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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [64, 0, 0, 0, 0, 0, -38, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 5416809268248576, 'disc_rad': 66, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[6, 2]]], [7, [[2, 6]]], [11, [0]], [13, [[2, 6]]], [17, [[2, 6]]], [19, [[2, 6]]], [23, [[6, 2]]], [29, [[2, 4], [1, 4]]], [31, [[6, 2]]], [37, [[6, 2]]], [41, [[2, 6]]], [43, [[2, 6]]], [47, [[2, 6]]], [53, [[2, 6]]], [59, [[6, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [44, 12, 12], 'galois_label': '12T10', 'galt': 10, 'grd': 20.471293992310418, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '12.4.5416809268248576.2', 'local_algs': ['2.1.6.11a1.2', '2.1.6.11a1.2', '3.3.2.3a1.2', '3.3.2.3a1.2', '11.2.2.2a1.2', '11.2.2.2a1.2', '11.2.2.2a1.2'], 'minimal_sibling': [4, 0, 0, 0, 4, 0, 4, 0, 4, 0, 2, 0, 1], 'monogenic': 0, 'narrow_class_group': [2, 2], 'narrow_class_number': 4, 'num_ram': 3, 'r2': 4, 'ramps': [2, 3, 11], 'rd': 20.4712939923, 'regulator': {'__RealLiteral__': 0, 'data': '4360.86280645', 'prec': 44}, 'res': {'gal': ['16,0,64,0,176,0,288,0,320,0,-56,0,-24,0,112,0,4,0,-16,0,0,0,-2,0,1'], 'sib': ['16,0,152,0,412,0,226,0,64,0,12,0,1', '4,0,0,0,4,0,4,0,4,0,2,0,1', '484,0,440,0,268,0,76,0,16,0,6,0,1']}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['-6.0.1', '-22.0.1', '-8.-1.1', '1.1.-1.1', '16.0.-14.0.1', '-54.0.0.0.6.0.1', '-22.0.20.0.-6.0.1', '-2.-6.-2.7.1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{144} a^{10} - \\frac{1}{36} a^{8} - \\frac{11}{72} a^{4} + \\frac{17}{18} a^{2} - \\frac{1}{3} \\)', '\\( \\frac{5}{288} a^{11} + \\frac{1}{48} a^{10} + \\frac{1}{72} a^{9} - \\frac{79}{144} a^{5} - \\frac{19}{24} a^{4} - \\frac{23}{36} a^{3} - \\frac{1}{3} a^{2} - \\frac{1}{3} \\)', '\\( \\frac{5}{288} a^{11} - \\frac{1}{48} a^{10} + \\frac{1}{72} a^{9} - \\frac{79}{144} a^{5} + \\frac{19}{24} a^{4} - \\frac{23}{36} a^{3} + \\frac{1}{3} a^{2} + \\frac{1}{3} \\)', '\\( \\frac{1}{48} a^{10} + \\frac{1}{72} a^{9} - \\frac{1}{18} a^{7} - \\frac{19}{24} a^{4} - \\frac{23}{36} a^{3} - \\frac{1}{3} a^{2} + \\frac{14}{9} a - \\frac{1}{3} \\)', '\\( \\frac{1}{96} a^{11} + \\frac{1}{144} a^{10} + \\frac{1}{72} a^{9} - \\frac{1}{36} a^{8} - \\frac{1}{18} a^{7} - \\frac{19}{48} a^{5} - \\frac{35}{72} a^{4} - \\frac{11}{36} a^{3} + \\frac{11}{18} a^{2} + \\frac{8}{9} a + \\frac{1}{3} \\)', '\\( \\frac{1}{96} a^{11} - \\frac{1}{144} a^{10} - \\frac{1}{72} a^{9} - \\frac{1}{36} a^{8} + \\frac{1}{18} a^{7} - \\frac{1}{9} a^{6} - \\frac{19}{48} a^{5} + \\frac{35}{72} a^{4} - \\frac{1}{36} a^{3} + \\frac{17}{18} a^{2} - \\frac{2}{9} a + \\frac{7}{9} \\)', '\\( \\frac{1}{72} a^{11} - \\frac{1}{48} a^{10} + \\frac{1}{72} a^{9} + \\frac{1}{18} a^{7} - \\frac{23}{36} a^{5} + \\frac{11}{24} a^{4} - \\frac{23}{36} a^{3} + a^{2} - \\frac{5}{9} a + 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/3*a^4 + 1/3*a^2 + 1/3', '1/3*a^5 + 1/3*a^3 + 1/3*a', '1/6*a^6 + 1/3', '1/6*a^7 + 1/3*a', '1/36*a^8 + 1/18*a^6 - 5/18*a^2 + 4/9', '1/72*a^9 - 1/18*a^7 + 13/36*a^3 - 4/9*a', '1/144*a^10 + 1/18*a^6 - 11/72*a^4 - 1/3*a^2 + 1/9', '1/288*a^11 - 1/18*a^7 + 13/144*a^5 - 4/9*a']}
Number field data - 12.4.5416809268248576.2