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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-6075, -6750, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 10, 'dirichlet_group': [], 'disc_abs': 76886718750000000000, 'disc_rad': 30, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[8, 1], [1, 2]]], [11, [[9, 1], [1, 1]]], [13, [[4, 1], [3, 1], [2, 1], [1, 1]]], [17, [[5, 1], [4, 1], [1, 1]]], [19, [[6, 1], [3, 1], [1, 1]]], [23, [[7, 1], [3, 1]]], [29, [[5, 1], [4, 1], [1, 1]]], [31, [[7, 1], [2, 1], [1, 1]]], [37, [[8, 1], [2, 1]]], [41, [[7, 1], [2, 1], [1, 1]]], [43, [[8, 1], [1, 2]]], [47, [[8, 1], [2, 1]]], [53, [[10, 1]]], [59, [[4, 1], [3, 1], [2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [6350400, 4233600, 7366464], 'galois_label': '10T45', 'galt': 45, 'grd': 317.9457799689622, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 49, 'label': '10.2.76886718750000000000.49', 'local_algs': ['2.1.2.2a1.1', '2.4.2.8a5.1', '3.1.1.0a1.1', '3.1.3.3a1.1', '3.2.3.6a2.1', '5.2.5.18a1.15'], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 4, 'ramps': [2, 3, 5], 'rd': 97.4058706789, 'regulator': {'__RealLiteral__': 0, 'data': '4374170.6999', 'prec': 40}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{585} a^{9} + \\frac{17}{5265} a^{8} + \\frac{16}{1755} a^{7} + \\frac{2}{351} a^{6} - \\frac{127}{1755} a^{5} - \\frac{7}{39} a^{4} - \\frac{83}{117} a^{3} - \\frac{86}{117} a^{2} + \\frac{20}{39} a + \\frac{8}{13} \\)', '\\( \\frac{34}{1755} a^{9} - \\frac{323}{5265} a^{8} + \\frac{11}{195} a^{7} - \\frac{346}{1755} a^{6} - \\frac{239}{1755} a^{5} + \\frac{16}{39} a^{4} - \\frac{724}{117} a^{3} + \\frac{1010}{117} a^{2} - \\frac{1888}{39} a - \\frac{724}{13} \\)', '\\( \\frac{11}{2106} a^{9} + \\frac{3221}{10530} a^{8} + \\frac{1093}{3510} a^{7} - \\frac{1295}{702} a^{6} - \\frac{3125}{702} a^{5} + \\frac{665}{78} a^{4} + \\frac{1113}{26} a^{3} - \\frac{4115}{234} a^{2} - \\frac{25651}{78} a - \\frac{6701}{26} \\)', '\\( \\frac{89}{10530} a^{9} + \\frac{2927}{10530} a^{8} - \\frac{4789}{3510} a^{7} + \\frac{5453}{1170} a^{6} - \\frac{46753}{3510} a^{5} + \\frac{2603}{78} a^{4} - \\frac{16909}{234} a^{3} + \\frac{29467}{234} a^{2} - \\frac{3199}{26} a - \\frac{7757}{26} \\)', '\\( \\frac{4729}{10530} a^{9} - \\frac{753}{130} a^{8} - \\frac{32639}{1170} a^{7} - \\frac{53383}{702} a^{6} - \\frac{26293}{234} a^{5} + \\frac{19819}{234} a^{4} + \\frac{284693}{234} a^{3} + \\frac{117333}{26} a^{2} + \\frac{790649}{78} a + \\frac{164027}{26} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', '1/3*a^3', '1/9*a^4 + 1/3*a^2 - 1/3*a', '1/45*a^5 + 1/3*a^2', '1/45*a^6', '1/135*a^7 + 1/3*a^2 + 1/3*a', '1/405*a^8 - 1/135*a^6 + 1/135*a^5 - 1/9*a^3 - 1/9*a^2 - 1/3*a', '1/10530*a^9 - 1/10530*a^8 + 1/390*a^7 + 17/3510*a^6 + 7/702*a^5 - 11/234*a^4 - 5/78*a^3 - 11/234*a^2 + 7/26*a + 11/26']}
Number field data - 10.2.76886718750000000000.49