-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [20, -120, 20, -60, 65, -12, 40, 0, 10, 0, 1], 'conductor': 0, 'degree': 10, 'dirichlet_group': [], 'disc_abs': 1640250000000000, 'disc_rad': 30, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[7, 1], [3, 1]]], [11, [[7, 1], [3, 1]]], [13, [[3, 3], [1, 1]]], [17, [[7, 1], [3, 1]]], [19, [[6, 1], [4, 1]]], [23, [[9, 1], [1, 1]]], [29, [[7, 1], [1, 3]]], [31, [[9, 1], [1, 1]]], [37, [[9, 1], [1, 1]]], [41, [[9, 1], [1, 1]]], [43, [[7, 1], [3, 1]]], [47, [[8, 1], [2, 1]]], [53, [[9, 1], [1, 1]]], [59, [[6, 1], [4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [4082400, 1451520, 2957472], 'galois_label': '10T44', 'galt': 44, 'grd': 157.8830840055145, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 8, 'label': '10.2.1640250000000000.8', 'local_algs': ['2.2.0.1', '2.2.3.2', '2.2.3.4', '2.4.4.4', '3.5.4.1', '3.5.4.1', '5.5.5.4', '5.5.7.3'], 'monogenic': -1, 'num_ram': 3, 'r2': 4, 'ramps': [2, 3, 5], 'rd': 33.2269902974, 'regulator': {'__RealLiteral__': 0, 'data': '57946.6700139', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{77}{996} a^{9} + \\frac{95}{498} a^{8} + \\frac{337}{498} a^{7} + \\frac{187}{166} a^{6} + \\frac{291}{166} a^{5} + \\frac{259}{166} a^{4} - \\frac{713}{996} a^{3} - \\frac{691}{249} a^{2} - \\frac{1255}{498} a + \\frac{39}{83} \\)', '\\( \\frac{26}{249} a^{9} - \\frac{167}{996} a^{8} + \\frac{95}{249} a^{7} - \\frac{99}{83} a^{6} + \\frac{51}{83} a^{5} - \\frac{308}{83} a^{4} + \\frac{406}{249} a^{3} - \\frac{1531}{996} a^{2} + \\frac{1387}{249} a - \\frac{273}{166} \\)', '\\( \\frac{295}{996} a^{9} + \\frac{157}{498} a^{8} + \\frac{1013}{498} a^{7} + \\frac{171}{166} a^{6} + \\frac{757}{166} a^{5} - \\frac{215}{166} a^{4} - \\frac{1063}{996} a^{3} - \\frac{2117}{249} a^{2} - \\frac{449}{498} a + \\frac{33}{83} \\)', '\\( \\frac{6}{83} a^{9} - \\frac{61}{498} a^{8} + \\frac{355}{498} a^{7} - \\frac{175}{498} a^{6} + \\frac{741}{166} a^{5} + \\frac{129}{166} a^{4} + \\frac{2339}{166} a^{3} + \\frac{1403}{249} a^{2} + \\frac{4459}{249} a - \\frac{823}{249} \\)', '\\( \\frac{77}{498} a^{9} + \\frac{431}{332} a^{8} - \\frac{135}{166} a^{7} + \\frac{5687}{498} a^{6} - \\frac{995}{166} a^{5} + \\frac{3921}{166} a^{4} - \\frac{3469}{249} a^{3} + \\frac{5157}{332} a^{2} - \\frac{3766}{83} a + \\frac{1879}{498} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/2*a^7 - 1/2*a^6 - 1/2*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2*a^2', '1/12*a^8 + 1/6*a^7 - 1/6*a^6 - 1/2*a^5 - 1/2*a^4 - 1/2*a^3 - 1/12*a^2 + 1/3*a + 1/6', '1/1992*a^9 - 1/498*a^8 - 35/498*a^7 - 32/83*a^6 + 19/83*a^5 + 13/166*a^4 - 559/1992*a^3 + 23/249*a^2 + 223/996*a - 24/83']}
Number field data - 10.2.1640250000000000.8