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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [676, 0, -1432, 0, 1228, 0, -548, 0, 136, 0, -18, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 10453488727228416, 'disc_rad': 258, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[6, 2]]], [7, [[6, 1], [2, 3]]], [11, [[2, 6]]], [13, [[6, 1], [2, 3]]], [17, [[6, 2]]], [19, [[3, 4]]], [23, [[6, 2]]], [29, [[6, 2]]], [31, [[6, 1], [2, 3]]], [37, [[6, 1], [2, 3]]], [41, [[2, 6]]], [43, [0]], [47, [[2, 6]]], [53, [[6, 2]]], [59, [[2, 6]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [66, 18, 24], 'galois_label': '12T18', 'galt': 18, 'grd': 75.75789922542675, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.0.10453488727228416.1', 'local_algs': ['2.2.6.22a1.1', '3.3.2.3a1.2', '3.3.2.3a1.2', '43.1.1.0a1.1', '43.1.1.0a1.1', '43.1.1.0a1.1', '43.1.1.0a1.1', '43.1.1.0a1.1', '43.1.1.0a1.1', '43.1.3.2a1.1', '43.1.3.2a1.1'], 'maximal_cm_subfield': [4, 0, -2, 0, 1], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 6, 'ramps': [2, 3, 43], 'rd': 21.62411976019196, 'regulator': {'__RealLiteral__': 0, 'data': '2787.1636304529407', 'prec': 60}, 'subfield_mults': [1, 1, 1, 1, 1], 'subfields': ['1.-1.1', '2.0.1', '-6.0.1', '4.0.-2.0.1', '7.-1.-2.1.4.-3.1'], 'torsion_gen': '\\( \\frac{1}{4} a^{8} - 3 a^{6} + 14 a^{4} - \\frac{59}{2} a^{2} + 23 \\)', 'torsion_order': 6, 'units': ['\\( -\\frac{9}{52} a^{11} + \\frac{34}{13} a^{9} - \\frac{1}{4} a^{8} - \\frac{417}{26} a^{7} + 3 a^{6} + \\frac{1283}{26} a^{5} - 14 a^{4} - \\frac{969}{13} a^{3} + \\frac{59}{2} a^{2} + \\frac{557}{13} a - 21 \\)', '\\( -\\frac{1}{13} a^{11} + \\frac{18}{13} a^{9} - \\frac{1}{4} a^{8} - \\frac{259}{26} a^{7} + \\frac{7}{2} a^{6} + \\frac{470}{13} a^{5} - 19 a^{4} - \\frac{864}{13} a^{3} + \\frac{93}{2} a^{2} + \\frac{639}{13} a - 42 \\)', '\\( -\\frac{3}{13} a^{11} - \\frac{1}{4} a^{10} + \\frac{95}{26} a^{9} + \\frac{15}{4} a^{8} - \\frac{621}{26} a^{7} - \\frac{47}{2} a^{6} + \\frac{1033}{13} a^{5} + \\frac{151}{2} a^{4} - \\frac{1721}{13} a^{3} - \\frac{245}{2} a^{2} + \\frac{1111}{13} a + 78 \\)', '\\( \\frac{1}{4} a^{8} - \\frac{7}{2} a^{6} + 19 a^{4} - \\frac{95}{2} a^{2} + 45 \\)', '\\( -\\frac{1}{2} a^{10} + 7 a^{8} - \\frac{79}{2} a^{6} + 110 a^{4} - 146 a^{2} + 74 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6', '1/2*a^7', '1/4*a^8 - 1/2*a^2', '1/4*a^9 - 1/2*a^3', '1/4*a^10 - 1/2*a^4', '1/52*a^11 - 5/52*a^9 + 3/26*a^7 - 1/26*a^5 + 3/26*a^3 + 6/13*a']}
Number field data - 12.0.10453488727228416.1