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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-196, 344, -681, 757, -808, 650, -451, 159, 3, -55, 24, 0, -3, 1], 'conductor': 0, 'degree': 13, 'dirichlet_group': [], 'disc_abs': 9332639163597796201, 'disc_rad': 1451, 'disc_sign': 1, 'frobs': [[2, [[2, 6], [1, 1]]], [3, [[13, 1]]], [5, [[13, 1]]], [7, [[2, 6], [1, 1]]], [11, [[13, 1]]], [13, [[2, 6], [1, 1]]], [17, [[2, 6], [1, 1]]], [19, [[2, 6], [1, 1]]], [23, [[2, 6], [1, 1]]], [29, [[13, 1]]], [31, [[2, 6], [1, 1]]], [37, [[2, 6], [1, 1]]], [41, [[13, 1]]], [43, [[13, 1]]], [47, [[13, 1]]], [53, [[2, 6], [1, 1]]], [59, [[2, 6], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [13], 'galois_label': '13T2', 'galt': 2, 'grd': 38.09199390948182, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '13.1.9332639163597796201.1', 'local_algs': ['m1451.1.1.0', 'm1451.2.1.1', 'm1451.2.1.1', 'm1451.2.1.1', 'm1451.2.1.1', 'm1451.2.1.1', 'm1451.2.1.1'], 'monogenic': -1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 1, 'r2': 6, 'ramps': [1451], 'rd': 28.7893005382, 'regulator': {'__RealLiteral__': 0, 'data': '120307.36238', 'prec': 40}, 'res': {'gal': ['92864,0,1565952,0,-547104,0,-594479,0,-1300018,0,1018807,0,196700,0,131053,0,15818,0,6141,0,564,0,143,0,6,0,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{487}{3664384} a^{12} - \\frac{3}{6736} a^{11} + \\frac{177}{53888} a^{10} - \\frac{2925}{458048} a^{9} - \\frac{4277}{215552} a^{8} + \\frac{195933}{1832192} a^{7} - \\frac{509393}{3664384} a^{6} - \\frac{144357}{458048} a^{5} + \\frac{2032473}{1832192} a^{4} - \\frac{2477983}{1832192} a^{3} + \\frac{4219733}{3664384} a^{2} - \\frac{455931}{916096} a + \\frac{146833}{916096} \\)', '\\( \\frac{12475}{12825344} a^{12} - \\frac{8555}{188608} a^{11} + \\frac{2787}{94304} a^{10} + \\frac{580175}{3206336} a^{9} - \\frac{82427}{107776} a^{8} + \\frac{2080685}{6412672} a^{7} + \\frac{29109667}{12825344} a^{6} - \\frac{8749757}{3206336} a^{5} + \\frac{60057687}{6412672} a^{4} - \\frac{22467325}{6412672} a^{3} + \\frac{164473509}{12825344} a^{2} - \\frac{9299191}{3206336} a + \\frac{2765111}{458048} \\)', '\\( \\frac{1785559}{25650688} a^{12} - \\frac{88443}{754432} a^{11} - \\frac{170209}{754432} a^{10} + \\frac{18984845}{12825344} a^{9} - \\frac{354981}{215552} a^{8} - \\frac{44061113}{12825344} a^{7} + \\frac{206386447}{25650688} a^{6} - \\frac{220920255}{12825344} a^{5} + \\frac{94639879}{6412672} a^{4} - \\frac{62129867}{3206336} a^{3} + \\frac{396595559}{25650688} a^{2} - \\frac{52893695}{6412672} a + \\frac{3507101}{916096} \\)', '\\( \\frac{148557}{12825344} a^{12} - \\frac{92041}{754432} a^{11} + \\frac{57459}{754432} a^{10} + \\frac{8074771}{12825344} a^{9} - \\frac{59831}{26944} a^{8} + \\frac{2552911}{3206336} a^{7} + \\frac{88598045}{12825344} a^{6} - \\frac{146277617}{12825344} a^{5} + \\frac{306756117}{12825344} a^{4} - \\frac{177332345}{12825344} a^{3} + \\frac{174739333}{6412672} a^{2} - \\frac{31107815}{3206336} a + \\frac{2290131}{229024} \\)', '\\( \\frac{21153}{25650688} a^{12} + \\frac{1149}{377216} a^{11} - \\frac{51}{5894} a^{10} - \\frac{29261}{6412672} a^{9} + \\frac{12359}{215552} a^{8} - \\frac{1280305}{12825344} a^{7} - \\frac{2942183}{25650688} a^{6} + \\frac{2160167}{6412672} a^{5} - \\frac{7045455}{12825344} a^{4} + \\frac{675709}{12825344} a^{3} - \\frac{24918121}{25650688} a^{2} + \\frac{2840123}{6412672} a - \\frac{568355}{916096} \\)', '\\( \\frac{23089}{3664384} a^{12} - \\frac{397}{53888} a^{11} + \\frac{543}{26944} a^{10} + \\frac{111521}{916096} a^{9} - \\frac{41191}{215552} a^{8} + \\frac{870039}{1832192} a^{7} + \\frac{3038761}{3664384} a^{6} - \\frac{2254547}{916096} a^{5} + \\frac{9350525}{1832192} a^{4} - \\frac{9312543}{1832192} a^{3} + \\frac{20179743}{3664384} a^{2} - \\frac{3558725}{916096} a + \\frac{3377779}{916096} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2*a', '1/2*a^5 - 1/2*a^2', '1/2*a^6 - 1/2*a^3', '1/4*a^7 - 1/2*a^3 - 1/4*a - 1/2', '1/8*a^8 - 1/8*a^7 - 1/4*a^5 - 1/4*a^3 - 3/8*a^2 + 1/8*a - 1/4', '1/16*a^9 - 1/16*a^8 + 1/8*a^6 + 1/8*a^4 + 1/16*a^3 + 1/16*a^2 + 1/8*a - 1/2', '1/32*a^10 + 1/32*a^8 + 1/16*a^6 - 1/16*a^5 + 3/32*a^4 - 1/16*a^3 - 3/32*a^2 - 1/8*a + 1/8', '1/256*a^11 + 1/256*a^10 - 3/256*a^9 + 5/256*a^8 - 7/128*a^7 + 5/32*a^6 + 33/256*a^5 + 41/256*a^4 + 71/256*a^3 + 85/256*a^2 - 5/32*a - 7/64', '1/25650688*a^12 + 803/754432*a^11 + 6129/754432*a^10 + 268459/12825344*a^9 - 8627/215552*a^8 - 1239919/12825344*a^7 - 171991/25650688*a^6 + 2938519/12825344*a^5 - 1499083/6412672*a^4 + 1440147/3206336*a^3 - 10558271/25650688*a^2 - 2328857/6412672*a - 26053/916096']}
Number field data - 13.1.9332639163597796201.1