-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-64, 0, 0, -61, 0, 0, -12, 0, 0, 1], 'conductor': 0, 'degree': 9, 'dirichlet_group': [], 'disc_abs': 45281702992707, 'disc_rad': 327, 'disc_sign': -1, 'frobs': [[2, [[2, 3], [1, 3]]], [3, [0]], [5, [[6, 1], [3, 1]]], [7, [[3, 3]]], [11, [[6, 1], [3, 1]]], [13, [[3, 3]]], [17, [[2, 3], [1, 3]]], [19, [[3, 3]]], [23, [[2, 3], [1, 3]]], [29, [[6, 1], [3, 1]]], [31, [[3, 3]]], [37, [[3, 3]]], [41, [[2, 3], [1, 3]]], [43, [[3, 3]]], [47, [[6, 1], [3, 1]]], [53, [[6, 1], [3, 1]]], [59, [[6, 1], [3, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [9, 12], 'galois_label': '9T4', 'galt': 4, 'grd': 39.52255016061654, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '9.3.45281702992707.2', 'local_algs': ['3.3.1.0a1.1', '3.3.2.3a1.2', '109.1.3.2a1.1', '109.1.3.2a1.1', '109.1.3.2a1.1'], 'minimal_sibling': [4, 2, -5, 1, 4, -3, 1], 'monogenic': -1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 3, 'ramps': [3, 109], 'rd': 32.9097626568, 'regulator': {'__RealLiteral__': 0, 'data': '25902.399356', 'prec': 40}, 'res': {'sib': ['4,2,-5,1,4,-3,1', '432,-3888,15516,-34668,45543,-33069,10297,-1248,4284,-5256,3810,-1770,646,-336,216,-108,39,-9,1']}, 'subfield_mults': [1, 1], 'subfields': ['4.-36.-1.1', '-109.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{24} a^{8} - \\frac{1}{12} a^{7} + \\frac{1}{6} a^{6} - \\frac{2}{3} a^{5} + \\frac{4}{3} a^{4} - \\frac{5}{2} a^{3} - \\frac{3}{8} a^{2} + \\frac{17}{12} a - 4 \\)', '\\( \\frac{1}{4} a^{8} + \\frac{1}{3} a^{6} - \\frac{7}{2} a^{5} - \\frac{1}{6} a^{4} - \\frac{14}{3} a^{3} - \\frac{101}{12} a^{2} + \\frac{13}{6} a - \\frac{35}{3} \\)', '\\( \\frac{4}{3} a^{8} + \\frac{4}{3} a^{7} - \\frac{1}{3} a^{6} - \\frac{113}{6} a^{5} - \\frac{37}{2} a^{4} + \\frac{16}{3} a^{3} - \\frac{247}{6} a^{2} - \\frac{93}{2} a + \\frac{1}{3} \\)', '\\( \\frac{9}{8} a^{8} + \\frac{5}{12} a^{7} - \\frac{7}{6} a^{6} - \\frac{46}{3} a^{5} - 6 a^{4} + \\frac{33}{2} a^{3} - \\frac{1019}{24} a^{2} - \\frac{197}{12} a + \\frac{136}{3} \\)', '\\( \\frac{13}{2} a^{8} - \\frac{25}{4} a^{7} - \\frac{33}{2} a^{6} - \\frac{177}{2} a^{5} + 86 a^{4} + \\frac{451}{2} a^{3} - 254 a^{2} + \\frac{921}{4} a + 630 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2*a', '1/2*a^5 - 1/2*a^2', '1/6*a^6 + 1/6*a^4 + 1/6*a^3 - 1/3*a^2 - 1/6*a - 1/3', '1/12*a^7 - 1/6*a^5 - 1/6*a^4 + 1/3*a^3 + 1/6*a^2 + 1/12*a', '1/48*a^8 + 1/12*a^5 + 1/3*a^3 + 1/16*a^2 + 1/3*a - 1/3']}
Number field data - 9.3.45281702992707.2