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nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [-36, 0, -72, 0, 0, 0, 48, 0, 3, 0, -6, 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, [[3, 2], [2, 3]]], [29, [[6, 2]]], [31, [[4, 1], [2, 2], [1, 4]]], [37, [[4, 2], [2, 2]]], [41, [[4, 1], [2, 3], [1, 2]]], [43, [[8, 1], [2, 2]]], [47, [[4, 1], [3, 2], [1, 2]]], [53, [[6, 2]]], [59, [[8, 1], [2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [3960, 1600], 'galois_label': '12T200', 'galt': 200, 'grd': 49.82634369891186, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 8, 'label': '12.2.328683126924509184.8', 'local_algs': ['2.1.4.10a1.1', '2.1.8.26c1.8', '3.2.6.14a1.2'], 'minimal_sibling': [-1, -4, -2, -8, 1, 8, 2, -4, 1], 'monogenic': 0, 'narrow_class_group': [2, 2], 'narrow_class_number': 4, 'num_ram': 2, 'r2': 5, 'ramps': [2, 3], 'rd': 28.8224869242, 'regulator': {'__RealLiteral__': 0, 'data': '12241.4549258', '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}{4} a^{10} - \\frac{5}{3} a^{8} + \\frac{23}{12} a^{6} + \\frac{21}{2} a^{4} - \\frac{15}{2} a^{2} - 12 \\)', '\\( \\frac{1}{24} a^{10} - \\frac{7}{24} a^{8} + \\frac{11}{24} a^{6} + \\frac{9}{8} a^{4} - \\frac{3}{4} a^{2} - \\frac{5}{4} \\)', '\\( \\frac{1}{4} a^{11} + \\frac{5}{48} a^{10} - \\frac{41}{24} a^{9} - \\frac{17}{24} a^{8} + \\frac{13}{6} a^{7} + \\frac{15}{16} a^{6} + \\frac{81}{8} a^{5} + 4 a^{4} - 8 a^{3} - \\frac{23}{8} a^{2} - \\frac{49}{4} a - 4 \\)', '\\( \\frac{1}{4} a^{11} - \\frac{5}{48} a^{10} - \\frac{41}{24} a^{9} + \\frac{17}{24} a^{8} + \\frac{13}{6} a^{7} - \\frac{15}{16} a^{6} + \\frac{81}{8} a^{5} - 4 a^{4} - 8 a^{3} + \\frac{23}{8} a^{2} - \\frac{49}{4} a + 4 \\)', '\\( \\frac{5}{4} a^{10} - \\frac{69}{8} a^{8} + \\frac{23}{2} a^{6} + \\frac{399}{8} a^{4} - \\frac{89}{2} a^{2} - \\frac{203}{4} \\)', '\\( \\frac{5}{24} a^{11} - \\frac{1}{8} a^{10} - \\frac{5}{4} a^{9} + \\frac{5}{8} a^{8} + \\frac{7}{8} a^{7} + \\frac{1}{8} a^{6} + \\frac{17}{2} a^{5} - \\frac{45}{8} a^{4} + \\frac{1}{4} a^{3} - \\frac{19}{4} a^{2} - 4 a + \\frac{1}{4} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/3*a^6', '1/3*a^7', '1/24*a^8 - 1/12*a^6 + 3/8*a^4 + 1/4', '1/24*a^9 - 1/12*a^7 + 3/8*a^5 + 1/4*a', '1/48*a^10 - 1/6*a^7 + 5/48*a^6 - 1/8*a^4 - 1/2*a^3 - 3/8*a^2 + 1/4', '1/48*a^11 + 5/48*a^7 - 1/8*a^5 - 3/8*a^3 + 1/4*a']}
Number field data - 12.2.328683126924509184.8