-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -7, 23, -55, 104, -156, 201, -209, 190, -140, 89, -44, 18, -5, 1], 'conductor': 0, 'degree': 14, 'disc_abs': 489862582246303, 'disc_rad': 203, 'disc_sign': -1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [49, 84], 'galois_label': '14T8', 'galt': 8, 'grd': 47.427804193511, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '14.0.489862582246303.1', 'local_algs': ['7.7.2.7a1.2', '29.1.7.6a1.5', '29.7.1.0a1.1'], 'maximal_cm_subfield': [2, -1, 1], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 7, 'ramps': [7, 29], 'rd': 11.201882659887865, 'regulator': {'__RealLiteral__': 0, 'data': '30.78649932175806', 'prec': 57}, 'subfield_mults': [1], 'subfields': ['2.-1.1'], 'torsion_order': 2, 'unit_signature_rank': 0, 'used_grh': False} -
nf_fields_extra • Show schema
{'dirichlet_group': [], 'frobs': [[2, [[7, 2]]], [3, [[14, 1]]], [5, [[14, 1]]], [7, [0]], [11, [[7, 1], [1, 7]]], [13, [[14, 1]]], [17, [[2, 7]]], [19, [[14, 1]]], [23, [[7, 2]]], [29, [0]], [31, [[14, 1]]], [37, [[7, 2]]], [41, [[2, 7]]], [43, [[7, 2]]], [47, [[14, 1]]], [53, [[7, 2]]], [59, [[2, 7]]]], 'label': '14.0.489862582246303.1', 'res': {'sib': ['128,344,1380,-2330,-613,1277,1991,-2006,313,121,17,-47,23,-7,1', '1681,16318,45365,657,-24358,8744,755,-2759,1687,-843,337,-102,24,-4,1']}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{147}{11} a^{13} - \\frac{683}{11} a^{12} + \\frac{2413}{11} a^{11} - \\frac{5646}{11} a^{10} + \\frac{11185}{11} a^{9} - \\frac{16811}{11} a^{8} + \\frac{22303}{11} a^{7} - \\frac{23187}{11} a^{6} + \\frac{21728}{11} a^{5} - \\frac{15479}{11} a^{4} + \\frac{9971}{11} a^{3} - \\frac{4555}{11} a^{2} + \\frac{1751}{11} a - \\frac{376}{11} \\)', '\\( \\frac{249}{11} a^{13} - \\frac{1154}{11} a^{12} + \\frac{4066}{11} a^{11} - \\frac{9490}{11} a^{10} + \\frac{18757}{11} a^{9} - \\frac{28124}{11} a^{8} + \\frac{37240}{11} a^{7} - \\frac{38655}{11} a^{6} + \\frac{36176}{11} a^{5} - \\frac{25760}{11} a^{4} + \\frac{16583}{11} a^{3} - \\frac{7611}{11} a^{2} + \\frac{2935}{11} a - \\frac{647}{11} \\)', '\\( \\frac{153}{11} a^{13} - \\frac{701}{11} a^{12} + \\frac{2463}{11} a^{11} - \\frac{5711}{11} a^{10} + \\frac{11259}{11} a^{9} - \\frac{16777}{11} a^{8} + \\frac{22180}{11} a^{7} - \\frac{22883}{11} a^{6} + \\frac{21430}{11} a^{5} - \\frac{15163}{11} a^{4} + \\frac{9819}{11} a^{3} - \\frac{4474}{11} a^{2} + \\frac{1743}{11} a - \\frac{379}{11} \\)', '\\( \\frac{447}{11} a^{13} - \\frac{2045}{11} a^{12} + \\frac{7179}{11} a^{11} - \\frac{16629}{11} a^{10} + \\frac{32760}{11} a^{9} - \\frac{48771}{11} a^{8} + \\frac{64432}{11} a^{7} - \\frac{66408}{11} a^{6} + \\frac{62103}{11} a^{5} - \\frac{43855}{11} a^{4} + \\frac{28287}{11} a^{3} - \\frac{12880}{11} a^{2} + \\frac{4959}{11} a - \\frac{1087}{11} \\)', '\\( \\frac{138}{11} a^{13} - \\frac{634}{11} a^{12} + \\frac{2217}{11} a^{11} - \\frac{5125}{11} a^{10} + \\frac{10040}{11} a^{9} - \\frac{14871}{11} a^{8} + \\frac{19479}{11} a^{7} - \\frac{19925}{11} a^{6} + \\frac{18424}{11} a^{5} - \\frac{12884}{11} a^{4} + \\frac{8186}{11} a^{3} - \\frac{3703}{11} a^{2} + \\frac{1411}{11} a - \\frac{311}{11} \\)', '\\( \\frac{340}{11} a^{13} - \\frac{1559}{11} a^{12} + \\frac{5477}{11} a^{11} - \\frac{12707}{11} a^{10} + \\frac{25053}{11} a^{9} - \\frac{37358}{11} a^{8} + \\frac{49383}{11} a^{7} - \\frac{50977}{11} a^{6} + \\frac{47665}{11} a^{5} - \\frac{33709}{11} a^{4} + \\frac{21710}{11} a^{3} - \\frac{9897}{11} a^{2} + \\frac{3811}{11} a - \\frac{841}{11} \\)'], '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', '1/11*a^13 - 3/11*a^12 + 1/11*a^11 + 2/11*a^10 + 5/11*a^9 + 2/11*a^8 - 4/11*a^7 + 3/11*a^6 - 2/11*a^5 + 5/11*a^4 + 4/11*a^3 - 3/11*a^2 - 5/11*a + 5/11']}
Number field data - 14.0.489862582246303.1