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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -1, 2, 1, -6, 7, 1, -10, 8, 2, -8, 4, 2, -3, 1], 'conductor': 0, 'degree': 14, 'dirichlet_group': [], 'disc_abs': 63097400703125, 'disc_rad': 4038233645, 'disc_sign': 1, 'frobs': [[2, [[14, 1]]], [3, [[6, 1], [4, 2]]], [5, [0]], [7, [[14, 1]]], [11, [[7, 1], [5, 1], [2, 1]]], [13, [[8, 1], [2, 3]]], [17, [[6, 1], [2, 4]]], [19, [[7, 1], [4, 1], [2, 1], [1, 1]]], [23, [[6, 2], [2, 1]]], [29, [[7, 2]]], [31, [[5, 1], [4, 1], [3, 1], [2, 1]]], [37, [[10, 1], [2, 2]]], [41, [[6, 1], [4, 1], [2, 1], [1, 2]]], [43, [[10, 1], [4, 1]]], [47, [[12, 1], [2, 1]]], [53, [[6, 2], [2, 1]]], [59, [[7, 1], [3, 2], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [25401600, 25401600], 'galois_label': '14T61', 'galt': 61, 'grd': 63547.09784876096, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '14.2.63097400703125.1', 'local_algs': ['5.4.2.1', '5.10.5.1', 'm807646729.1.1.0', 'm807646729.1.1.0', 'm807646729.2.1.1', 'm807646729.1.3.0', 'm807646729.1.7.0'], 'monogenic': 0, 'num_ram': 2, 'r2': 6, 'ramps': [5, 807646729], 'rd': 9.6764287896, 'regulator': {'__RealLiteral__': 0, 'data': '10.6889300961', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{2}{17} a^{13} - \\frac{7}{17} a^{12} - \\frac{1}{17} a^{11} + 2 a^{10} - \\frac{50}{17} a^{9} - \\frac{5}{17} a^{8} + \\frac{78}{17} a^{7} - \\frac{59}{17} a^{6} - \\frac{28}{17} a^{5} + \\frac{79}{17} a^{4} - \\frac{43}{17} a^{3} - \\frac{19}{17} a^{2} + \\frac{39}{17} a - \\frac{13}{17} \\)', '\\( \\frac{5}{17} a^{13} - \\frac{9}{17} a^{12} - \\frac{11}{17} a^{11} + 2 a^{10} - \\frac{6}{17} a^{9} - \\frac{55}{17} a^{8} + \\frac{59}{17} a^{7} + \\frac{14}{17} a^{6} - \\frac{70}{17} a^{5} + \\frac{36}{17} a^{4} + \\frac{37}{17} a^{3} - \\frac{39}{17} a^{2} + \\frac{4}{17} a + \\frac{10}{17} \\)', '\\( \\frac{1}{17} a^{13} + \\frac{5}{17} a^{12} - \\frac{26}{17} a^{11} + 2 a^{10} + \\frac{9}{17} a^{9} - \\frac{62}{17} a^{8} + \\frac{39}{17} a^{7} + \\frac{47}{17} a^{6} - \\frac{82}{17} a^{5} + \\frac{14}{17} a^{4} + \\frac{38}{17} a^{3} - \\frac{18}{17} a^{2} - \\frac{6}{17} a + \\frac{2}{17} \\)', '\\( \\frac{15}{17} a^{13} - \\frac{44}{17} a^{12} + \\frac{35}{17} a^{11} + 2 a^{10} - \\frac{86}{17} a^{9} + \\frac{39}{17} a^{8} + \\frac{58}{17} a^{7} - \\frac{111}{17} a^{6} + \\frac{45}{17} a^{5} + \\frac{40}{17} a^{4} - \\frac{59}{17} a^{3} + \\frac{19}{17} a^{2} + \\frac{12}{17} a - \\frac{4}{17} \\)', '\\( \\frac{1}{17} a^{13} + \\frac{5}{17} a^{12} - \\frac{9}{17} a^{11} - a^{10} + \\frac{43}{17} a^{9} - \\frac{11}{17} a^{8} - \\frac{46}{17} a^{7} + \\frac{47}{17} a^{6} + \\frac{3}{17} a^{5} - \\frac{54}{17} a^{4} + \\frac{38}{17} a^{3} - \\frac{1}{17} a^{2} - \\frac{23}{17} a + \\frac{19}{17} \\)', '\\( \\frac{18}{17} a^{13} - \\frac{46}{17} a^{12} + \\frac{25}{17} a^{11} + 3 a^{10} - \\frac{93}{17} a^{9} + \\frac{23}{17} a^{8} + \\frac{90}{17} a^{7} - \\frac{123}{17} a^{6} + \\frac{20}{17} a^{5} + \\frac{65}{17} a^{4} - \\frac{64}{17} a^{3} + \\frac{16}{17} a^{2} + \\frac{28}{17} a + \\frac{2}{17} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12', '1/17*a^13 + 5/17*a^12 + 8/17*a^11 - 8/17*a^9 + 6/17*a^8 + 5/17*a^7 - 4/17*a^6 + 3/17*a^5 - 3/17*a^4 + 4/17*a^3 - 1/17*a^2 - 6/17*a + 2/17']}
Number field data - 14.2.63097400703125.1