-
nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [41, -109, 221, -238, 258, -297, 305, -217, 116, -54, 19, -5, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 300342961072265625, 'disc_rad': 13485, 'disc_sign': 1, 'frobs': [[2, [[4, 2], [2, 2]]], [3, [0]], [5, [0]], [7, [[4, 3]]], [11, [[2, 5], [1, 2]]], [13, [[12, 1]]], [17, [[4, 2], [2, 2]]], [19, [[6, 1], [2, 2], [1, 2]]], [23, [[12, 1]]], [29, [0]], [31, [0]], [37, [[4, 2], [2, 2]]], [41, [[6, 1], [2, 2], [1, 2]]], [43, [[4, 2], [2, 2]]], [47, [[4, 2], [2, 2]]], [53, [[12, 1]]], [59, [[3, 2], [1, 6]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1800, 972, 648, 864], 'galois_label': '12T209', 'galt': 209, 'grd': 817.2144566356151, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '12.0.300342961072265625.2', 'local_algs': ['3.2.1.0a1.1', '3.2.2.2a1.1', '3.2.3.6a5.1', '5.3.4.9a1.1', '29.3.1.0a1.1', '29.3.1.0a1.1', '29.3.2.3a1.2', '31.3.1.0a1.1', '31.1.3.2a1.3', '31.6.1.0a1.1'], 'maximal_cm_subfield': [11, -1, 6, -1, 1], 'monogenic': -1, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 4, 'r2': 6, 'ramps': [3, 5, 29, 31], 'rd': 28.6067237118, 'regulator': {'__RealLiteral__': 0, 'data': '5193.55523784', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '11.-1.6.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{139234}{32046783} a^{11} - \\frac{319733}{32046783} a^{10} + \\frac{336677}{10682261} a^{9} - \\frac{984719}{32046783} a^{8} - \\frac{507381}{10682261} a^{7} + \\frac{7457585}{32046783} a^{6} - \\frac{27663640}{32046783} a^{5} + \\frac{49331143}{32046783} a^{4} - \\frac{54882805}{32046783} a^{3} + \\frac{10630860}{10682261} a^{2} - \\frac{12331583}{32046783} a + \\frac{21221683}{32046783} \\)', '\\( \\frac{1698331}{705029226} a^{11} - \\frac{13464349}{705029226} a^{10} + \\frac{22866574}{352514613} a^{9} - \\frac{22890255}{117504871} a^{8} + \\frac{48888429}{117504871} a^{7} - \\frac{478796797}{705029226} a^{6} + \\frac{569069563}{705029226} a^{5} - \\frac{137296409}{352514613} a^{4} - \\frac{256156990}{352514613} a^{3} + \\frac{442187054}{352514613} a^{2} - \\frac{369402985}{705029226} a + \\frac{16684747}{235009742} \\)', '\\( \\frac{6209416}{352514613} a^{11} - \\frac{59087377}{705029226} a^{10} + \\frac{34894429}{117504871} a^{9} - \\frac{282262781}{352514613} a^{8} + \\frac{186239489}{117504871} a^{7} - \\frac{997654705}{352514613} a^{6} + \\frac{2667883555}{705029226} a^{5} - \\frac{1096512029}{352514613} a^{4} + \\frac{904570259}{352514613} a^{3} - \\frac{300230696}{117504871} a^{2} + \\frac{702149500}{352514613} a - \\frac{481733785}{705029226} \\)', '\\( \\frac{10063479}{470019484} a^{11} - \\frac{112820809}{1410058452} a^{10} + \\frac{100325293}{352514613} a^{9} - \\frac{481378243}{705029226} a^{8} + \\frac{142874605}{117504871} a^{7} - \\frac{944336685}{470019484} a^{6} + \\frac{2563367971}{1410058452} a^{5} - \\frac{221060369}{705029226} a^{4} + \\frac{214686388}{352514613} a^{3} - \\frac{812972465}{705029226} a^{2} + \\frac{788574989}{1410058452} a + \\frac{1931842513}{1410058452} \\)', '\\( \\frac{170348267}{1410058452} a^{11} - \\frac{799069151}{1410058452} a^{10} + \\frac{704757439}{352514613} a^{9} - \\frac{1294936653}{235009742} a^{8} + \\frac{1274988646}{117504871} a^{7} - \\frac{27365043869}{1410058452} a^{6} + \\frac{34929651509}{1410058452} a^{5} - \\frac{12195422647}{705029226} a^{4} + \\frac{5770124054}{352514613} a^{3} - \\frac{13496085233}{705029226} a^{2} + \\frac{14893972843}{1410058452} a - \\frac{2255893043}{470019484} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/12*a^10 - 1/3*a^9 - 1/3*a^8 - 1/2*a^7 - 1/2*a^6 - 1/12*a^5 - 1/6*a^4 - 1/3*a^3 + 1/3*a^2 - 1/6*a - 1/12', '1/1410058452*a^11 - 22687589/1410058452*a^10 + 11369208/117504871*a^9 + 331148975/705029226*a^8 - 24527737/117504871*a^7 + 592477481/1410058452*a^6 - 558884365/1410058452*a^5 - 102998281/705029226*a^4 + 133260041/352514613*a^3 + 13097343/235009742*a^2 + 659987473/1410058452*a - 311278343/1410058452']}
Number field data - 12.0.300342961072265625.2