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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 4, 2, -4, -7, -4, 4, 12, 6, -12, -14, 8, 12, -4, -4, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 401647199580061696, 'disc_rad': 2686, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[16, 1]]], [5, [[8, 2]]], [7, [[8, 1], [4, 2]]], [11, [[8, 2]]], [13, [[8, 2]]], [17, [0]], [19, [[4, 4]]], [23, [[8, 1], [4, 1], [2, 2]]], [29, [[16, 1]]], [31, [[4, 2], [2, 2], [1, 4]]], [37, [[16, 1]]], [41, [[4, 3], [2, 2]]], [43, [[8, 1], [4, 2]]], [47, [[4, 1], [2, 4], [1, 4]]], [53, [[8, 1], [4, 2]]], [59, [[8, 1], [4, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_label': '16T1771', 'galt': 1771, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '16.2.401647199580061696.1', 'local_algs': ['m2.4.4.44', '17.1.0.1', '17.1.0.1', '17.2.0.1', '17.4.2.1', '17.4.0.1', '17.4.0.1', '79.1.0.1', '79.1.0.1', '79.1.0.1', '79.1.0.1', '79.1.0.1', '79.1.0.1', '79.2.1.1', '79.2.0.1', '79.2.0.1', '79.4.0.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 7, 'ramps': [2, 17, 79], 'rd': 12.5962217178, 'regulator': {'__RealLiteral__': 0, 'data': '159.18386616', 'prec': 40}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-2.0.1', '2.0.-4.0.1', '-1.4.-2.-8.15.-16.10.-4.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{4} a^{15} - \\frac{3}{4} a^{14} - \\frac{7}{4} a^{13} + a^{12} + 8 a^{11} - \\frac{3}{2} a^{10} - \\frac{49}{4} a^{9} - 3 a^{8} + 11 a^{7} + \\frac{33}{4} a^{6} - \\frac{11}{4} a^{5} - 8 a^{4} - 4 a^{3} + \\frac{5}{4} a^{2} + \\frac{9}{2} a + \\frac{11}{4} \\)', '\\( a \\)', '\\( \\frac{3}{4} a^{15} - \\frac{1}{2} a^{14} - \\frac{13}{4} a^{13} - \\frac{5}{4} a^{12} + \\frac{47}{4} a^{11} + \\frac{7}{4} a^{10} - \\frac{31}{2} a^{9} - 5 a^{8} + \\frac{21}{2} a^{7} + \\frac{33}{4} a^{6} - \\frac{1}{2} a^{5} - 6 a^{4} - \\frac{11}{2} a^{3} - \\frac{3}{4} a^{2} + \\frac{17}{4} a + 3 \\)', '\\( \\frac{1}{2} a^{15} + a^{14} - \\frac{1}{2} a^{13} - \\frac{9}{2} a^{12} - 2 a^{11} + \\frac{13}{2} a^{10} + 8 a^{9} - 4 a^{8} - 11 a^{7} - \\frac{5}{2} a^{6} + \\frac{11}{2} a^{5} + 7 a^{4} + \\frac{5}{2} a^{3} - \\frac{7}{2} a^{2} - \\frac{9}{2} a - 2 \\)', '\\( 2 a^{15} + \\frac{3}{2} a^{14} - \\frac{21}{4} a^{13} - \\frac{23}{2} a^{12} + 11 a^{11} + \\frac{69}{4} a^{10} - \\frac{13}{4} a^{9} - 19 a^{8} - \\frac{31}{4} a^{7} + 8 a^{6} + \\frac{41}{4} a^{5} + \\frac{27}{4} a^{4} - \\frac{11}{4} a^{3} - \\frac{31}{4} a^{2} - \\frac{21}{4} a \\)', '\\( \\frac{3}{4} a^{15} + a^{14} - 2 a^{13} - \\frac{11}{2} a^{12} + \\frac{11}{4} a^{11} + \\frac{21}{2} a^{10} - \\frac{1}{2} a^{9} - \\frac{39}{4} a^{8} - \\frac{21}{4} a^{7} + 4 a^{6} + \\frac{21}{4} a^{5} + 3 a^{4} - a^{3} - \\frac{13}{4} a^{2} - \\frac{7}{4} a - \\frac{3}{4} \\)', '\\( \\frac{3}{4} a^{15} - \\frac{3}{4} a^{14} - \\frac{13}{4} a^{13} - \\frac{3}{4} a^{12} + \\frac{25}{2} a^{11} - \\frac{31}{2} a^{9} - \\frac{19}{4} a^{8} + \\frac{23}{2} a^{7} + 9 a^{6} - \\frac{11}{4} a^{5} - \\frac{23}{4} a^{4} - \\frac{17}{4} a^{3} - \\frac{3}{2} a^{2} + \\frac{15}{4} a + 3 \\)', '\\( \\frac{3}{2} a^{15} + \\frac{1}{4} a^{14} - 5 a^{13} - \\frac{23}{4} a^{12} + \\frac{57}{4} a^{11} + \\frac{33}{4} a^{10} - \\frac{59}{4} a^{9} - 9 a^{8} + 3 a^{7} + \\frac{19}{2} a^{6} + \\frac{17}{4} a^{5} - \\frac{3}{2} a^{4} - \\frac{11}{2} a^{3} - 4 a^{2} + \\frac{5}{4} a + \\frac{9}{4} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/2*a^8 - 1/2*a^2 - 1/2', '1/2*a^9 - 1/2*a^3 - 1/2*a', '1/2*a^10 - 1/2*a^4 - 1/2*a^2', '1/2*a^11 - 1/2*a^5 - 1/2*a^3', '1/4*a^12 - 1/4*a^9 - 1/4*a^8 - 1/2*a^7 - 1/4*a^6 - 1/4*a^4 - 1/4*a^3 + 1/4*a^2 - 1/4*a - 1/4', '1/4*a^13 - 1/4*a^10 - 1/4*a^9 - 1/4*a^7 - 1/4*a^5 - 1/4*a^4 + 1/4*a^3 + 1/4*a^2 - 1/4*a - 1/2', '1/4*a^14 - 1/4*a^11 - 1/4*a^10 - 1/4*a^8 - 1/4*a^6 - 1/4*a^5 + 1/4*a^4 + 1/4*a^3 - 1/4*a^2 - 1/2*a', '1/4*a^15 - 1/4*a^11 - 1/4*a^8 + 1/4*a^7 - 1/2*a^6 + 1/4*a^5 - 1/4*a^2 + 1/4*a - 1/4']}
Number field data - 16.2.401647199580061696.1