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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -3, 2, 3, -1, -3, 4, -3, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 11634921, 'disc_rad': 1137, 'disc_sign': 1, 'frobs': [[2, [[4, 2]]], [3, [0]], [5, [[6, 1], [2, 1]]], [7, [[4, 2]]], [11, [[2, 4]]], [13, [[2, 2], [1, 4]]], [17, [[2, 4]]], [19, [[3, 2], [1, 2]]], [23, [[6, 1], [2, 1]]], [29, [[4, 2]]], [31, [[4, 2]]], [37, [[3, 2], [1, 2]]], [41, [[6, 1], [2, 1]]], [43, [[2, 2], [1, 4]]], [47, [[4, 2]]], [53, [[2, 4]]], [59, [[4, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [24, 24], 'galois_label': '8T24', 'galt': 24, 'grd': 33.71943060017473, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '8.0.11634921.1', 'local_algs': ['3.8.4.1', 'm379.1.2.0', 'm379.1.2.0', 'm379.2.1.1', 'm379.2.1.1'], 'minimal_sibling': [4, -1, 2, -3, 4, -3, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 4, 'ramps': [3, 379], 'rd': 7.6422357332, 'regulator': {'__RealLiteral__': 0, 'data': '3.60551138703', 'prec': 44}, 'res': {'sib': ['4,-1,2,-3,4,-3,1', '-11,73,-10,32,0,-1,1', '-1,10,-33,36,0,2,-4,17,-19,7,4,-3,1', '-212,-3566,1669,3567,-1477,-1182,-193,263,82,-4,-13,-2,1', '1,-10,67,-258,729,-1190,1284,75,117,-449,580,-1000,646,-36,340,-331,246,-255,168,-69,56,-26,5,-3,1', '1,1,3,-6,0,-7,5,7,0,6,3,-1,1', '1156,1836,4939,2243,1652,905,248,-234,153,16,-1,-2,1', '121,-803,5219,-26,-2236,-309,1075,53,42,-64,1,-1,1', '16,64,32,1770,3327,-6811,-10454,21131,5191,-41225,25399,23765,-44815,29592,-4994,-8500,9276,-5547,2426,-938,363,-132,40,-8,1', '169,156,-711,206,211,18,-29,-2,1', '329311,-545162,896624,-824410,742151,-472836,296406,-141068,64872,-22978,8142,-2340,754,-196,48,-8,1', '49,0,29,0,-49,0,93,0,-14,0,12,0,1', '51529,-54707,-10019,-34618,77488,-28321,45480,-47081,11954,-4959,432,602,278,438,66,1455,-1385,759,-164,-72,101,-58,23,-6,1', '81,-324,1269,-1458,3654,-3564,7260,-5973,12400,-10487,16630,-15721,21800,-20904,23193,-20571,15776,-10074,5280,-2324,829,-242,55,-9,1']}, 'subfield_mults': [1, 1], 'subfields': ['1.-1.1', '1.-2.-4.-1.1'], 'torsion_gen': '\\( -\\frac{10}{13} a^{7} + 2 a^{6} - \\frac{27}{13} a^{5} + \\frac{14}{13} a^{4} + 2 a^{3} - \\frac{30}{13} a^{2} - \\frac{32}{13} a + \\frac{25}{13} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{25}{13} a^{7} - 5 a^{6} + \\frac{74}{13} a^{5} - \\frac{48}{13} a^{4} - 3 a^{3} + \\frac{49}{13} a^{2} + \\frac{80}{13} a - \\frac{43}{13} \\)', '\\( \\frac{6}{13} a^{7} - a^{6} + \\frac{11}{13} a^{5} + \\frac{2}{13} a^{4} - 2 a^{3} + \\frac{18}{13} a^{2} + \\frac{14}{13} a - \\frac{2}{13} \\)', '\\( \\frac{4}{13} a^{7} - a^{6} + \\frac{16}{13} a^{5} - \\frac{16}{13} a^{4} + \\frac{12}{13} a^{2} + \\frac{5}{13} a + \\frac{3}{13} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/13*a^7 + 4/13*a^5 - 4/13*a^4 + 3/13*a^2 - 2/13*a + 4/13']}
Number field data - 8.0.11634921.1