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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-441, 0, 54, 0, 441, 0, -132, 0, 51, 0, -6, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 328683126924509184, 'disc_rad': 6, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[4, 2], [2, 2]]], [7, [[4, 1], [2, 4]]], [11, [[8, 1], [2, 2]]], [13, [[8, 1], [4, 1]]], [17, [[4, 1], [2, 3], [1, 2]]], [19, [[8, 1], [2, 2]]], [23, [[3, 2], [2, 1], [1, 4]]], [29, [[4, 2], [2, 2]]], [31, [[6, 1], [3, 2]]], [37, [[8, 1], [4, 1]]], [41, [[6, 2]]], [43, [[8, 1], [2, 2]]], [47, [[4, 1], [2, 2], [1, 4]]], [53, [[8, 1], [4, 1]]], [59, [[4, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [9864, 3200], 'galois_label': '12T241', 'galt': 241, 'grd': 89.42379121066101, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.2.328683126924509184.1', 'local_algs': ['2.2.2.6a1.5', '2.1.8.30a1.72', '3.2.6.14a1.2'], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 5, 'ramps': [2, 3], 'rd': 28.8224869242, 'regulator': {'__RealLiteral__': 0, 'data': '20420.2934177', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-2.0.1', '-4.12.-9.-4.6.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{456} a^{10} - \\frac{1}{456} a^{8} + \\frac{23}{228} a^{6} - \\frac{9}{76} a^{4} + \\frac{11}{8} a^{2} - \\frac{153}{152} \\)', '\\( \\frac{6437}{874608} a^{11} - \\frac{29}{41648} a^{10} - \\frac{15471}{291536} a^{9} - \\frac{65}{124944} a^{8} + \\frac{181339}{437304} a^{7} - \\frac{1241}{62472} a^{6} - \\frac{197089}{145768} a^{5} + \\frac{2075}{20824} a^{4} + \\frac{9153}{2192} a^{3} - \\frac{1341}{2192} a^{2} - \\frac{1110261}{291536} a + \\frac{66359}{41648} \\)', '\\( \\frac{2059}{874608} a^{11} - \\frac{21}{41648} a^{10} - \\frac{1801}{291536} a^{9} + \\frac{671}{124944} a^{8} + \\frac{22429}{437304} a^{7} - \\frac{4489}{62472} a^{6} - \\frac{519}{145768} a^{5} + \\frac{5811}{20824} a^{4} + \\frac{463}{2192} a^{3} - \\frac{1349}{2192} a^{2} + \\frac{102365}{291536} a - \\frac{35961}{41648} \\)', '\\( \\frac{93}{72884} a^{11} + \\frac{433}{62472} a^{10} - \\frac{464}{54663} a^{9} - \\frac{1069}{20824} a^{8} + \\frac{429}{36442} a^{7} + \\frac{2737}{10412} a^{6} - \\frac{3013}{18221} a^{5} - \\frac{8951}{10412} a^{4} - \\frac{209}{548} a^{3} + \\frac{1043}{1096} a^{2} - \\frac{22751}{18221} a + \\frac{37681}{20824} \\)', '\\( \\frac{163}{291536} a^{11} - \\frac{623}{124944} a^{10} - \\frac{13637}{874608} a^{9} + \\frac{851}{124944} a^{8} + \\frac{45751}{437304} a^{7} - \\frac{5057}{62472} a^{6} - \\frac{64441}{145768} a^{5} - \\frac{1537}{20824} a^{4} + \\frac{1973}{2192} a^{3} - \\frac{1893}{2192} a^{2} - \\frac{129917}{291536} a + \\frac{36571}{41648} \\)', '\\( \\frac{1}{16} a^{11} - \\frac{1}{16} a^{10} - \\frac{5}{16} a^{9} + \\frac{5}{16} a^{8} + \\frac{23}{8} a^{7} - \\frac{23}{8} a^{6} - \\frac{43}{8} a^{5} + \\frac{43}{8} a^{4} + \\frac{355}{16} a^{3} - \\frac{355}{16} a^{2} + \\frac{409}{16} a - \\frac{425}{16} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/3*a^6', '1/3*a^7', '1/6*a^8 - 1/2', '1/12*a^9 - 1/12*a^8 - 1/2*a^5 - 1/2*a^4 + 1/4*a - 1/4', '1/62472*a^10 - 279/20824*a^8 + 1401/10412*a^6 + 1891/10412*a^4 + 91/1096*a^2 + 75/20824', '1/874608*a^11 - 1/124944*a^10 - 10691/291536*a^9 - 9575/124944*a^8 - 9011/145768*a^7 + 6209/62472*a^6 + 43539/145768*a^5 - 1891/20824*a^4 + 13/2192*a^3 - 91/2192*a^2 - 51985/291536*a + 10337/41648']}
Number field data - 12.2.328683126924509184.1