-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [90, 2805, -10950, -5075, -1400, 796, 232, 70, -50, -5, -2, 1], 'conductor': 0, 'degree': 11, 'dirichlet_group': [], 'disc_abs': 6561000000000000000000, 'disc_rad': 30, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[11, 1]]], [11, [[11, 1]]], [13, [[5, 2], [1, 1]]], [17, [[6, 1], [3, 1], [2, 1]]], [19, [[6, 1], [3, 1], [2, 1]]], [23, [[5, 2], [1, 1]]], [29, [[5, 2], [1, 1]]], [31, [[11, 1]]], [37, [[11, 1]]], [41, [[5, 2], [1, 1]]], [43, [[6, 1], [3, 1], [2, 1]]], [47, [[6, 1], [3, 1], [2, 1]]], [53, [[11, 1]]], [59, [[8, 1], [2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [17160, 6930, 15444], 'galois_label': '11T6', 'galt': 6, 'grd': 270.8346732868732, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '11.3.6561000000000000000000.1', 'local_algs': ['2.1.0.1', '2.4.8.7', '2.6.10.4', '3.1.0.1', '3.2.1.1', '3.8.7.1', '5.1.0.1', '5.5.9.4', '5.5.9.4'], 'monogenic': -1, 'num_ram': 3, 'r2': 4, 'ramps': [2, 3, 5], 'rd': 96.2411740906, 'regulator': {'__RealLiteral__': 0, 'data': '107079411.141', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1159417007769}{315674476992268} a^{10} - \\frac{1819656396269}{315674476992268} a^{9} - \\frac{371515294331}{78918619248067} a^{8} - \\frac{50131292142773}{157837238496134} a^{7} + \\frac{65889121906}{78918619248067} a^{6} - \\frac{11818870512630}{78918619248067} a^{5} + \\frac{714004225151158}{78918619248067} a^{4} + \\frac{787898438993871}{78918619248067} a^{3} + \\frac{9731772782584325}{315674476992268} a^{2} - \\frac{6234838871611353}{315674476992268} a + \\frac{446393138482111}{157837238496134} \\)', '\\( \\frac{26458468060787}{631348953984536} a^{10} - \\frac{275759954464135}{631348953984536} a^{9} + \\frac{234819293358001}{315674476992268} a^{8} + \\frac{218128785801087}{157837238496134} a^{7} + \\frac{3051260262820327}{315674476992268} a^{6} - \\frac{11334303710958157}{315674476992268} a^{5} - \\frac{15179524308350355}{315674476992268} a^{4} + \\frac{16592906247999989}{315674476992268} a^{3} + \\frac{294605812490391481}{631348953984536} a^{2} - \\frac{73782237028016717}{631348953984536} a - \\frac{990781312138379}{315674476992268} \\)', '\\( \\frac{360099135298729}{1894046861953608} a^{10} - \\frac{5581316621134799}{1894046861953608} a^{9} + \\frac{9295931894544635}{947023430976804} a^{8} - \\frac{642037775782840}{236755857744201} a^{7} + \\frac{37375696033835687}{947023430976804} a^{6} - \\frac{163833242996702851}{947023430976804} a^{5} - \\frac{152946882716948251}{947023430976804} a^{4} + \\frac{13549449731261507}{947023430976804} a^{3} + \\frac{5509787760845421199}{1894046861953608} a^{2} - \\frac{115446951953200739}{631348953984536} a - \\frac{32514424473264769}{315674476992268} \\)', '\\( \\frac{6613342010219}{1894046861953608} a^{10} + \\frac{109537184178281}{1894046861953608} a^{9} - \\frac{387910435431827}{947023430976804} a^{8} + \\frac{298738201686047}{473511715488402} a^{7} - \\frac{3512072813117609}{947023430976804} a^{6} + \\frac{16168550796490915}{947023430976804} a^{5} - \\frac{21910779568370039}{947023430976804} a^{4} + \\frac{46921810587685177}{947023430976804} a^{3} - \\frac{373471601464131415}{1894046861953608} a^{2} + \\frac{38762352630064801}{631348953984536} a - \\frac{1118293506512417}{315674476992268} \\)', '\\( \\frac{3135605312247435}{631348953984536} a^{10} + \\frac{3782484608668523}{631348953984536} a^{9} - \\frac{46144993661457067}{315674476992268} a^{8} - \\frac{1589695478107467}{78918619248067} a^{7} + \\frac{39236447341606421}{315674476992268} a^{6} + \\frac{978448882165236151}{315674476992268} a^{5} + \\frac{260901309122406507}{315674476992268} a^{4} - \\frac{3626076774867901927}{315674476992268} a^{3} - \\frac{25976014107937124179}{631348953984536} a^{2} + \\frac{6313940432210155045}{631348953984536} a + \\frac{101895689494453487}{315674476992268} \\)', '\\( \\frac{1408599913468387}{1894046861953608} a^{10} + \\frac{3209466978110167}{1894046861953608} a^{9} + \\frac{3345115554073829}{947023430976804} a^{8} - \\frac{5224778189945083}{236755857744201} a^{7} - \\frac{40287350785710391}{947023430976804} a^{6} - \\frac{9870584758665925}{947023430976804} a^{5} + \\frac{516338092012849427}{947023430976804} a^{4} + \\frac{1224635967699300125}{947023430976804} a^{3} + \\frac{3366982386939985549}{1894046861953608} a^{2} - \\frac{313632209587377333}{631348953984536} a - \\frac{4225764464861863}{315674476992268} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/2*a^7 - 1/2*a^5 - 1/2*a^3 - 1/2*a', '1/2*a^8 - 1/2*a^6 - 1/2*a^4 - 1/2*a^2', '1/4*a^9 - 1/2*a^6 - 1/2*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2*a^2 - 1/4*a - 1/2', '1/1894046861953608*a^10 + 23569802922049/1894046861953608*a^9 + 19593327064199/947023430976804*a^8 - 97955798617415/473511715488402*a^7 + 302323532157431/947023430976804*a^6 + 196073990354663/947023430976804*a^5 - 422970158627623/947023430976804*a^4 - 307579548304303/947023430976804*a^3 - 800733488315849/1894046861953608*a^2 + 40061575935705/631348953984536*a + 49459480584111/315674476992268']}
Number field data - 11.3.6561000000000000000000.1