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nf_fields • Show schema
{'class_group': [3], 'class_number': 3, 'cm': False, 'coeffs': [-36, 0, 36, 0, 153, 0, 12, 0, 30, 0, 0, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 328683126924509184, 'disc_rad': 6, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[4, 2], [2, 2]]], [7, [[2, 5], [1, 2]]], [11, [[4, 3]]], [13, [[4, 2], [2, 2]]], [17, [[2, 4], [1, 4]]], [19, [[4, 3]]], [23, [[6, 1], [1, 6]]], [29, [[4, 2], [2, 2]]], [31, [[6, 1], [3, 2]]], [37, [[4, 2], [2, 2]]], [41, [[6, 2]]], [43, [[4, 3]]], [47, [[2, 5], [1, 2]]], [53, [[4, 2], [2, 2]]], [59, [[4, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [486, 200], 'galois_label': '12T82', 'galt': 82, 'grd': 47.713870191292706, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 13, 'label': '12.2.328683126924509184.13', 'local_algs': ['2.1.4.10a1.2', '2.1.8.26c1.10', '3.2.6.14a1.2'], 'minimal_sibling': [-128, 0, 0, 0, -111, 0, -44, 0, 18, 0, 12, 0, 1], 'monogenic': 0, 'narrow_class_group': [6], 'narrow_class_number': 6, 'num_ram': 2, 'r2': 5, 'ramps': [2, 3], 'rd': 28.8224869242, 'regulator': {'__RealLiteral__': 0, 'data': '14842.120621', 'prec': 40}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-2.0.1', '-9.0.-6.0.1', '-4.12.-9.-4.6.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{60} a^{10} - \\frac{1}{60} a^{8} + \\frac{31}{60} a^{6} - \\frac{3}{20} a^{4} + \\frac{27}{10} a^{2} - \\frac{3}{5} \\)', '\\( \\frac{9}{560} a^{11} + \\frac{17}{1680} a^{10} + \\frac{13}{1680} a^{9} + \\frac{1}{560} a^{8} + \\frac{767}{1680} a^{7} + \\frac{199}{560} a^{6} + \\frac{219}{560} a^{5} + \\frac{29}{560} a^{4} + \\frac{23}{10} a^{3} + \\frac{23}{10} a^{2} + \\frac{109}{140} a + \\frac{79}{140} \\)', '\\( \\frac{1}{60} a^{11} + \\frac{1}{210} a^{10} - \\frac{1}{60} a^{9} + \\frac{11}{840} a^{8} + \\frac{31}{60} a^{7} + \\frac{9}{140} a^{6} - \\frac{3}{20} a^{5} + \\frac{83}{280} a^{4} + \\frac{27}{10} a^{3} - \\frac{4}{5} a^{2} + \\frac{7}{5} a - \\frac{107}{70} \\)', '\\( \\frac{1}{120} a^{11} - \\frac{41}{1680} a^{10} - \\frac{1}{120} a^{9} + \\frac{1}{1680} a^{8} + \\frac{31}{120} a^{7} - \\frac{1061}{1680} a^{6} - \\frac{3}{40} a^{5} - \\frac{177}{560} a^{4} + \\frac{27}{20} a^{3} - \\frac{7}{5} a^{2} + \\frac{6}{5} a - \\frac{67}{140} \\)', '\\( \\frac{1}{120} a^{11} + \\frac{41}{1680} a^{10} - \\frac{1}{120} a^{9} - \\frac{1}{1680} a^{8} + \\frac{31}{120} a^{7} + \\frac{1061}{1680} a^{6} - \\frac{3}{40} a^{5} + \\frac{177}{560} a^{4} + \\frac{27}{20} a^{3} + \\frac{7}{5} a^{2} + \\frac{6}{5} a + \\frac{67}{140} \\)', '\\( \\frac{1}{280} a^{10} - \\frac{3}{140} a^{8} + \\frac{31}{280} a^{6} + \\frac{9}{70} a^{4} + \\frac{2}{5} a^{2} + \\frac{8}{35} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/6*a^6 - 1/2*a^2', '1/12*a^7 + 1/4*a^3 - 1/2*a', '1/24*a^8 - 1/12*a^6 + 1/8*a^4 - 1/2', '1/24*a^9 + 1/8*a^5 + 1/4*a^3', '1/1680*a^10 + 29/1680*a^8 - 13/560*a^6 - 1/2*a^5 + 47/560*a^4 - 1/2*a^3 - 1/10*a^2 + 17/140', '1/1680*a^11 + 29/1680*a^9 - 13/560*a^7 + 47/560*a^5 - 1/2*a^4 - 1/10*a^3 - 1/2*a^2 + 17/140*a']}
Number field data - 12.2.328683126924509184.13