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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': True, 'coeffs': [17, -34, 123, -2, -38, -4, 1, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 2385443281, 'disc_rad': 221, 'disc_sign': 1, 'frobs': [[2, [[2, 4]]], [3, [[2, 4]]], [5, [[4, 2]]], [7, [[4, 2]]], [11, [[4, 2]]], [13, [0]], [17, [0]], [19, [[2, 4]]], [23, [[2, 4]]], [29, [[2, 4]]], [31, [[4, 2]]], [37, [[4, 2]]], [41, [[4, 2]]], [43, [[2, 4]]], [47, [[2, 4]]], [53, [[2, 4]]], [59, [[2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4, 4], 'galois_label': '8T4', 'galt': 4, 'grd': 14.866068747318506, 'inessentialp': [2, 3], 'is_galois': True, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '8.0.2385443281.2', 'local_algs': ['13.4.2.1', '13.4.2.1', '17.2.1.1', '17.2.1.1', '17.2.1.1', '17.2.1.1'], 'minimal_sibling': [4, -2, 1, -1, 1], 'monogenic': -1, 'num_ram': 2, 'r2': 4, 'ramps': [13, 17], 'rd': 14.8660687473, 'regulator': {'__RealLiteral__': 0, 'data': '54.1296002906', 'prec': 44}, 'relative_class_number': 1, 'res': {'sib': ['2,-5,6,-2,1', '4,-2,1,-1,1']}, 'subfield_mults': [1, 1, 1, 1, 2, 2], 'subfields': ['-55.-1.1', '-4.-1.1', '-3.-1.1', '1.0.-15.0.1', '2.-5.6.-2.1', '4.-2.1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{635}{4848} a^{7} + \\frac{935}{4848} a^{6} + \\frac{1219}{2424} a^{5} + \\frac{913}{2424} a^{4} - \\frac{2405}{606} a^{3} - \\frac{13871}{2424} a^{2} + \\frac{26339}{4848} a - \\frac{7111}{4848} \\)', '\\( \\frac{737}{4848} a^{7} + \\frac{103}{1616} a^{6} + \\frac{187}{808} a^{5} - \\frac{877}{2424} a^{4} - \\frac{3383}{606} a^{3} - \\frac{5221}{2424} a^{2} + \\frac{79513}{4848} a - \\frac{4183}{1616} \\)', '\\( \\frac{17}{1616} a^{7} + \\frac{91}{4848} a^{6} + \\frac{25}{808} a^{5} - \\frac{29}{808} a^{4} - \\frac{287}{606} a^{3} - \\frac{1735}{2424} a^{2} + \\frac{731}{4848} a + \\frac{917}{4848} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2', '1/2*a^4 - 1/2*a', '1/6*a^5 - 1/6*a^4 + 1/6*a^3 + 1/6*a^2 - 1/2*a - 1/6', '1/12*a^6 + 1/6*a^3 + 1/3*a^2 - 1/3*a + 5/12', '1/4848*a^7 + 27/1616*a^6 + 49/2424*a^5 - 159/808*a^4 - 23/202*a^3 - 541/2424*a^2 - 1063/4848*a + 319/4848']}
Number field data - 8.0.2385443281.2