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nf_fields • Show schema
{'class_group': [2, 2], 'class_number': 4, 'cm': False, 'coeffs': [547, -1095, 473, 147, -54, -3, -7, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 49991146569, 'disc_rad': 273, 'disc_sign': 1, 'frobs': [[2, [[4, 2]]], [3, [0]], [5, [[4, 2]]], [7, [0]], [11, [[4, 2]]], [13, [0]], [17, [[2, 4]]], [19, [[2, 2], [1, 4]]], [23, [[4, 2]]], [29, [[4, 2]]], [31, [[2, 4]]], [37, [[2, 2], [1, 4]]], [41, [[4, 2]]], [43, [[2, 4]]], [47, [[4, 2]]], [53, [[4, 2]]], [59, [[4, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [24, 16, 16], 'galois_label': '8T18', 'galt': 18, 'grd': 21.745111415357325, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 6, 'label': '8.0.49991146569.6', 'local_algs': ['3.4.3.1', '3.4.3.1', '7.2.1.2', '7.2.1.2', '7.4.2.1', '13.2.1.1', '13.2.1.1', '13.2.1.2', '13.2.1.2'], 'minimal_sibling': [1, 1, 5, 1, 4, -1, 5, -1, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 4, 'ramps': [3, 7, 13], 'rd': 21.7451114154, 'regulator': {'__RealLiteral__': 0, 'data': '189.845040565', 'prec': 44}, 'res': {'sib': ['1,-1,8,4,8,25,39,0,88,0,39,25,8,4,8,-1,1', '1,-3,3,-9,16,-9,24,-27,9,-24,21,0,7,-9,0,0,1', '144,-504,468,-54,1203,-1752,693,-249,-2,57,2,-3,48,-21,11,-3,1', '2401,3087,1911,3696,2902,-1479,-1188,1320,423,-534,6,129,-38,-6,9,-3,1', '256,0,576,-96,-416,936,276,-666,1143,-333,69,117,-26,-3,9,0,1', '784,-1176,-420,2982,-629,-2487,1104,1266,-501,-360,111,75,25,-3,-9,0,1', '81,0,27,0,-216,0,57,0,91,0,-19,0,-24,0,-1,0,1']}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['1.-1.1', '19.-1.-6.-1.1', '217.-10.30.-1.1', '39.-9.13.-1.1'], 'torsion_gen': '\\( -\\frac{8551}{625089} a^{7} - \\frac{8515}{625089} a^{6} + \\frac{16200}{208363} a^{5} + \\frac{24829}{208363} a^{4} + \\frac{172770}{208363} a^{3} - \\frac{243082}{208363} a^{2} - \\frac{4550033}{625089} a + \\frac{4867264}{625089} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{561373}{13126869} a^{7} + \\frac{616321}{13126869} a^{6} - \\frac{1110412}{4375623} a^{5} - \\frac{1761094}{4375623} a^{4} - \\frac{3917092}{1458541} a^{3} + \\frac{14100119}{4375623} a^{2} + \\frac{310888259}{13126869} a - \\frac{268139752}{13126869} \\)', '\\( \\frac{262465}{3750534} a^{7} + \\frac{127427}{1875267} a^{6} - \\frac{253934}{625089} a^{5} - \\frac{341321}{625089} a^{4} - \\frac{1792063}{416726} a^{3} + \\frac{3696133}{625089} a^{2} + \\frac{139214141}{3750534} a - \\frac{163133557}{3750534} \\)', '\\( \\frac{17915}{2917082} a^{7} + \\frac{29644}{1458541} a^{6} + \\frac{6133}{1458541} a^{5} - \\frac{146731}{1458541} a^{4} - \\frac{1813135}{2917082} a^{3} - \\frac{597988}{1458541} a^{2} + \\frac{5942859}{2917082} a - \\frac{2718665}{2917082} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/6*a^6 - 1/6*a^5 - 1/6*a^4 - 1/6*a^3 + 1/3*a^2 + 1/3*a + 1/6', '1/26253738*a^7 - 920308/13126869*a^6 + 98394/1458541*a^5 + 249815/1458541*a^4 + 3351259/8751246*a^3 - 412522/1458541*a^2 - 8263567/26253738*a - 5717893/26253738']}
Number field data - 8.0.49991146569.6