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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 3, 9, 11, 13, 14, 15, 7, 5, 4, 1, -1, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 4077334216081, 'disc_rad': 203, 'disc_sign': 1, 'frobs': [[2, [[6, 2]]], [3, [[6, 2]]], [5, [[3, 4]]], [7, [0]], [11, [[6, 2]]], [13, [[2, 6]]], [17, [[6, 2]]], [19, [[6, 2]]], [23, [[3, 4]]], [29, [0]], [31, [[6, 2]]], [37, [[6, 2]]], [41, [[2, 4], [1, 4]]], [43, [[2, 6]]], [47, [[6, 2]]], [53, [[3, 4]]], [59, [[3, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [16, 12], 'galois_label': '12T6', 'galt': 6, 'grd': 19.705964328162043, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.0.4077334216081.1', 'local_algs': ['7.3.2.2', '7.3.2.2', '7.3.2.2', '7.3.2.2', '29.2.1.2', '29.2.0.1', '29.2.1.2', '29.2.0.1', '29.4.2.1'], 'minimal_sibling': [-1, 3, -4, 3, 1, -2, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 6, 'ramps': [7, 29], 'rd': 11.2425465032, 'regulator': {'__RealLiteral__': 0, 'data': '20.3909313008', 'prec': 44}, 'res': {'gal': ['49,-49,294,-1176,2387,-2877,1819,-837,1719,-3402,3992,-2950,1675,-1459,1761,-1678,1203,-789,565,-405,251,-119,41,-9,1'], 'sib': ['-1,3,-4,3,1,-2,1', '1,1,1,3,3,-3,1,-1,1', '169,-247,-473,209,319,-10,-116,-23,36,1,-2,-3,1']}, 'subfield_mults': [1, 2, 1], 'subfields': ['1.-2.-1.1', '-1.3.-4.3.1.-2.1', '-13.19.-9.7.3.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{7} a^{11} + \\frac{3}{7} a^{10} - \\frac{2}{7} a^{9} + \\frac{3}{7} a^{8} + \\frac{25}{7} a^{7} + \\frac{27}{7} a^{6} + \\frac{36}{7} a^{5} + 8 a^{4} + 6 a^{3} + \\frac{27}{7} a^{2} + \\frac{20}{7} a + \\frac{6}{7} \\)', '\\( \\frac{5}{7} a^{11} - \\frac{9}{7} a^{10} + \\frac{10}{7} a^{9} + 2 a^{8} + \\frac{10}{7} a^{7} + 3 a^{6} + \\frac{46}{7} a^{5} + \\frac{8}{7} a^{4} + \\frac{20}{7} a^{3} + a^{2} + \\frac{4}{7} a - \\frac{9}{7} \\)', '\\( \\frac{1}{7} a^{11} - \\frac{2}{7} a^{10} + \\frac{2}{7} a^{8} + \\frac{5}{7} a^{7} - \\frac{9}{7} a^{6} - \\frac{13}{7} a^{5} - \\frac{19}{7} a^{4} - \\frac{25}{7} a^{3} - 5 a^{2} - \\frac{12}{7} a - \\frac{9}{7} \\)', '\\( \\frac{5}{7} a^{11} - \\frac{3}{7} a^{10} + \\frac{1}{7} a^{9} + 3 a^{8} + \\frac{33}{7} a^{7} + \\frac{39}{7} a^{6} + \\frac{64}{7} a^{5} + \\frac{68}{7} a^{4} + \\frac{50}{7} a^{3} + \\frac{33}{7} a^{2} + \\frac{22}{7} a + \\frac{3}{7} \\)', '\\( \\frac{1}{7} a^{10} + \\frac{2}{7} a^{9} - a^{8} + \\frac{12}{7} a^{7} + \\frac{10}{7} a^{6} + \\frac{10}{7} a^{5} + \\frac{3}{7} a^{4} + \\frac{19}{7} a^{3} - \\frac{5}{7} a^{2} - \\frac{11}{7} a - \\frac{5}{7} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/7*a^9 - 3/7*a^8 + 1/7*a^7 + 3/7*a^5 + 2/7*a^4 - 2/7*a^2 - 2/7*a - 1/7', '1/7*a^10 - 1/7*a^8 + 3/7*a^7 + 3/7*a^6 - 3/7*a^5 - 1/7*a^4 - 2/7*a^3 - 1/7*a^2 - 3/7', '1/7*a^11 - 3/7*a^7 - 3/7*a^6 + 2/7*a^5 - 1/7*a^3 - 2/7*a^2 + 2/7*a - 1/7']}
Number field data - 12.0.4077334216081.1