-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 23, 'dirichlet_group': [], 'disc_abs': 687394316682267077687567046704171943344271, 'disc_rad': 65714254895821712119634919243957, 'disc_sign': -1, 'frobs': [[2, [[13, 1], [8, 1], [2, 1]]], [3, [0]], [5, [[15, 1], [6, 1], [2, 1]]], [7, [0]], [11, [[20, 1], [1, 3]]], [13, [[8, 1], [5, 1], [4, 2], [1, 2]]], [17, [[9, 1], [8, 1], [5, 1], [1, 1]]], [19, [[15, 1], [6, 1], [2, 1]]], [23, [[22, 1], [1, 1]]], [29, [[19, 1], [2, 2]]], [31, [[20, 1], [3, 1]]], [37, [[10, 1], [6, 1], [4, 1], [3, 1]]], [41, [[12, 1], [9, 1], [1, 2]]], [43, [[17, 1], [3, 1], [1, 3]]], [47, [[10, 2], [2, 1], [1, 1]]], [53, [[14, 1], [7, 1], [2, 1]]], [59, [[12, 1], [4, 1], [2, 3], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [24728016011107368960000, 12926008369442488320000, 12926008369442488320000, 12926008369442488320000, 12926008369442488320000], 'galois_label': '23T7', 'galt': 7, 'grd': 1.3385852001185396e+16, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '23.1.687394316682267077687567046704171943344271.1', 'local_algs': ['3.23.22.1', '7.1.0.1', '7.2.1.2', '7.3.0.1', '7.17.0.1', 'm467399.1.1.0', 'm467399.1.2.0', 'm467399.2.1.1', 'm467399.1.5.0', 'm467399.1.13.0', 'm10931299891.1.1.0', 'm10931299891.1.1.0', 'm10931299891.1.2.0', 'm10931299891.2.1.1', 'm10931299891.1.7.0', 'm10931299891.1.10.0', 'm612464196024013.1.2.0', 'm612464196024013.2.1.1', 'm612464196024013.1.6.0', 'm612464196024013.1.13.0'], 'monogenic': 1, 'num_ram': 5, 'r2': 11, 'ramps': [3, 7, 467399, 10931299891, 612464196024013], 'rd': 65.9187485478, 'regulator': 993709440615, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 1 \\)', '\\( a^{6} + a^{5} - a^{3} - a^{2} + 1 \\)', '\\( a^{17} - a^{15} + a^{13} - a^{11} + a^{10} + a^{7} - a^{6} - 2 a^{5} + a^{4} + 3 a^{3} - 2 a^{2} - a + 1 \\)', '\\( a^{22} + a^{21} - a^{20} - 3 a^{19} - a^{18} + a^{17} + 2 a^{16} + 3 a^{15} - a^{14} - 3 a^{13} + a^{11} + 4 a^{10} + 4 a^{9} - 2 a^{8} - 3 a^{7} - a^{6} + a^{5} + 5 a^{4} + 4 a^{3} - 3 a^{2} - 5 a + 1 \\)', '\\( a^{22} - 2 a^{21} - 5 a^{20} - 6 a^{19} - 4 a^{18} + a^{17} + 5 a^{16} + 6 a^{15} + 3 a^{14} - a^{13} - 6 a^{12} - 8 a^{11} - 6 a^{10} + a^{9} + 7 a^{8} + 8 a^{7} + 5 a^{6} - 6 a^{4} - 11 a^{3} - 8 a^{2} + 11 \\)', '\\( a^{22} + 3 a^{21} + 2 a^{20} - 3 a^{19} - a^{18} - a^{17} - 4 a^{16} + a^{15} - 4 a^{13} + 3 a^{12} + 2 a^{11} + 8 a^{9} + a^{8} - 4 a^{7} + 3 a^{6} - 4 a^{5} - 5 a^{4} + 6 a^{3} - 6 a^{2} - 6 a + 10 \\)', '\\( 2 a^{22} + 2 a^{21} + 2 a^{20} - a^{19} - 3 a^{18} - a^{17} - a^{15} - a^{14} - 2 a^{13} - 5 a^{12} - 4 a^{11} + a^{10} + a^{9} - 2 a^{8} - a^{7} - 2 a^{6} - 4 a^{5} + 2 a^{4} + 7 a^{3} + a^{2} - 3 a + 7 \\)', '\\( 5 a^{22} - 6 a^{21} + 5 a^{20} + a^{19} - 4 a^{18} + 10 a^{17} - 7 a^{16} + 5 a^{15} + 6 a^{14} - 9 a^{13} + 14 a^{12} - 7 a^{11} + a^{10} + 11 a^{9} - 17 a^{8} + 17 a^{7} - 7 a^{6} - 9 a^{5} + 21 a^{4} - 26 a^{3} + 16 a^{2} - 8 \\)', '\\( a^{22} + 2 a^{21} + a^{19} - a^{18} + a^{17} - 2 a^{13} + 2 a^{12} + a^{11} + 6 a^{10} + 3 a^{9} + 3 a^{8} + 2 a^{7} - a^{6} + 3 a^{5} - 3 a^{4} + 2 a^{3} - 6 a^{2} - 4 a - 1 \\)', '\\( 11 a^{22} + 6 a^{21} + 4 a^{20} + 6 a^{19} + 10 a^{18} + 13 a^{17} + 8 a^{16} + 2 a^{15} - 2 a^{14} + 3 a^{13} + 11 a^{12} + 12 a^{11} + 6 a^{10} - 4 a^{9} - 4 a^{8} + 2 a^{7} + 11 a^{6} + 11 a^{5} + 4 a^{4} - 4 a^{3} - 8 a^{2} + a + 40 \\)', '\\( 7 a^{22} + 2 a^{21} + 10 a^{20} - 2 a^{19} + 10 a^{18} - a^{17} + 7 a^{16} + 4 a^{15} - 2 a^{14} + 10 a^{13} - 7 a^{12} + 15 a^{11} - 9 a^{10} + 8 a^{9} - a^{7} + 13 a^{6} - 17 a^{5} + 21 a^{4} - 18 a^{3} + 19 a^{2} - 8 a + 19 \\)'], 'used_grh': True, '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', 'a^14', 'a^15', 'a^16', 'a^17', 'a^18', 'a^19', 'a^20', 'a^21', 'a^22']}
Number field data - 23.1.687394316682267077687567046704171943344271.1