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nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [16, -96, 236, -300, 182, 16, -120, 100, -34, -8, 14, -6, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 323921668734976, 'disc_rad': 26, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[6, 2]]], [5, [[6, 2]]], [7, [[3, 4]]], [11, [[4, 2], [2, 2]]], [13, [0]], [17, [[3, 4]]], [19, [[2, 4], [1, 4]]], [23, [[4, 2], [2, 2]]], [29, [[4, 2], [2, 2]]], [31, [[2, 4], [1, 4]]], [37, [[6, 2]]], [41, [[4, 2], [2, 2]]], [43, [[6, 2]]], [47, [[3, 4]]], [53, [[4, 2], [2, 2]]], [59, [[4, 2], [2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [132, 24], 'galois_label': '12T23', 'galt': 23, 'grd': 24.255161140409015, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 15, 'label': '12.0.323921668734976.15', 'local_algs': ['2.1.2.2a1.2', '2.1.2.2a1.2', '2.1.8.22d1.22', '13.1.2.1a1.1', '13.1.2.1a1.1', '13.2.2.2a1.2', '13.2.2.2a1.2'], 'maximal_cm_subfield': [13, 0, 1], 'minimal_sibling': [-2, 0, -1, 0, 0, 0, 1], 'monogenic': -1, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 6, 'ramps': [2, 13], 'rd': 16.1883778798, 'regulator': {'__RealLiteral__': 0, 'data': '512.823336015', 'prec': 44}, 'res': {'sib': ['-2,0,-1,0,0,0,1', '4,10,14,8,2,-1,1', '-2,8,-4,0,-2,0,4,-4,1', '14,-48,82,-48,19,-4,4,-4,1']}, 'subfield_mults': [1, 1, 1, 1, 1], 'subfields': ['13.0.1', '-2.-1.0.1', '4.10.14.8.2.-1.1', '13.0.-1.0.3.0.1', '-1.0.5.0.-1.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{101}{32} a^{11} - \\frac{135}{8} a^{10} + \\frac{527}{16} a^{9} - \\frac{23}{8} a^{8} - \\frac{1761}{16} a^{7} + 242 a^{6} - \\frac{859}{4} a^{5} - 97 a^{4} + \\frac{8183}{16} a^{3} - \\frac{1201}{2} a^{2} + \\frac{2679}{8} a - \\frac{301}{4} \\)', '\\( \\frac{193}{32} a^{11} - \\frac{259}{8} a^{10} + \\frac{1027}{16} a^{9} - \\frac{67}{8} a^{8} - \\frac{3357}{16} a^{7} + 472 a^{6} - \\frac{1719}{4} a^{5} - 170 a^{4} + \\frac{15851}{16} a^{3} - \\frac{2385}{2} a^{2} + \\frac{5443}{8} a - \\frac{617}{4} \\)', '\\( a^{11} - 5 a^{10} + 9 a^{9} + a^{8} - 33 a^{7} + 67 a^{6} - 53 a^{5} - 37 a^{4} + 145 a^{3} - 155 a^{2} + 81 a - 15 \\)', '\\( \\frac{9}{8} a^{11} - \\frac{11}{2} a^{10} + \\frac{35}{4} a^{9} + \\frac{9}{2} a^{8} - \\frac{153}{4} a^{7} + 65 a^{6} - 37 a^{5} - 62 a^{4} + \\frac{603}{4} a^{3} - 122 a^{2} + \\frac{75}{2} a - 2 \\)', '\\( \\frac{815}{32} a^{11} - \\frac{1093}{8} a^{10} + \\frac{4317}{16} a^{9} - \\frac{261}{8} a^{8} - \\frac{14179}{16} a^{7} + 1984 a^{6} - \\frac{7189}{4} a^{5} - 732 a^{4} + \\frac{66709}{16} a^{3} - \\frac{9989}{2} a^{2} + \\frac{22741}{8} a - \\frac{2567}{4} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/2*a^8', '1/2*a^9', '1/4*a^10 - 1/2*a^6 - 1/2*a^2', '1/32*a^11 - 1/8*a^10 + 3/16*a^9 + 1/8*a^8 + 3/16*a^7 - 1/2*a^6 + 1/4*a^5 - 5/16*a^3 + 3/8*a - 1/4']}
Number field data - 12.0.323921668734976.15