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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-2, 0, 0, 0, 5, 0, -4, 0, 20, 0, -4, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 329990927286272, 'disc_rad': 14, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [[4, 2], [2, 2]]], [5, [[4, 3]]], [7, [0]], [11, [[4, 2], [2, 2]]], [13, [[4, 3]]], [17, [[6, 2]]], [19, [[4, 2], [2, 2]]], [23, [[6, 1], [3, 2]]], [29, [[4, 3]]], [31, [[2, 5], [1, 2]]], [37, [[4, 3]]], [41, [[2, 6]]], [43, [[4, 2], [2, 2]]], [47, [[2, 5], [1, 2]]], [53, [[4, 3]]], [59, [[4, 2], [2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [486, 96], 'galois_label': '12T82', 'galt': 82, 'grd': 37.964259098544694, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 3, 'label': '12.2.329990927286272.3', 'local_algs': ['2.1.4.11a1.14', '2.1.8.26c1.3', '7.1.3.2a1.2', '7.1.3.2a1.2', '7.6.1.0a1.1'], 'minimal_sibling': [-4, 0, -20, 0, 9, 0, -4, 0, 2, 0, 0, 0, 1], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 5, 'ramps': [2, 7], 'rd': 16.2134399216, 'regulator': {'__RealLiteral__': 0, 'data': '962.205672057', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-2.0.1', '-2.0.0.0.1', '2.-4.6.0.-1.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{19}{88} a^{10} - \\frac{71}{88} a^{8} + \\frac{359}{88} a^{6} + \\frac{37}{88} a^{4} + \\frac{35}{44} a^{2} + \\frac{37}{44} \\)', '\\( \\frac{9}{44} a^{10} - \\frac{10}{11} a^{8} + \\frac{199}{44} a^{6} - \\frac{61}{22} a^{4} + \\frac{49}{22} a^{2} + \\frac{16}{11} \\)', '\\( \\frac{5}{176} a^{11} - \\frac{5}{176} a^{10} + \\frac{1}{176} a^{9} - \\frac{1}{176} a^{8} + \\frac{25}{176} a^{7} - \\frac{25}{176} a^{6} + \\frac{349}{176} a^{5} - \\frac{349}{176} a^{4} + \\frac{81}{88} a^{3} - \\frac{81}{88} a^{2} - \\frac{47}{88} a + \\frac{47}{88} \\)', '\\( \\frac{5}{176} a^{11} + \\frac{5}{176} a^{10} + \\frac{1}{176} a^{9} + \\frac{1}{176} a^{8} + \\frac{25}{176} a^{7} + \\frac{25}{176} a^{6} + \\frac{349}{176} a^{5} + \\frac{349}{176} a^{4} + \\frac{81}{88} a^{3} + \\frac{81}{88} a^{2} - \\frac{47}{88} a - \\frac{47}{88} \\)', '\\( \\frac{7}{88} a^{11} - \\frac{47}{88} a^{9} + \\frac{211}{88} a^{7} - \\frac{387}{88} a^{5} - \\frac{1}{44} a^{3} - \\frac{35}{44} a - 1 \\)', '\\( \\frac{51}{176} a^{11} + \\frac{49}{176} a^{10} - \\frac{179}{176} a^{9} - \\frac{197}{176} a^{8} + \\frac{915}{176} a^{7} + \\frac{993}{176} a^{6} + \\frac{317}{176} a^{5} - \\frac{245}{176} a^{4} + \\frac{43}{88} a^{3} + \\frac{169}{88} a^{2} + \\frac{97}{88} a + \\frac{63}{88} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6 - 1/2*a^4', '1/2*a^7 - 1/2*a^5', '1/4*a^8 + 1/4*a^4 - 1/2', '1/8*a^9 - 1/8*a^8 - 1/4*a^7 - 1/4*a^6 + 3/8*a^5 + 1/8*a^4 - 1/2*a^3 - 1/2*a^2 - 1/4*a + 1/4', '1/88*a^10 + 9/88*a^8 + 5/88*a^6 - 27/88*a^4 - 19/44*a^2 + 17/44', '1/176*a^11 - 1/176*a^10 + 9/176*a^9 - 9/176*a^8 + 5/176*a^7 - 5/176*a^6 - 27/176*a^5 + 27/176*a^4 - 19/88*a^3 + 19/88*a^2 + 17/88*a - 17/88']}
Number field data - 12.2.329990927286272.3