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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -2, 6, -7, 12, -7, 10, -7, 12, -7, 6, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 2071265703125, 'disc_rad': 25745, 'disc_sign': 1, 'frobs': [[2, [[8, 1], [2, 2]]], [3, [[12, 1]]], [5, [0]], [7, [[12, 1]]], [11, [[4, 2], [2, 2]]], [13, [[12, 1]]], [17, [[12, 1]]], [19, [0]], [23, [[4, 3]]], [29, [[6, 1], [2, 1], [1, 4]]], [31, [[3, 2], [2, 2], [1, 2]]], [37, [[8, 1], [2, 2]]], [41, [[4, 1], [3, 2], [2, 1]]], [43, [[4, 3]]], [47, [[4, 3]]], [53, [[8, 1], [2, 2]]], [59, [[4, 2], [1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1728, 1152, 1152], 'galois_label': '12T237', 'galt': 237, 'grd': 239.93242815578742, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.0.2071265703125.1', 'local_algs': ['5.1.4.3a1.4', '5.4.2.4a1.2', '19.2.1.0a1.1', '19.2.2.2a1.2', '19.6.1.0a1.1', 'm271.1.1.0', 'm271.1.1.0', 'm271.2.1.1', 'm271.2.1.1', 'm271.1.3.0', 'm271.1.3.0'], 'monogenic': -1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 6, 'ramps': [5, 19, 271], 'rd': 10.6255882954, 'regulator': {'__RealLiteral__': 0, 'data': '17.5482156786', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '-4.4.-3.3.0.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{11} - 2 a^{10} + 6 a^{9} - 7 a^{8} + 12 a^{7} - 7 a^{6} + 10 a^{5} - 7 a^{4} + 12 a^{3} - 7 a^{2} + 6 a - 2 \\)', '\\( \\frac{7}{8} a^{11} - \\frac{15}{8} a^{10} + \\frac{43}{8} a^{9} - \\frac{27}{4} a^{8} + \\frac{43}{4} a^{7} - \\frac{59}{8} a^{6} + \\frac{67}{8} a^{5} - \\frac{31}{4} a^{4} + \\frac{39}{4} a^{3} - \\frac{67}{8} a^{2} + \\frac{31}{8} a - \\frac{23}{8} \\)', '\\( \\frac{15}{8} a^{11} - \\frac{23}{8} a^{10} + \\frac{75}{8} a^{9} - \\frac{31}{4} a^{8} + \\frac{63}{4} a^{7} - \\frac{19}{8} a^{6} + \\frac{91}{8} a^{5} - \\frac{19}{4} a^{4} + \\frac{59}{4} a^{3} - \\frac{27}{8} a^{2} + \\frac{31}{8} a + \\frac{1}{8} \\)', '\\( \\frac{3}{2} a^{11} - \\frac{19}{8} a^{10} + \\frac{31}{4} a^{9} - \\frac{57}{8} a^{8} + \\frac{111}{8} a^{7} - \\frac{37}{8} a^{6} + 11 a^{5} - \\frac{55}{8} a^{4} + \\frac{97}{8} a^{3} - \\frac{43}{8} a^{2} + \\frac{17}{4} a - \\frac{13}{8} \\)', '\\( \\frac{1}{8} a^{11} + a^{10} - \\frac{13}{8} a^{9} + \\frac{49}{8} a^{8} - \\frac{47}{8} a^{7} + \\frac{47}{4} a^{6} - \\frac{31}{8} a^{5} + \\frac{63}{8} a^{4} - \\frac{33}{8} a^{3} + \\frac{23}{2} a^{2} - \\frac{37}{8} a + \\frac{13}{4} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/2*a^9 - 1/2*a^8 - 1/2*a^6 - 1/2*a^3 - 1/2*a - 1/2', '1/8*a^10 - 1/4*a^9 + 3/8*a^8 - 1/8*a^7 + 3/8*a^6 - 1/2*a^5 + 1/8*a^4 - 3/8*a^3 + 1/8*a^2 + 1/4*a + 3/8', '1/16*a^11 - 1/16*a^10 + 1/16*a^9 + 1/8*a^8 + 1/8*a^7 - 1/16*a^6 - 3/16*a^5 + 3/8*a^4 - 1/8*a^3 + 3/16*a^2 + 5/16*a - 5/16']}
Number field data - 12.0.2071265703125.1