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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-2, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 17, 'dirichlet_group': [], 'disc_abs': 1072818875260874969805419538268160, 'disc_rad': 130959335358993526587575627230, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[17, 1]]], [5, [0]], [7, [[16, 1], [1, 1]]], [11, [[17, 1]]], [13, [[9, 1], [6, 1], [2, 1]]], [17, [[16, 1], [1, 1]]], [19, [[14, 1], [3, 1]]], [23, [[8, 1], [6, 1], [3, 1]]], [29, [[17, 1]]], [31, [[10, 1], [4, 1], [3, 1]]], [37, [[10, 1], [4, 1], [3, 1]]], [41, [[16, 1], [1, 1]]], [43, [[4, 2], [3, 2], [2, 1], [1, 1]]], [47, [[15, 1], [2, 1]]], [53, [[9, 1], [8, 1]]], [59, [[13, 1], [3, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [331974932889600, 177843714048000, 177843714048000, 177843714048000, 177843714048000], 'galois_label': '17T10', 'galt': 10, 'grd': 488668744925295.3, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '17.3.1072818875260874969805419538268160.1', 'local_algs': ['2.1.0.1', '2.1.0.1', '2.15.14.1', '5.2.1.1', '5.3.0.1', '5.12.0.1', 'm3251.1.1.0', 'm3251.1.1.0', 'm3251.2.1.1', 'm3251.1.13.0', 'm9473.1.2.0', 'm9473.2.1.1', 'm9473.1.5.0', 'm9473.1.8.0', 'm425237890924282842001.1.1.0', 'm425237890924282842001.1.2.0', 'm425237890924282842001.2.1.1', 'm425237890924282842001.1.12.0'], 'monogenic': -1, 'num_ram': 5, 'r2': 7, 'ramps': [2, 5, 3251, 9473, 425237890924282842001], 'rd': 87.6944566406, 'regulator': {'__RealLiteral__': 0, 'data': '35856250594.5', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{16} + 2 a^{15} + 2 a^{14} + a^{13} - 2 a^{12} - 3 a^{11} - 4 a^{10} - a^{9} + 2 a^{8} + 6 a^{7} + 7 a^{6} + 2 a^{5} - 4 a^{4} - 11 a^{3} - 9 a^{2} - 5 a - 1 \\)', '\\( 2 a^{16} - 3 a^{15} - 2 a^{14} - 2 a^{13} - 2 a^{12} - a^{11} + 3 a^{9} + 4 a^{8} + 5 a^{7} + 6 a^{6} + 9 a^{5} + 5 a^{4} + 2 a^{3} - a^{2} - 3 a - 27 \\)', '\\( a^{16} - a^{15} + a^{14} - a^{13} + a^{12} - a^{11} + a^{10} - a^{9} - 2 a^{8} + 2 a^{7} - 2 a^{6} + 2 a^{5} - 2 a^{4} + 2 a^{3} - 2 a^{2} + 2 a - 1 \\)', '\\( 4 a^{16} - 5 a^{14} + 4 a^{13} + 3 a^{12} - 8 a^{11} + 3 a^{10} + 7 a^{9} - 9 a^{8} - 2 a^{7} + 13 a^{6} - 9 a^{5} - 10 a^{4} + 20 a^{3} - 5 a^{2} - 20 a - 7 \\)', '\\( 2 a^{16} - 4 a^{14} + a^{13} + 4 a^{12} + a^{11} - 2 a^{10} + 8 a^{8} + 3 a^{7} - 8 a^{6} - a^{5} + 6 a^{4} - 14 a^{2} - 14 a - 1 \\)', '\\( 24 a^{16} - 9 a^{14} + 6 a^{13} + 6 a^{12} - 14 a^{11} + 15 a^{10} - 10 a^{9} - 7 a^{8} + 25 a^{7} - 23 a^{6} + 9 a^{5} + 10 a^{4} - 37 a^{3} + 43 a^{2} - 10 a - 193 \\)', '\\( 2 a^{16} - a^{14} + 4 a^{12} - 10 a^{11} + 16 a^{10} - 19 a^{9} + 18 a^{8} - 13 a^{7} + 7 a^{6} - 3 a^{5} + 4 a^{4} - 8 a^{3} + 12 a^{2} - 11 a - 9 \\)', '\\( 2 a^{16} + 6 a^{15} + 5 a^{14} - 2 a^{13} - 7 a^{12} - 3 a^{11} + 7 a^{10} + 10 a^{9} + a^{8} - 10 a^{7} - 6 a^{6} + 13 a^{5} + 29 a^{4} + 22 a^{3} - a^{2} - 12 a - 3 \\)', '\\( 30 a^{16} - 38 a^{15} + 32 a^{14} - 13 a^{13} - 7 a^{12} + 13 a^{11} + 5 a^{10} - 41 a^{9} + 76 a^{8} - 87 a^{7} + 65 a^{6} - 20 a^{5} - 20 a^{4} + 27 a^{3} + 17 a^{2} - 99 a - 29 \\)'], 'used_grh': True, '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', 'a^13', 'a^14', 'a^15', '1/2*a^16 - 1/2*a^15 - 1/2*a^14 - 1/2*a^13 - 1/2*a^12 - 1/2*a^11 - 1/2*a^10 - 1/2*a^9 - 1/2*a^8 - 1/2*a^7 - 1/2*a^6 - 1/2*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2*a^2 - 1/2*a']}
Number field data - 17.3.1072818875260874969805419538268160.1