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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [168, 882, 1008, -396, -748, 106, 168, -31, -8, 6, -4, 1], 'conductor': 0, 'degree': 11, 'dirichlet_group': [], 'disc_abs': 9678619238400000000, 'disc_rad': 210, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [0]], [11, [[5, 1], [3, 2]]], [13, [[8, 1], [3, 1]]], [17, [[9, 1], [2, 1]]], [19, [[6, 1], [5, 1]]], [23, [[4, 2], [2, 1], [1, 1]]], [29, [[7, 1], [3, 1], [1, 1]]], [31, [[11, 1]]], [37, [[7, 1], [4, 1]]], [41, [[9, 1], [2, 1]]], [43, [[7, 1], [4, 1]]], [47, [[10, 1], [1, 1]]], [53, [[11, 1]]], [59, [[6, 1], [2, 1], [1, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [95634000, 49896000, 36590400, 26611200], 'galois_label': '11T8', 'galt': 8, 'grd': 332.46081383675426, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '11.5.9678619238400000000.1', 'local_algs': ['2.1.1.0a1.1', '2.1.4.8b1.4', '2.1.6.11a1.7', '3.1.3.3a1.2', '3.1.4.3a1.1', '3.1.4.3a1.1', '5.1.1.0a1.1', '5.1.4.3a1.4', '5.1.6.5a1.1', '7.1.3.2a1.1', '7.1.3.2a1.1', '7.5.1.0a1.1'], 'monogenic': -1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 4, 'r2': 3, 'ramps': [2, 3, 5, 7], 'rd': 53.2087475948, 'regulator': {'__RealLiteral__': 0, 'data': '8123279.63873', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{8963491}{182960160} a^{10} - \\frac{10056487}{60986720} a^{9} + \\frac{16646411}{60986720} a^{8} - \\frac{79086779}{182960160} a^{7} - \\frac{23067149}{15246680} a^{6} + \\frac{104280257}{15246680} a^{5} + \\frac{584905709}{91480080} a^{4} - \\frac{703866419}{30493360} a^{3} - \\frac{480683453}{30493360} a^{2} + \\frac{369229039}{30493360} a + \\frac{34307451}{7623340} \\)', '\\( \\frac{731981}{36592032} a^{10} - \\frac{7767359}{36592032} a^{9} + \\frac{18373447}{36592032} a^{8} - \\frac{8917603}{12197344} a^{7} + \\frac{3237371}{9148008} a^{6} + \\frac{70683029}{9148008} a^{5} - \\frac{250105429}{18296016} a^{4} - \\frac{245132825}{6098672} a^{3} + \\frac{247209029}{6098672} a^{2} + \\frac{516674421}{6098672} a + \\frac{31234753}{1524668} \\)', '\\( \\frac{3116037}{30493360} a^{10} - \\frac{28726021}{91480080} a^{9} + \\frac{58671773}{91480080} a^{8} - \\frac{116973379}{91480080} a^{7} - \\frac{52029887}{22870020} a^{6} + \\frac{256144951}{22870020} a^{5} + \\frac{626886689}{45740040} a^{4} - \\frac{373865579}{15246680} a^{3} - \\frac{398453713}{15246680} a^{2} - \\frac{437904241}{15246680} a - \\frac{26287959}{3811670} \\)', '\\( \\frac{12287}{1143501} a^{10} - \\frac{66829}{3049336} a^{9} - \\frac{4835}{4574004} a^{8} - \\frac{1019803}{9148008} a^{7} - \\frac{457505}{762334} a^{6} + \\frac{651431}{1143501} a^{5} + \\frac{2717239}{762334} a^{4} + \\frac{1217335}{1524668} a^{3} - \\frac{3879423}{762334} a^{2} - \\frac{5994709}{1524668} a - \\frac{266950}{381167} \\)', '\\( \\frac{28686697}{60986720} a^{10} - \\frac{123344327}{60986720} a^{9} + \\frac{148152931}{60986720} a^{8} + \\frac{156926487}{60986720} a^{7} - \\frac{614725989}{15246680} a^{6} + \\frac{2382925057}{15246680} a^{5} - \\frac{2959992457}{30493360} a^{4} - \\frac{11095501299}{30493360} a^{3} + \\frac{6794978427}{30493360} a^{2} + \\frac{10402929599}{30493360} a + \\frac{522763091}{7623340} \\)', '\\( \\frac{10590127}{36592032} a^{10} - \\frac{30362609}{36592032} a^{9} + \\frac{31761989}{36592032} a^{8} - \\frac{21522143}{36592032} a^{7} - \\frac{115070107}{9148008} a^{6} + \\frac{367532479}{9148008} a^{5} + \\frac{1162017713}{18296016} a^{4} - \\frac{1004460263}{6098672} a^{3} - \\frac{880992849}{6098672} a^{2} + \\frac{895696467}{6098672} a + \\frac{163602367}{1524668} \\)', '\\( \\frac{26388401}{60986720} a^{10} - \\frac{134306351}{60986720} a^{9} + \\frac{301399323}{60986720} a^{8} - \\frac{529028609}{60986720} a^{7} - \\frac{64258837}{15246680} a^{6} + \\frac{1186243521}{15246680} a^{5} - \\frac{1136307041}{30493360} a^{4} - \\frac{8844651467}{30493360} a^{3} + \\frac{4111787971}{30493360} a^{2} + \\frac{9386922247}{30493360} a + \\frac{548395483}{7623340} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/2*a^7 - 1/2*a^6', '1/6*a^8 - 1/6*a^7 + 1/3*a^5 - 1/3*a^4', '1/24*a^9 - 1/12*a^8 + 1/24*a^7 - 1/6*a^6 + 1/3*a^5 - 1/6*a^4 - 1/4*a^3 - 1/2*a^2 - 1/4*a', '1/182960160*a^10 - 2833111/182960160*a^9 + 13893323/182960160*a^8 + 5281277/60986720*a^7 - 9078017/45740040*a^6 + 17000761/45740040*a^5 + 7439119/91480080*a^4 - 9805169/30493360*a^3 + 7890337/30493360*a^2 - 5158011/30493360*a - 3467259/7623340']}
Number field data - 11.5.9678619238400000000.1