-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 2, 0, -1, 2, -1, -7, 2, 4, -4, -1, 0, 3, -1, -1, 1], 'conductor': 0, 'degree': 15, 'dirichlet_group': [], 'disc_abs': 12853809661090929, 'disc_rad': 12853809661090929, 'disc_sign': 1, 'frobs': [[2, [[15, 1]]], [3, [0]], [5, [[15, 1]]], [7, [[11, 1], [4, 1]]], [11, [[15, 1]]], [13, [[9, 1], [6, 1]]], [17, [[12, 1], [3, 1]]], [19, [[13, 1], [2, 1]]], [23, [[9, 1], [3, 2]]], [29, [[12, 1], [2, 1], [1, 1]]], [31, [[12, 1], [3, 1]]], [37, [[14, 1], [1, 1]]], [41, [[14, 1], [1, 1]]], [43, [[13, 1], [2, 1]]], [47, [[6, 1], [4, 2], [1, 1]]], [53, [[7, 1], [5, 1], [3, 1]]], [59, [[9, 1], [4, 1], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [653837184000, 653837184000], 'galois_label': '15T104', 'galt': 104, 'grd': 113374642.9369942, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '15.3.12853809661090929.1', 'local_algs': ['3.2.1.2', '3.3.0.1', '3.4.0.1', '3.6.0.1', 'm4284603220363643.1.1.0', 'm4284603220363643.2.1.1', 'm4284603220363643.1.12.0'], 'monogenic': 0, 'num_ram': 2, 'r2': 6, 'ramps': [3, 4284603220363643], 'rd': 11.855925391, 'regulator': {'__RealLiteral__': 0, 'data': '108.091851993', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{1453}{709} a^{14} - \\frac{2610}{709} a^{13} + \\frac{759}{709} a^{12} + \\frac{3719}{709} a^{11} - \\frac{3078}{709} a^{10} + \\frac{1361}{709} a^{9} - \\frac{6784}{709} a^{8} + \\frac{11254}{709} a^{7} - \\frac{6577}{709} a^{6} - \\frac{4968}{709} a^{5} + \\frac{2865}{709} a^{4} - \\frac{443}{709} a^{3} - \\frac{1880}{709} a^{2} + \\frac{667}{709} a + \\frac{1742}{709} \\)', '\\( \\frac{1514}{709} a^{14} - \\frac{2601}{709} a^{13} + \\frac{441}{709} a^{12} + \\frac{4002}{709} a^{11} - \\frac{2730}{709} a^{10} + \\frac{816}{709} a^{9} - \\frac{7142}{709} a^{8} + \\frac{11401}{709} a^{7} - \\frac{5217}{709} a^{6} - \\frac{5787}{709} a^{5} + \\frac{2085}{709} a^{4} + \\frac{446}{709} a^{3} - \\frac{700}{709} a^{2} + \\frac{452}{709} a + \\frac{1780}{709} \\)', '\\( \\frac{2077}{709} a^{14} - \\frac{3564}{709} a^{13} + \\frac{435}{709} a^{12} + \\frac{5626}{709} a^{11} - \\frac{3807}{709} a^{10} + \\frac{993}{709} a^{9} - \\frac{9958}{709} a^{8} + \\frac{14815}{709} a^{7} - \\frac{6101}{709} a^{6} - \\frac{8906}{709} a^{5} + \\frac{3301}{709} a^{4} + \\frac{329}{709} a^{3} - \\frac{758}{709} a^{2} + \\frac{2187}{709} a + \\frac{2677}{709} \\)', '\\( \\frac{291}{709} a^{14} - \\frac{329}{709} a^{13} - \\frac{192}{709} a^{12} + \\frac{920}{709} a^{11} - \\frac{432}{709} a^{10} - \\frac{8}{709} a^{9} - \\frac{778}{709} a^{8} + \\frac{771}{709} a^{7} + \\frac{72}{709} a^{6} - \\frac{1966}{709} a^{5} + \\frac{1335}{709} a^{4} - \\frac{199}{709} a^{3} - \\frac{1147}{709} a^{2} + \\frac{927}{709} a + \\frac{1053}{709} \\)', '\\( \\frac{2833}{709} a^{14} - \\frac{4638}{709} a^{13} + \\frac{97}{709} a^{12} + \\frac{8250}{709} a^{11} - \\frac{4922}{709} a^{10} + \\frac{329}{709} a^{9} - \\frac{12140}{709} a^{8} + \\frac{19252}{709} a^{7} - \\frac{6506}{709} a^{6} - \\frac{14686}{709} a^{5} + \\frac{5629}{709} a^{4} + \\frac{2246}{709} a^{3} - \\frac{3789}{709} a^{2} + \\frac{2556}{709} a + \\frac{4287}{709} \\)', '\\( \\frac{3490}{709} a^{14} - \\frac{5622}{709} a^{13} + \\frac{124}{709} a^{12} + \\frac{10159}{709} a^{11} - \\frac{6102}{709} a^{10} + \\frac{596}{709} a^{9} - \\frac{14357}{709} a^{8} + \\frac{23032}{709} a^{7} - \\frac{8200}{709} a^{6} - \\frac{18021}{709} a^{5} + \\frac{7247}{709} a^{4} + \\frac{2418}{709} a^{3} - \\frac{5655}{709} a^{2} + \\frac{2902}{709} a + \\frac{5568}{709} \\)', '\\( \\frac{2786}{709} a^{14} - \\frac{4982}{709} a^{13} + \\frac{435}{709} a^{12} + \\frac{8462}{709} a^{11} - \\frac{5934}{709} a^{10} + \\frac{284}{709} a^{9} - \\frac{12085}{709} a^{8} + \\frac{20487}{709} a^{7} - \\frac{7519}{709} a^{6} - \\frac{15287}{709} a^{5} + \\frac{7555}{709} a^{4} + \\frac{2456}{709} a^{3} - \\frac{2885}{709} a^{2} + \\frac{2896}{709} a + \\frac{4095}{709} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12', 'a^13', '1/709*a^14 + 128/709*a^13 + 204/709*a^12 + 86/709*a^11 - 250/709*a^10 - 346/709*a^9 + 29/709*a^8 + 200/709*a^7 + 278/709*a^6 - 304/709*a^5 - 222/709*a^4 - 276/709*a^3 - 155/709*a^2 - 143/709*a - 11/709']}
Number field data - 15.3.12853809661090929.1