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nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [41, -52, 92, -60, 79, -52, 58, -36, 28, -16, 10, -4, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 34162868224000000, 'disc_rad': 190, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[6, 2]]], [5, [0]], [7, [[3, 4]]], [11, [[6, 2]]], [13, [[6, 2]]], [17, [[6, 2]]], [19, [0]], [23, [[3, 2], [1, 6]]], [29, [[6, 2]]], [31, [[2, 6]]], [37, [[6, 2]]], [41, [[3, 2], [1, 6]]], [43, [[6, 2]]], [47, [[3, 4]]], [53, [[6, 1], [2, 3]]], [59, [[6, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [72, 18, 24], 'galois_label': '12T18', 'galt': 18, 'grd': 63.686501757102, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.0.34162868224000000.1', 'local_algs': ['2.12.24.318', '5.12.6.1', '19.6.0.1', '19.6.4.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 6, 'ramps': [2, 5, 19], 'rd': 23.866909911259135, 'regulator': {'__RealLiteral__': 0, 'data': '597.4033513730107', 'prec': 57}, 'res': {'gal': ['1868689,0,8741436,0,20464211,0,32537756,0,39392549,0,36907184,0,27655133,0,16579120,0,8092153,0,3234840,0,1141289,0,352448,0,103616,0,24672,0,6314,0,684,0,149,0,20,0,1'], 'sib': ['-151,3312,18846,30650,15360,822,-2581,-2214,5689,830,-2655,852,381,-240,-16,46,-9,-2,1', '68921,-127756,97785,-58082,39442,-10038,-13003,2468,7265,-232,-1417,-978,431,90,42,-26,-2,-2,1']}, 'subfield_mults': [1, 1, 1, 1, 1], 'subfields': ['5.0.1', '-2.0.1', '10.0.1', '9.0.4.0.1', '1.-4.12.-14.7.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{550170}{3993007} a^{11} - \\frac{1691309}{3993007} a^{10} + \\frac{3342832}{3993007} a^{9} - \\frac{3723044}{3993007} a^{8} + \\frac{7776039}{3993007} a^{7} - \\frac{7597758}{3993007} a^{6} + \\frac{15840434}{3993007} a^{5} - \\frac{5517266}{3993007} a^{4} + \\frac{22665085}{3993007} a^{3} - \\frac{8788382}{3993007} a^{2} + \\frac{24340913}{3993007} a - \\frac{5387547}{3993007} \\)', '\\( \\frac{286945}{3993007} a^{11} - \\frac{691779}{3993007} a^{10} + \\frac{1016394}{3993007} a^{9} - \\frac{556852}{3993007} a^{8} + \\frac{2520738}{3993007} a^{7} - \\frac{953157}{3993007} a^{6} + \\frac{3739663}{3993007} a^{5} + \\frac{3024885}{3993007} a^{4} + \\frac{7788535}{3993007} a^{3} + \\frac{1989865}{3993007} a^{2} + \\frac{3340017}{3993007} a + \\frac{3115802}{3993007} \\)', '\\( \\frac{270776}{3993007} a^{11} - \\frac{1370049}{3993007} a^{10} + \\frac{3399539}{3993007} a^{9} - \\frac{5348810}{3993007} a^{8} + \\frac{8138580}{3993007} a^{7} - \\frac{12268674}{3993007} a^{6} + \\frac{16658165}{3993007} a^{5} - \\frac{17820015}{3993007} a^{4} + \\frac{18366419}{3993007} a^{3} - \\frac{24035095}{3993007} a^{2} + \\frac{18928520}{3993007} a - \\frac{13427362}{3993007} \\)', '\\( \\frac{217406}{3993007} a^{11} - \\frac{1064237}{3993007} a^{10} + \\frac{2354131}{3993007} a^{9} - \\frac{3233811}{3993007} a^{8} + \\frac{5307081}{3993007} a^{7} - \\frac{9102395}{3993007} a^{6} + \\frac{11512616}{3993007} a^{5} - \\frac{11901790}{3993007} a^{4} + \\frac{13351166}{3993007} a^{3} - \\frac{16826284}{3993007} a^{2} + \\frac{13744169}{3993007} a - \\frac{6628144}{3993007} \\)', '\\( \\frac{354281}{3993007} a^{11} - \\frac{1644284}{3993007} a^{10} + \\frac{3652603}{3993007} a^{9} - \\frac{5121782}{3993007} a^{8} + \\frac{8094408}{3993007} a^{7} - \\frac{12584463}{3993007} a^{6} + \\frac{15494222}{3993007} a^{5} - \\frac{14965110}{3993007} a^{4} + \\frac{16251183}{3993007} a^{3} - \\frac{24072616}{3993007} a^{2} + \\frac{13805347}{3993007} a - \\frac{17210937}{3993007} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/3993007*a^11 - 369155/3993007*a^10 + 594519/3993007*a^9 + 360356/3993007*a^8 + 1250477/3993007*a^7 + 732179/3993007*a^6 - 1959148/3993007*a^5 + 29442/3993007*a^4 + 421391/3993007*a^3 - 1335402/3993007*a^2 + 318595/3993007*a + 365281/3993007']}
Number field data - 12.0.34162868224000000.1