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nf_fields • Show schema
{'class_group': [3, 3], 'class_number': 9, 'cm': False, 'coeffs': [361, -114, -249, 670, -180, -234, 177, -126, 90, -50, 21, -6, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 131621703842267136, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 6]]], [7, [[6, 2]]], [11, [[2, 6]]], [13, [[2, 6]]], [17, [[2, 6]]], [19, [[1, 12]]], [23, [[2, 6]]], [29, [[2, 6]]], [31, [[6, 2]]], [37, [[6, 2]]], [41, [[2, 6]]], [43, [[3, 4]]], [47, [[2, 6]]], [53, [[2, 6]]], [59, [[2, 6]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [22, 22], 'galois_label': '12T3', 'galt': 3, 'grd': 26.706109521254483, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': False, 'iso_number': 67, 'label': '12.0.131621703842267136.67', 'local_algs': ['2.2.6.22a1.1', '3.1.6.11a1.3', '3.1.6.11a1.3'], 'maximal_cm_subfield': [4, 0, -2, 0, 1], 'minimal_sibling': [18, 0, 0, 0, 0, 0, 1], 'monogenic': 0, 'narrow_class_group': [3, 3], 'narrow_class_number': 9, 'num_ram': 2, 'r2': 6, 'ramps': [2, 3], 'rd': 26.7061095213, 'regulator': {'__RealLiteral__': 0, 'data': '3703.01164497', 'prec': 44}, 'res': {'sib': ['-96,0,0,0,0,0,1', '18,0,0,0,0,0,1']}, 'subfield_mults': [1, 1, 1, 3, 1, 1, 3, 3], 'subfields': ['1.-1.1', '2.0.1', '-6.0.1', '-12.0.0.1', '4.0.-2.0.1', '12.0.0.0.0.0.1', '18.0.0.0.0.0.1', '-96.0.0.0.0.0.1'], 'torsion_gen': '\\( -\\frac{308}{64125} a^{11} + \\frac{1694}{64125} a^{10} - \\frac{6496}{64125} a^{9} + \\frac{5509}{21375} a^{8} - \\frac{11548}{21375} a^{7} + \\frac{18662}{21375} a^{6} - \\frac{30716}{21375} a^{5} + \\frac{2114}{1125} a^{4} - \\frac{14812}{21375} a^{3} - \\frac{34328}{64125} a^{2} + \\frac{140528}{64125} a - \\frac{1546}{3375} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{91}{64125} a^{11} - \\frac{313}{64125} a^{10} + \\frac{442}{64125} a^{9} + \\frac{182}{21375} a^{8} - \\frac{1304}{21375} a^{7} + \\frac{364}{2375} a^{6} - \\frac{1456}{7125} a^{5} + \\frac{552}{2375} a^{4} - \\frac{23101}{21375} a^{3} + \\frac{9256}{64125} a^{2} + \\frac{140219}{64125} a + \\frac{3292}{3375} \\)', '\\( \\frac{2296}{192375} a^{11} - \\frac{10003}{192375} a^{10} + \\frac{29902}{192375} a^{9} - \\frac{17783}{64125} a^{8} + \\frac{25676}{64125} a^{7} - \\frac{20594}{64125} a^{6} + \\frac{43792}{64125} a^{5} - \\frac{25942}{64125} a^{4} - \\frac{288731}{64125} a^{3} + \\frac{658036}{192375} a^{2} + \\frac{707189}{192375} a - \\frac{13748}{10125} \\)', '\\( \\frac{91}{192375} a^{11} - \\frac{1063}{192375} a^{10} + \\frac{4192}{192375} a^{9} - \\frac{3818}{64125} a^{8} + \\frac{7196}{64125} a^{7} - \\frac{10724}{64125} a^{6} + \\frac{13132}{64125} a^{5} - \\frac{17032}{64125} a^{4} - \\frac{7976}{64125} a^{3} + \\frac{424756}{192375} a^{2} - \\frac{22699}{10125} a + \\frac{20167}{10125} \\)', '\\( \\frac{1568}{192375} a^{11} - \\frac{5999}{192375} a^{10} + \\frac{18866}{192375} a^{9} - \\frac{11239}{64125} a^{8} + \\frac{19108}{64125} a^{7} - \\frac{18802}{64125} a^{6} + \\frac{43736}{64125} a^{5} - \\frac{21686}{64125} a^{4} - \\frac{176923}{64125} a^{3} + \\frac{137738}{192375} a^{2} - \\frac{41063}{192375} a - \\frac{19834}{10125} \\)', '\\( \\frac{3227}{192375} a^{11} - \\frac{13061}{192375} a^{10} + \\frac{41924}{192375} a^{9} - \\frac{1384}{3375} a^{8} + \\frac{45412}{64125} a^{7} - \\frac{48328}{64125} a^{6} + \\frac{100604}{64125} a^{5} - \\frac{60404}{64125} a^{4} - \\frac{319072}{64125} a^{3} + \\frac{315482}{192375} a^{2} - \\frac{128657}{192375} a - \\frac{33001}{10125} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/3*a^3 + 1/3', '1/3*a^4 + 1/3*a', '1/3*a^5 + 1/3*a^2', '1/9*a^6 - 1/9*a^3 - 2/9', '1/9*a^7 - 1/9*a^4 - 2/9*a', '1/27*a^8 - 1/27*a^7 + 1/27*a^6 + 2/27*a^5 - 2/27*a^4 + 2/27*a^3 - 8/27*a^2 + 8/27*a - 8/27', '1/27*a^9 - 1/9*a^3 - 2/27', '1/513*a^10 - 5/513*a^9 - 1/171*a^8 - 5/171*a^7 + 2/57*a^6 - 17/171*a^5 + 4/171*a^4 + 2/171*a^3 + 56/171*a^2 - 188/513*a - 8/27', '1/192375*a^11 + 182/192375*a^10 + 487/192375*a^9 - 1123/64125*a^8 + 781/64125*a^7 + 2036/64125*a^6 - 547/7125*a^5 + 1466/21375*a^4 + 71/7125*a^3 + 94441/192375*a^2 - 77716/192375*a + 1462/10125']}
Number field data - 12.0.131621703842267136.67