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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [9, -12, 16, -12, 5, 2, 2, -2, 5, -6, 3, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 24904730935296, 'disc_rad': 114, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[6, 2]]], [7, [[2, 6]]], [11, [[6, 2]]], [13, [[6, 2]]], [17, [[6, 2]]], [19, [0]], [23, [[6, 2]]], [29, [[6, 2]]], [31, [[2, 6]]], [37, [[2, 6]]], [41, [[6, 1], [2, 3]]], [43, [[3, 4]]], [47, [[6, 2]]], [53, [[6, 2]]], [59, [[6, 1], [2, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_label': '12T18', 'galt': 18, 'index': 1, 'inessentialp': [], 'is_galois': False, 'iso_number': 2, 'label': '12.0.24904730935296.2', 'local_algs': ['2.12.18.15', '3.2.1.2', '3.2.1.2', '3.2.1.2', '3.6.3.2', '19.3.2.1', '19.3.0.1', '19.3.0.1', '19.3.2.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 6, 'ramps': [2, 3, 19], 'rd': 13.07244493634025, 'regulator': {'__RealLiteral__': 0, 'data': '300.56279584783476', 'prec': 60}, 'res': {'gal': ['64,0,-576,0,3440,0,-9792,0,16956,0,-11338,0,3913,0,-39700,0,84566,0,-60618,0,24623,0,-17454,0,17424,0,-11316,0,2367,0,532,0,-29,0,4,0,1'], 'sib': ['49,-686,2963,-4532,3595,1628,-6575,7990,-5876,3000,-1427,662,-165,-60,91,-52,19,-6,1', '49,35,270,-427,925,-1133,1505,-1446,1457,-1065,750,-356,168,-37,20,-2,7,0,1']}, 'subfield_mults': [1, 1, 1, 1, 1], 'subfields': ['1.-1.1', '-6.0.1', '2.0.1', '4.0.-2.0.1', '3.-4.0.2.1.-2.1'], 'torsion_gen': '\\( \\frac{302}{2073} a^{11} - \\frac{296}{691} a^{10} + \\frac{1256}{2073} a^{9} - \\frac{1753}{2073} a^{8} + \\frac{702}{691} a^{7} - \\frac{201}{691} a^{6} - \\frac{412}{691} a^{5} + \\frac{755}{2073} a^{4} + \\frac{2182}{2073} a^{3} - \\frac{4207}{2073} a^{2} + \\frac{6610}{2073} a - \\frac{876}{691} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{985}{6219} a^{11} - \\frac{2338}{6219} a^{10} + \\frac{2591}{6219} a^{9} - \\frac{5308}{6219} a^{8} + \\frac{4471}{6219} a^{7} + \\frac{1097}{6219} a^{6} - \\frac{677}{6219} a^{5} + \\frac{245}{2073} a^{4} + \\frac{5387}{6219} a^{3} - \\frac{17101}{6219} a^{2} + \\frac{4250}{2073} a - \\frac{719}{691} \\)', '\\( \\frac{1039}{6219} a^{11} - \\frac{3952}{6219} a^{10} + \\frac{6536}{6219} a^{9} - \\frac{8779}{6219} a^{8} + \\frac{10792}{6219} a^{7} - \\frac{6232}{6219} a^{6} - \\frac{3932}{6219} a^{5} + \\frac{1672}{2073} a^{4} + \\frac{10184}{6219} a^{3} - \\frac{24388}{6219} a^{2} + \\frac{3952}{691} a - \\frac{3192}{691} \\)', '\\( \\frac{425}{6219} a^{11} + \\frac{3958}{6219} a^{10} - \\frac{8300}{6219} a^{9} + \\frac{6349}{6219} a^{8} - \\frac{16549}{6219} a^{7} + \\frac{14374}{6219} a^{6} + \\frac{11504}{6219} a^{5} - \\frac{381}{691} a^{4} - \\frac{1748}{6219} a^{3} + \\frac{20770}{6219} a^{2} - \\frac{14638}{2073} a + \\frac{4632}{691} \\)', '\\( \\frac{124}{2073} a^{11} + \\frac{121}{691} a^{10} - \\frac{333}{691} a^{9} + \\frac{859}{2073} a^{8} - \\frac{2453}{2073} a^{7} + \\frac{2672}{2073} a^{6} + \\frac{664}{2073} a^{5} - \\frac{127}{691} a^{4} + \\frac{140}{691} a^{3} + \\frac{2231}{2073} a^{2} - \\frac{6722}{2073} a + \\frac{2235}{691} \\)', '\\( \\frac{574}{2073} a^{11} - \\frac{677}{691} a^{10} + \\frac{2854}{2073} a^{9} - \\frac{3881}{2073} a^{8} + \\frac{1769}{691} a^{7} - \\frac{350}{691} a^{6} - \\frac{989}{691} a^{5} + \\frac{1435}{2073} a^{4} + \\frac{2390}{2073} a^{3} - \\frac{10124}{2073} a^{2} + \\frac{15515}{2073} a - \\frac{2928}{691} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/3*a^9 - 1/3*a^7 + 1/3*a^6 - 1/3*a^5 + 1/3*a^4 - 1/3*a^3 - 1/3*a^2 + 1/3*a', '1/3*a^10 - 1/3*a^8 + 1/3*a^7 - 1/3*a^6 + 1/3*a^5 - 1/3*a^4 - 1/3*a^3 + 1/3*a^2', '1/6219*a^11 - 337/6219*a^10 + 956/6219*a^9 + 1049/6219*a^8 + 3073/6219*a^7 - 1249/6219*a^6 - 329/6219*a^5 + 116/2073*a^4 - 487/6219*a^3 - 2707/6219*a^2 + 320/2073*a - 33/691']}
Number field data - 12.0.24904730935296.2