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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [324, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 16, 'disc_abs': 1494186269970473680896, 'disc_rad': 6, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [128, 16], 'galois_label': '16T50', 'galt': 50, 'grd': 27.712812921102035, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 43, 'label': '16.0.1494186269970473680896.43', 'local_algs': ['2.1.16.64g1.589', '3.2.2.2a1.1', '3.2.2.2a1.1', '3.4.1.0a1.1', '3.4.1.0a1.1'], 'maximal_cm_subfield': [1, 0, 0, 0, 1], 'maxp': 3, 'minimal_sibling': [4, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 1], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 8, 'ramps': [2, 3], 'rd': 21.057184207239878, 'regulator': {'__RealLiteral__': 0, 'data': '39128.59405383013', 'prec': 57}, 'subfield_mults': [1, 1, 1, 2, 2, 1, 1], 'subfields': ['2.0.1', '-2.0.1', '1.0.1', '2.0.0.0.1', '-2.0.0.0.1', '1.0.0.0.1', '1.0.-4.0.8.0.-4.0.1'], 'torsion_order': 8, 'unit_signature_rank': 0, 'used_grh': False} -
nf_fields_extra • Show schema
{'dirichlet_group': [], 'frobs': [[2, [0]], [3, [0]], [5, [[8, 2]]], [7, [[4, 4]]], [11, [[4, 4]]], [13, [[8, 2]]], [17, [[4, 4]]], [19, [[4, 4]]], [23, [[2, 8]]], [29, [[8, 2]]], [31, [[4, 4]]], [37, [[8, 2]]], [41, [[4, 4]]], [43, [[4, 4]]], [47, [[2, 8]]], [53, [[8, 2]]], [59, [[4, 4]]]], 'label': '16.0.1494186269970473680896.43', 'res': {'gal': ['16,0,0,0,0,0,0,0,112,0,0,0,0,0,0,0,780,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,1'], 'sib': ['4,0,0,0,0,0,0,0,-28,0,0,0,0,0,0,0,1']}, 'torsion_gen': '\\( \\frac{1}{72} a^{12} - \\frac{1}{16} a^{8} + \\frac{5}{36} a^{4} - \\frac{7}{8} \\)', 'units': ['\\( \\frac{5}{864} a^{14} + \\frac{1}{24} a^{10} + \\frac{43}{432} a^{6} + \\frac{5}{12} a^{2} \\)', '\\( \\frac{5}{864} a^{14} - \\frac{1}{72} a^{12} + \\frac{1}{16} a^{8} + \\frac{43}{432} a^{6} - \\frac{5}{36} a^{4} - \\frac{1}{2} a^{2} + \\frac{15}{8} \\)', '\\( -\\frac{5}{864} a^{14} - \\frac{1}{144} a^{12} + \\frac{1}{24} a^{10} - \\frac{1}{16} a^{8} - \\frac{43}{432} a^{6} + \\frac{13}{72} a^{4} + \\frac{5}{12} a^{2} - \\frac{7}{8} \\)', '\\( \\frac{7}{864} a^{15} + \\frac{1}{72} a^{14} + \\frac{1}{96} a^{13} + \\frac{1}{144} a^{12} - \\frac{1}{48} a^{10} - \\frac{1}{16} a^{8} + \\frac{17}{432} a^{7} + \\frac{5}{36} a^{6} - \\frac{1}{48} a^{5} - \\frac{13}{72} a^{4} - \\frac{1}{2} a^{3} - \\frac{23}{24} a^{2} - \\frac{1}{2} a - \\frac{7}{8} \\)', '\\( -\\frac{5}{432} a^{15} + \\frac{5}{432} a^{14} - \\frac{1}{96} a^{13} + \\frac{1}{48} a^{12} - \\frac{1}{48} a^{11} - \\frac{43}{216} a^{7} + \\frac{43}{216} a^{6} + \\frac{1}{48} a^{5} - \\frac{1}{24} a^{4} + \\frac{1}{24} a^{3} - a^{2} + \\frac{3}{2} a - 1 \\)', '\\( \\frac{1}{216} a^{15} - \\frac{5}{216} a^{14} - \\frac{1}{288} a^{13} + \\frac{1}{18} a^{12} - \\frac{1}{48} a^{11} - \\frac{1}{24} a^{10} + \\frac{1}{8} a^{9} - \\frac{13}{108} a^{7} - \\frac{43}{108} a^{6} + \\frac{49}{144} a^{5} + \\frac{5}{9} a^{4} - \\frac{23}{24} a^{3} + \\frac{1}{12} a^{2} + \\frac{9}{4} a - 2 \\)', '\\( -\\frac{1}{288} a^{15} - \\frac{7}{432} a^{14} + \\frac{1}{32} a^{13} - \\frac{1}{144} a^{12} - \\frac{1}{24} a^{11} + \\frac{1}{24} a^{10} + \\frac{1}{16} a^{9} - \\frac{1}{8} a^{8} - \\frac{23}{144} a^{7} - \\frac{17}{216} a^{6} + \\frac{7}{16} a^{5} - \\frac{23}{72} a^{4} - \\frac{5}{12} a^{3} + \\frac{11}{12} a^{2} + \\frac{3}{8} a - \\frac{11}{4} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/16*a^8 - 1/2*a^4 - 1/8', '1/16*a^9 - 1/2*a^5 - 1/8*a', '1/48*a^10 - 1/2*a^6 - 1/24*a^2', '1/48*a^11 - 1/2*a^7 - 1/24*a^3', '1/144*a^12 + 23/72*a^4', '1/288*a^13 - 1/2*a^7 - 49/144*a^5 - 1/2*a', '1/864*a^14 + 95/432*a^6 - 1/2*a^2', '1/864*a^15 + 95/432*a^7 - 1/2*a^3']}
Number field data - 16.0.1494186269970473680896.43