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nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [1, 0, -8, 0, 46, 0, 42, 0, 17, 0, -10, 0, 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, [[6, 2]]], [11, [[6, 2]]], [13, [[3, 4]]], [17, [[6, 2]]], [19, [0]], [23, [[6, 1], [2, 3]]], [29, [[6, 2]]], [31, [[2, 6]]], [37, [[3, 4]]], [41, [[3, 2], [1, 6]]], [43, [[6, 2]]], [47, [[6, 2]]], [53, [[3, 2], [1, 6]]], [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': 2, 'label': '12.0.34162868224000000.2', 'local_algs': ['2.12.24.315', '5.6.3.2', '5.6.3.2', '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': '1054.7017720420233', 'prec': 60}, 'res': {'gal': ['218089,1085308,2700488,-9596360,12761339,-9654832,5065608,200,-4658499,4316376,-3545120,2261008,1328637,-1295204,2171648,-4922012,5410721,-2748660,2298240,-2657008,2172297,-1015780,554144,-474272,348152,-162272,66528,-38164,24626,-11792,4392,-1620,693,-264,72,-12,1'], 'sib': ['-1000,0,700,0,-10750,0,-1639,0,2952,0,693,0,-770,0,194,0,-22,0,1', '1,0,35,0,581,0,1449,0,549,0,-395,0,-44,0,50,0,-11,0,1']}, 'subfield_mults': [1, 1, 1, 1, 1], 'subfields': ['1.0.1', '10.0.1', '-10.0.1', '25.0.0.0.1', '1.-4.12.-14.7.-2.1'], 'torsion_gen': '\\( \\frac{50}{131} a^{11} - \\frac{495}{131} a^{9} + \\frac{1601}{262} a^{7} + \\frac{4347}{262} a^{5} + \\frac{2537}{131} a^{3} - \\frac{83}{262} a \\)', 'torsion_order': 4, 'units': ['\\( \\frac{5}{131} a^{10} - \\frac{99}{262} a^{8} + \\frac{147}{262} a^{6} + \\frac{237}{131} a^{4} + \\frac{717}{262} a^{2} - \\frac{50}{131} \\)', '\\( \\frac{21}{262} a^{10} - \\frac{221}{262} a^{8} + \\frac{479}{262} a^{6} + \\frac{275}{131} a^{4} + \\frac{445}{131} a^{2} - \\frac{79}{262} \\)', '\\( \\frac{831}{524} a^{11} - \\frac{68}{131} a^{10} - \\frac{2060}{131} a^{9} + \\frac{2719}{524} a^{8} + \\frac{6717}{262} a^{7} - \\frac{4601}{524} a^{6} + \\frac{18031}{262} a^{5} - \\frac{5739}{262} a^{4} + \\frac{41151}{524} a^{3} - \\frac{12769}{524} a^{2} - \\frac{3463}{524} a + \\frac{967}{262} \\)', '\\( \\frac{32}{131} a^{11} - \\frac{45}{262} a^{10} - \\frac{1241}{524} a^{9} + \\frac{891}{524} a^{8} + \\frac{1803}{524} a^{7} - \\frac{727}{262} a^{6} + \\frac{2955}{262} a^{5} - \\frac{3873}{524} a^{4} + \\frac{7527}{524} a^{3} - \\frac{4095}{524} a^{2} + \\frac{539}{262} a + \\frac{507}{524} \\)', '\\( \\frac{20}{131} a^{11} - \\frac{73}{524} a^{10} - \\frac{198}{131} a^{9} + \\frac{381}{262} a^{8} + \\frac{1307}{524} a^{7} - \\frac{396}{131} a^{6} + \\frac{3137}{524} a^{5} - \\frac{1193}{262} a^{4} + \\frac{1303}{131} a^{3} - \\frac{1815}{524} a^{2} - \\frac{145}{524} a + \\frac{337}{524} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6 - 1/2*a^4 - 1/2', '1/2*a^7 - 1/2*a^5 - 1/2*a', '1/2*a^8 - 1/2*a^4 - 1/2*a^2 - 1/2', '1/4*a^9 - 1/4*a^8 - 1/4*a^7 + 1/4*a^4 + 1/4*a^3 - 1/4*a^2 - 1/4', '1/524*a^10 + 27/131*a^8 - 1/4*a^7 + 27/262*a^6 + 1/4*a^5 + 63/262*a^4 - 151/524*a^2 - 1/4*a - 141/524', '1/524*a^11 - 23/524*a^9 - 77/524*a^7 - 1/4*a^6 - 34/131*a^5 + 1/4*a^4 + 121/262*a^3 + 121/524*a - 1/4']}
Number field data - 12.0.34162868224000000.2