{91206}{45787} \\)', '\\( \\frac{68686}{45787} a^{19} - \\frac{224214}{45787} a^{18} + \\frac{610818}{45787} a^{17} - \\frac{39966}{1477} a^{16} + \\frac{2189190}{45787} a^{15} - \\frac{3386624}{45787} a^{14} + \\frac{4656110}{45787} a^{13} - \\frac{5719649}{45787} a^{12} + \\frac{6308718}{45787} a^{11} - \\frac{209656}{1477} a^{10} + \\frac{825413}{6541} a^{9} - \\frac{692456}{6541} a^{8} + \\frac{3364292}{45787} a^{7} - \\frac{271292}{6541} a^{6} + \\frac{1040386}{45787} a^{5} - \\frac{476337}{45787} a^{4} + \\frac{414248}{45787} a^{3} - \\frac{298176}{45787} a^{2} + \\frac{135655}{45787} a - \\frac{57236}{45787} \\)', '\\( \\frac{24053}{45787} a^{19} - \\frac{10215}{6541} a^{18} + \\frac{185589}{45787} a^{17} - \\frac{11359}{1477} a^{16} + \\frac{605328}{45787} a^{15} - \\frac{891826}{45787} a^{14} + \\frac{1199022}{45787} a^{13} - \\frac{1401564}{45787} a^{12} + \\frac{1522494}{45787} a^{11} - \\frac{49158}{1477} a^{10} + \\frac{1347873}{45787} a^{9} - \\frac{1081798}{45787} a^{8} + \\frac{782752}{45787} a^{7} - \\frac{415451}{45787} a^{6} + \\frac{298575}{45787} a^{5} - \\frac{171945}{45787} a^{4} + \\frac{26042}{6541} a^{3} - \\frac{64349}{45787} a^{2} - \\frac{2874}{45787} a + \\frac{5918}{45787} \\)', '\\( \\frac{50161}{45787} a^{19} - \\frac{100545}{45787} a^{18} + \\frac{314689}{45787} a^{17} - \\frac{16151}{1477} a^{16} + \\frac{956173}{45787} a^{15} - \\frac{1263852}{45787} a^{14} + \\frac{259000}{6541} a^{13} - \\frac{1938996}{45787} a^{12} + \\frac{322946}{6541} a^{11} - \\frac{67446}{1477} a^{10} + \\frac{1858984}{45787} a^{9} - \\frac{1558503}{45787} a^{8} + \\frac{133995}{6541} a^{7} - \\frac{708082}{45787} a^{6} + \\frac{339436}{45787} a^{5} - \\frac{305021}{45787} a^{4} + \\frac{213173}{45787} a^{3} - \\frac{93131}{45787} a^{2} + \\frac{10056}{6541} a - \\frac{22007}{45787} \\)', '\\( \\frac{41851}{45787} a^{19} - \\frac{139535}{45787} a^{18} + \\frac{377159}{45787} a^{17} - \\frac{25554}{1477} a^{16} + \\frac{1398661}{45787} a^{15} - \\frac{2216463}{45787} a^{14} + \\frac{3061290}{45787} a^{13} - \\frac{549375}{6541} a^{12} + \\frac{4290341}{45787} a^{11} - \\frac{145744}{1477} a^{10} + \\frac{4085017}{45787} a^{9} - \\frac{3527214}{45787} a^{8} + \\frac{2616203}{45787} a^{7} - \\frac{1538141}{45787} a^{6} + \\frac{995612}{45787} a^{5} - \\frac{453844}{45787} a^{4} + \\frac{346348}{45787} a^{3} - \\frac{288664}{45787} a^{2} + \\frac{147557}{45787} a - \\frac{86396}{45787} \\)', '\\( \\frac{1507}{6541} a^{19} - \\frac{37112}{45787} a^{18} + \\frac{147398}{45787} a^{17} - \\frac{1472}{211} a^{16} + \\frac{682554}{45787} a^{15} - \\frac{159536}{6541} a^{14} + \\frac{1764291}{45787} a^{13} - \\frac{2324900}{45787} a^{12} + \\frac{2927543}{45787} a^{11} - \\frac{101697}{1477} a^{10} + \\frac{3254680}{45787} a^{9} - \\frac{2970881}{45787} a^{8} + \\frac{2409562}{45787} a^{7} - \\frac{1783153}{45787} a^{6} + \\frac{1044038}{45787} a^{5} - \\frac{82257}{6541} a^{4} + \\frac{273657}{45787} a^{3} - \\frac{257414}{45787} a^{2} + \\frac{135753}{45787} a - \\frac{92619}{45787} \\)', '\\( \\frac{9505}{45787} a^{19} + \\frac{3191}{6541} a^{18} - \\frac{44455}{45787} a^{17} + \\frac{6613}{1477} a^{16} - \\frac{358179}{45787} a^{15} + \\frac{724708}{45787} a^{14} - \\frac{1053457}{45787} a^{13} + \\frac{1529293}{45787} a^{12} - \\frac{1785295}{45787} a^{11} + \\frac{64516}{1477} a^{10} - \\frac{2050337}{45787} a^{9} + \\frac{1715018}{45787} a^{8} - \\frac{1564407}{45787} a^{7} + \\frac{863332}{45787} a^{6} - \\frac{594276}{45787} a^{5} + \\frac{261440}{45787} a^{4} - \\frac{15027}{6541} a^{3} + \\frac{236682}{45787} a^{2} - \\frac{8396}{45787} a + \\frac{92740}{45787} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12', 'a^13', 'a^14', 'a^15', 'a^16', 'a^17', '1/7*a^18 + 3/7*a^17 - 1/7*a^15 + 2/7*a^13 - 2/7*a^12 - 2/7*a^11 + 2/7*a^10 + 1/7*a^9 - 2/7*a^8 - 3/7*a^7 + 3/7*a^6 + 1/7*a^5 + 3/7*a^3 + 2/7*a^2 + 1/7*a - 1/7', '1/45787*a^19 + 1453/45787*a^18 - 3707/45787*a^17 + 387/1477*a^16 + 22819/45787*a^15 - 3869/45787*a^14 - 198/6541*a^13 + 16138/45787*a^12 - 1616/6541*a^11 - 216/1477*a^10 - 22793/45787*a^9 - 4219/45787*a^8 + 2691/6541*a^7 - 6338/45787*a^6 - 18367/45787*a^5 - 15845/45787*a^4 + 6340/45787*a^3 - 11400/45787*a^2 - 554/6541*a + 18136/45787']}
Number field data - 20.0.2392595214874267578125.1