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nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [686, 0, 1176, 0, 469, 0, 148, 0, 52, 0, -4, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 113186888059191296, 'disc_rad': 14, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 3]]], [5, [[4, 2], [2, 2]]], [7, [0]], [11, [[4, 2], [2, 2]]], [13, [[4, 2], [2, 2]]], [17, [[6, 1], [3, 2]]], [19, [[4, 3]]], [23, [[6, 1], [3, 2]]], [29, [[4, 3]]], [31, [[2, 4], [1, 4]]], [37, [[4, 3]]], [41, [[2, 5], [1, 2]]], [43, [[4, 2], [2, 2]]], [47, [[2, 4], [1, 4]]], [53, [[4, 3]]], [59, [[4, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [486, 120], 'galois_label': '12T82', 'galt': 82, 'grd': 52.5078942662214, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 7, 'label': '12.0.113186888059191296.7', 'local_algs': ['2.1.4.11a1.13', '2.1.8.26c1.11', '7.3.2.3a1.2', '7.2.3.4a1.1'], 'maximal_cm_subfield': [14, 0, 8, 0, 1], 'minimal_sibling': [28, 0, 28, 0, -7, 0, -12, 0, -2, 0, 0, 0, 1], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 6, 'ramps': [2, 7], 'rd': 26.3724013609, 'regulator': {'__RealLiteral__': 0, 'data': '4794.43933513', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-2.0.1', '14.0.8.0.1', '2.-4.6.0.-1.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{5577}{2836120} a^{10} - \\frac{33557}{2836120} a^{8} + \\frac{349553}{2836120} a^{6} + \\frac{17151}{567224} a^{4} + \\frac{112687}{202580} a^{2} + \\frac{7667}{28940} \\)', '\\( \\frac{69}{14470} a^{10} - \\frac{663}{28940} a^{8} + \\frac{1888}{7235} a^{6} + \\frac{2807}{5788} a^{4} + \\frac{13083}{7235} a^{2} + \\frac{24237}{14470} \\)', '\\( \\frac{183}{567224} a^{10} - \\frac{3553}{567224} a^{8} + \\frac{16243}{567224} a^{6} - \\frac{86925}{567224} a^{4} - \\frac{5709}{5788} a^{2} - \\frac{6581}{5788} \\)', '\\( \\frac{1623}{1418060} a^{11} - \\frac{423}{709030} a^{10} - \\frac{25661}{2836120} a^{9} + \\frac{20397}{2836120} a^{8} + \\frac{26923}{354515} a^{7} - \\frac{62969}{1418060} a^{6} - \\frac{34887}{567224} a^{5} + \\frac{69579}{567224} a^{4} - \\frac{10891}{50645} a^{3} + \\frac{107629}{101290} a^{2} - \\frac{41559}{28940} a - \\frac{2797}{28940} \\)', '\\( \\frac{9353}{5672240} a^{11} - \\frac{293}{115760} a^{10} - \\frac{41003}{5672240} a^{9} - \\frac{637}{115760} a^{8} + \\frac{625817}{5672240} a^{7} - \\frac{10477}{115760} a^{6} + \\frac{83849}{1134448} a^{5} - \\frac{12681}{23152} a^{4} + \\frac{30003}{405160} a^{3} - \\frac{87641}{57880} a^{2} + \\frac{9633}{57880} a - \\frac{109497}{57880} \\)'], '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', '1/28*a^8 - 1/7*a^6 - 11/28*a^4 + 2/7*a^2 - 1/2', '1/56*a^9 - 1/56*a^8 + 5/28*a^7 - 5/28*a^6 + 3/56*a^5 - 3/56*a^4 - 5/14*a^3 + 5/14*a^2 + 1/4*a - 1/4', '1/2836120*a^10 + 17139/2836120*a^8 + 275509/2836120*a^6 + 182227/567224*a^4 - 24509/202580*a^2 - 969/28940', '1/5672240*a^11 - 1/5672240*a^10 + 17139/5672240*a^9 - 17139/5672240*a^8 + 275509/5672240*a^7 - 275509/5672240*a^6 + 182227/1134448*a^5 - 182227/1134448*a^4 + 178071/405160*a^3 - 178071/405160*a^2 + 27971/57880*a - 27971/57880']}
Number field data - 12.0.113186888059191296.7