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nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [36, 0, -72, 0, 16, 0, 4, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 326488817664, 'disc_rad': 186, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[3, 2], [1, 2]]], [7, [[4, 2]]], [11, [[6, 1], [2, 1]]], [13, [[6, 1], [2, 1]]], [17, [[6, 1], [2, 1]]], [19, [[3, 2], [1, 2]]], [23, [[4, 2]]], [29, [[2, 2], [1, 4]]], [31, [0]], [37, [[2, 4]]], [41, [[2, 4]]], [43, [[2, 2], [1, 4]]], [47, [[3, 2], [1, 2]]], [53, [[4, 2]]], [59, [[4, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [132, 24, 24], 'galois_label': '8T24', 'galt': 24, 'grd': 64.87449083902186, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 8, 'label': '8.4.326488817664.8', 'local_algs': ['2.1.8.22d1.22', '3.1.2.1a1.1', '3.1.2.1a1.1', '3.2.2.2a1.2', '31.2.1.0a1.1', '31.2.1.0a1.1', '31.2.2.2a1.2'], 'minimal_sibling': [-96, 0, -20, 0, 4, 0, 1], 'monogenic': 0, 'narrow_class_group': [2, 2], 'narrow_class_number': 4, 'num_ram': 3, 'r2': 2, 'ramps': [2, 3, 31], 'rd': 27.4937221181, 'regulator': {'__RealLiteral__': 0, 'data': '1319.19249096', 'prec': 44}, 'res': {'sib': ['279,0,129,0,19,0,1', '-96,0,-20,0,4,0,1', '1,0,-2,0,-21,0,-52,0,-21,0,-2,0,1', '168921,0,385152,0,2318458,0,2635408,0,-12257,0,-555456,0,291532,0,76768,0,1255,0,-1344,0,-38,0,16,0,1', '20736,0,-185856,0,270592,0,-299520,0,197696,0,-105856,0,41824,0,-12704,0,3268,0,-664,0,104,0,-12,0,1', '321,188,-96,-384,151,40,-96,0,23,-4,0,0,1', '576,0,-96,0,316,0,-12,0,85,0,18,0,1', '61504,0,18848,0,-11556,0,-860,0,381,0,38,0,1', '64,0,112,0,148,0,59,0,37,0,7,0,1', '65536,0,-337920,0,1813552,0,1249440,0,267440,0,125832,0,50449,0,6486,0,1787,0,516,0,43,0,6,0,1', '80,-224,264,-160,70,-32,10,0,1', '917230,-618936,917532,-614552,518682,-285376,173600,-80516,39495,-15316,5976,-1876,614,-164,44,-8,1', '9216,0,-7968,0,3712,0,-1022,0,183,0,-20,0,1', '9216,0,55296,0,162304,0,276736,0,381072,0,345664,0,184192,0,24288,0,3544,0,496,0,96,0,-8,0,1']}, 'subfield_mults': [1, 1], 'subfields': ['-6.0.1', '5.-4.-4.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{12} a^{7} - \\frac{1}{8} a^{6} + \\frac{1}{3} a^{5} - \\frac{5}{8} a^{4} + \\frac{4}{3} a^{3} - \\frac{5}{2} a^{2} - 6 a + \\frac{23}{4} \\)', '\\( \\frac{1}{48} a^{7} + \\frac{1}{24} a^{6} + \\frac{1}{12} a^{5} + \\frac{1}{24} a^{4} + \\frac{5}{24} a^{3} + \\frac{2}{3} a^{2} + \\frac{1}{4} a - \\frac{1}{4} \\)', '\\( \\frac{1}{48} a^{7} - \\frac{1}{24} a^{6} + \\frac{1}{12} a^{5} - \\frac{1}{24} a^{4} + \\frac{5}{24} a^{3} - \\frac{2}{3} a^{2} + \\frac{1}{4} a + \\frac{1}{4} \\)', '\\( \\frac{11}{48} a^{7} + \\frac{5}{24} a^{6} + \\frac{25}{24} a^{5} + \\frac{5}{6} a^{4} + \\frac{97}{24} a^{3} + \\frac{43}{12} a^{2} - \\frac{27}{2} a - \\frac{23}{2} \\)', '\\( \\frac{11}{48} a^{7} - \\frac{5}{24} a^{6} + \\frac{25}{24} a^{5} - \\frac{5}{6} a^{4} + \\frac{97}{24} a^{3} - \\frac{43}{12} a^{2} - \\frac{27}{2} a + \\frac{23}{2} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/8*a^4 - 1/2*a^3 + 1/4*a^2 - 1/4', '1/8*a^5 + 1/4*a^3 - 1/4*a', '1/24*a^6 + 1/24*a^4 - 1/2*a^3 + 1/6*a^2 - 1/4', '1/48*a^7 - 1/24*a^5 + 11/24*a^3 - 1/2*a^2 - 1/2*a']}
Number field data - 8.4.326488817664.8