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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [8, 0, -88, 0, 212, 0, -204, 0, 88, 0, -16, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 37913186137014272, 'disc_rad': 14, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[6, 1], [3, 2]]], [5, [[12, 1]]], [7, [0]], [11, [[12, 1]]], [13, [[4, 3]]], [17, [[6, 2]]], [19, [[6, 1], [3, 2]]], [23, [[6, 2]]], [29, [[2, 3], [1, 6]]], [31, [[6, 2]]], [37, [[6, 1], [3, 2]]], [41, [[2, 6]]], [43, [[4, 3]]], [47, [[6, 2]]], [53, [[6, 1], [3, 2]]], [59, [[6, 1], [3, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [66, 20], 'galois_label': '12T14', 'galt': 14, 'grd': 34.04715710793443, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.12.37913186137014272.1', 'local_algs': ['2.12.27.11', '7.12.10.1'], 'monogenic': 0, 'num_ram': 2, 'r2': 0, 'ramps': [2, 7], 'rd': 24.0749756711, 'regulator': {'__RealLiteral__': 0, 'data': '18736.3891264', 'prec': 44}, 'res': {'gal': ['1,-20,-344,-1080,2040,12076,208,-46304,-18461,91500,39960,-109468,-36628,83520,15244,-40252,-1438,11688,-940,-1888,306,148,-32,-4,1'], 'sib': ['7,0,-126,0,273,0,-230,0,90,0,-16,0,1']}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-7.0.1', '1.-2.-1.1', '2.0.-6.0.1', '-7.0.14.0.-7.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{2} a^{10} - \\frac{29}{4} a^{8} + 33 a^{6} - 51 a^{4} + 24 a^{2} \\)', '\\( \\frac{3}{4} a^{10} - 11 a^{8} + \\frac{103}{2} a^{6} - \\frac{173}{2} a^{4} + 52 a^{2} - 7 \\)', '\\( \\frac{1}{4} a^{8} - \\frac{7}{2} a^{6} + \\frac{29}{2} a^{4} - 16 a^{2} + 2 \\)', '\\( \\frac{3}{2} a^{10} - \\frac{87}{4} a^{8} + \\frac{199}{2} a^{6} - \\frac{317}{2} a^{4} + 88 a^{2} - 11 \\)', '\\( 2 a^{10} - 29 a^{8} + \\frac{265}{2} a^{6} - \\frac{419}{2} a^{4} + 112 a^{2} - 12 \\)', '\\( \\frac{5}{4} a^{11} - \\frac{1}{2} a^{10} - 18 a^{9} + \\frac{29}{4} a^{8} + 81 a^{7} - 33 a^{6} - \\frac{245}{2} a^{5} + 51 a^{4} + 56 a^{3} - 24 a^{2} - a + 1 \\)', '\\( \\frac{3}{4} a^{11} - \\frac{3}{4} a^{10} - 11 a^{9} + 11 a^{8} + \\frac{103}{2} a^{7} - \\frac{103}{2} a^{6} - \\frac{173}{2} a^{5} + \\frac{173}{2} a^{4} + 52 a^{3} - 52 a^{2} - 6 a + 6 \\)', '\\( \\frac{1}{2} a^{11} + \\frac{3}{4} a^{10} - \\frac{29}{4} a^{9} - 11 a^{8} + 33 a^{7} + \\frac{103}{2} a^{6} - \\frac{101}{2} a^{5} - \\frac{173}{2} a^{4} + 20 a^{3} + 52 a^{2} + 4 a - 7 \\)', '\\( \\frac{5}{4} a^{11} + \\frac{5}{4} a^{10} - 18 a^{9} - \\frac{73}{4} a^{8} + 81 a^{7} + \\frac{169}{2} a^{6} - \\frac{245}{2} a^{5} - \\frac{275}{2} a^{4} + 56 a^{3} + 76 a^{2} - a - 8 \\)', '\\( \\frac{1}{2} a^{11} - \\frac{29}{4} a^{9} + \\frac{1}{4} a^{8} + 33 a^{7} - \\frac{7}{2} a^{6} - \\frac{101}{2} a^{5} + 15 a^{4} + 20 a^{3} - 20 a^{2} + 5 a + 6 \\)', '\\( \\frac{1}{2} a^{11} + \\frac{1}{2} a^{10} - \\frac{29}{4} a^{9} - \\frac{29}{4} a^{8} + 33 a^{7} + 33 a^{6} - \\frac{101}{2} a^{5} - 51 a^{4} + 20 a^{3} + 24 a^{2} + 4 a \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4', '1/2*a^5', '1/2*a^6', '1/2*a^7', '1/4*a^8', '1/4*a^9', '1/4*a^10', '1/4*a^11']}
Number field data - 12.12.37913186137014272.1