-
nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [-46703, -97899, -44000, 1989, 3789, 153, -110, -3, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 2070185663499849, 'disc_rad': 357, 'disc_sign': 1, 'frobs': [[2, [[4, 2]]], [3, [0]], [5, [[4, 2]]], [7, [0]], [11, [[4, 2]]], [13, [[4, 2]]], [17, [0]], [19, [[4, 2]]], [23, [[4, 2]]], [29, [[4, 2]]], [31, [[4, 2]]], [37, [[4, 2]]], [41, [[4, 2]]], [43, [[2, 4]]], [47, [[1, 8]]], [53, [[4, 2]]], [59, [[2, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [6, 6, 6], 'galois_label': '8T5', 'galt': 5, 'grd': 82.12987504608633, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.8.2070185663499849.1', 'local_algs': ['3.8.6.1', '7.8.6.1', '17.4.3.2', '17.4.3.2'], 'monogenic': 0, 'num_ram': 3, 'r2': 0, 'ramps': [3, 7, 17], 'rd': 82.1298750461, 'regulator': {'__RealLiteral__': 0, 'data': '36250.7464952', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-5.-1.1', '-4.-1.1', '-89.-1.1', '1.0.-19.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{103169042}{1427439851} a^{7} - \\frac{642357662}{1427439851} a^{6} - \\frac{9279515057}{1427439851} a^{5} + \\frac{45718194520}{1427439851} a^{4} + \\frac{243750635968}{1427439851} a^{3} - \\frac{580393048852}{1427439851} a^{2} - \\frac{2674520342556}{1427439851} a - \\frac{1498274126077}{1427439851} \\)', '\\( \\frac{164631}{1427439851} a^{7} - \\frac{643358}{1427439851} a^{6} - \\frac{17126474}{1427439851} a^{5} + \\frac{40798000}{1427439851} a^{4} + \\frac{576533321}{1427439851} a^{3} - \\frac{262725835}{1427439851} a^{2} - \\frac{7586245064}{1427439851} a - \\frac{4622553539}{1427439851} \\)', '\\( \\frac{6557060}{1427439851} a^{7} - \\frac{42930596}{1427439851} a^{6} - \\frac{560635788}{1427439851} a^{5} + \\frac{2999069943}{1427439851} a^{4} + \\frac{13322566240}{1427439851} a^{3} - \\frac{36206924963}{1427439851} a^{2} - \\frac{139682981617}{1427439851} a - \\frac{74910208311}{1427439851} \\)', '\\( \\frac{287835508}{1427439851} a^{7} - \\frac{1790741186}{1427439851} a^{6} - \\frac{25886512942}{1427439851} a^{5} + \\frac{127420490479}{1427439851} a^{4} + \\frac{679484284208}{1427439851} a^{3} - \\frac{1616611344586}{1427439851} a^{2} - \\frac{7442116305214}{1427439851} a - \\frac{4168067459426}{1427439851} \\)', '\\( \\frac{10064659}{1427439851} a^{7} - \\frac{55502027}{1427439851} a^{6} - \\frac{956387873}{1427439851} a^{5} + \\frac{3963342724}{1427439851} a^{4} + \\frac{27122699685}{1427439851} a^{3} - \\frac{51061783127}{1427439851} a^{2} - \\frac{294213560417}{1427439851} a - \\frac{170465859985}{1427439851} \\)', '\\( \\frac{137146791}{1427439851} a^{7} - \\frac{860994286}{1427439851} a^{6} - \\frac{12268703509}{1427439851} a^{5} + \\frac{61239981949}{1427439851} a^{4} + \\frac{319267081966}{1427439851} a^{3} - \\frac{776666278472}{1427439851} a^{2} - \\frac{3494918831109}{1427439851} a - \\frac{1931541207543}{1427439851} \\)', '\\( \\frac{104414}{723487} a^{7} - \\frac{650496}{723487} a^{6} - \\frac{9389142}{723487} a^{5} + \\frac{46302480}{723487} a^{4} + \\frac{246501878}{723487} a^{3} - \\frac{588069258}{723487} a^{2} - \\frac{2703430408}{723487} a - \\frac{1513368325}{723487} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/1427439851*a^7 - 530654460/1427439851*a^6 + 229561142/1427439851*a^5 - 498841993/1427439851*a^4 + 376200939/1427439851*a^3 - 286450262/1427439851*a^2 - 191560992/1427439851*a + 415464251/1427439851']}
Number field data - 8.8.2070185663499849.1