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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-144, 0, -144, 0, 108, 0, 96, 0, 48, 0, 12, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 328683126924509184, 'disc_rad': 6, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[6, 2]]], [7, [[3, 2], [2, 3]]], [11, [[8, 1], [2, 2]]], [13, [[6, 2]]], [17, [[3, 4]]], [19, [[4, 3]]], [23, [[4, 1], [3, 2], [1, 2]]], [29, [[6, 2]]], [31, [[2, 5], [1, 2]]], [37, [[4, 2], [2, 2]]], [41, [[4, 1], [2, 3], [1, 2]]], [43, [[8, 1], [2, 2]]], [47, [[3, 2], [2, 3]]], [53, [[6, 2]]], [59, [[8, 1], [2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [4248, 1600], 'galois_label': '12T200', 'galt': 200, 'grd': 59.25384244131698, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 3, 'label': '12.2.328683126924509184.3', 'local_algs': ['2.1.4.8b1.6', '2.1.8.28a1.7', '3.2.6.14a1.2'], 'minimal_sibling': [63, -48, -32, 0, 18, 0, 0, 0, 1], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 5, 'ramps': [2, 3], 'rd': 28.8224869242, 'regulator': {'__RealLiteral__': 0, 'data': '23300.3648249', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-2.0.1', '-4.12.9.-4.-6.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{96} a^{10} + \\frac{5}{48} a^{8} + \\frac{7}{24} a^{6} + \\frac{1}{4} a^{4} - \\frac{3}{8} a^{2} - \\frac{11}{4} \\)', '\\( \\frac{1}{84} a^{10} + \\frac{11}{84} a^{8} + \\frac{37}{84} a^{6} + \\frac{11}{14} a^{4} + \\frac{3}{2} a^{2} + \\frac{2}{7} \\)', '\\( \\frac{1}{42} a^{10} + \\frac{11}{42} a^{8} + \\frac{37}{42} a^{6} + \\frac{11}{7} a^{4} + 2 a^{2} - \\frac{31}{7} \\)', '\\( \\frac{29}{336} a^{10} + \\frac{163}{168} a^{8} + \\frac{71}{21} a^{6} + \\frac{39}{7} a^{4} + \\frac{21}{4} a^{2} - \\frac{223}{14} \\)', '\\( \\frac{13}{1344} a^{11} + \\frac{1}{64} a^{10} + \\frac{89}{672} a^{9} + \\frac{19}{96} a^{8} + \\frac{227}{336} a^{7} + \\frac{15}{16} a^{6} + \\frac{111}{56} a^{5} + \\frac{21}{8} a^{4} + \\frac{63}{16} a^{3} + \\frac{71}{16} a^{2} + \\frac{153}{56} a + \\frac{11}{8} \\)', '\\( \\frac{29}{336} a^{11} + \\frac{1}{14} a^{10} + \\frac{163}{168} a^{9} + \\frac{15}{28} a^{8} + \\frac{83}{28} a^{7} - \\frac{5}{14} a^{6} + \\frac{11}{7} a^{5} - \\frac{81}{14} a^{4} - \\frac{5}{4} a^{3} - \\frac{27}{14} a + \\frac{19}{7} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4', '1/2*a^5', '1/12*a^6 - 1/2*a^2', '1/12*a^7 - 1/2*a^3', '1/12*a^8', '1/24*a^9 - 1/4*a^5 - 1/2*a^3', '1/1344*a^10 + 3/224*a^8 + 11/336*a^6 - 1/4*a^5 - 13/56*a^4 - 1/2*a^3 + 3/16*a^2 - 1/2*a + 1/56', '1/1344*a^11 + 3/224*a^9 + 11/336*a^7 - 13/56*a^5 + 3/16*a^3 + 1/56*a']}
Number field data - 12.2.328683126924509184.3