-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-450, 0, 2250, 0, 300, 0, -150, 0, -10, 0, 1], 'conductor': 0, 'degree': 10, 'dirichlet_group': [], 'disc_abs': 2332800000000000000, 'disc_rad': 30, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[8, 1], [2, 1]]], [11, [[4, 1], [2, 2], [1, 2]]], [13, [[4, 2], [2, 1]]], [17, [[4, 2], [1, 2]]], [19, [[4, 2], [2, 1]]], [23, [[4, 2], [1, 2]]], [29, [[10, 1]]], [31, [[5, 2]]], [37, [[4, 2], [2, 1]]], [41, [[2, 4], [1, 2]]], [43, [[4, 2], [2, 1]]], [47, [[8, 1], [2, 1]]], [53, [[4, 2], [2, 1]]], [59, [[10, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1816, 480, 992], 'galois_label': '10T29', 'galt': 29, 'grd': 197.43177973614576, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 12, 'label': '10.6.2332800000000000000.12', 'local_algs': ['2.1.10.19a1.61', '3.1.1.0a1.1', '3.1.1.0a1.1', '3.2.4.6a1.1', '5.2.5.14a1.1'], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 3, 'r2': 2, 'ramps': [2, 3, 5], 'rd': 68.6732736483, 'regulator': {'__RealLiteral__': 0, 'data': '1319522.14875', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-56.80.0.-20.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{21}{51995} a^{8} - \\frac{142}{155985} a^{6} - \\frac{2143}{31197} a^{4} - \\frac{1027}{10399} a^{2} - \\frac{651}{10399} \\)', '\\( \\frac{100}{31197} a^{8} - \\frac{1256}{51995} a^{6} - \\frac{17173}{31197} a^{4} - \\frac{888}{10399} a^{2} + \\frac{53761}{10399} \\)', '\\( \\frac{233}{155985} a^{8} - \\frac{2671}{155985} a^{6} - \\frac{6110}{31197} a^{4} + \\frac{9902}{10399} a^{2} + \\frac{46121}{10399} \\)', '\\( \\frac{3916}{155985} a^{8} - \\frac{8764}{31197} a^{6} - \\frac{96397}{31197} a^{4} + \\frac{84390}{10399} a^{2} - \\frac{16201}{10399} \\)', '\\( \\frac{1117}{10399} a^{9} - \\frac{490}{10399} a^{8} - \\frac{164534}{155985} a^{7} + \\frac{72028}{155985} a^{6} - \\frac{2546128}{155985} a^{5} + \\frac{222286}{31197} a^{4} + \\frac{304259}{10399} a^{3} - \\frac{136692}{10399} a^{2} + \\frac{2582600}{10399} a - \\frac{1140733}{10399} \\)', '\\( \\frac{5862}{51995} a^{9} - \\frac{196}{51995} a^{8} - \\frac{52828}{51995} a^{7} - \\frac{22939}{155985} a^{6} - \\frac{915794}{51995} a^{5} + \\frac{47732}{31197} a^{4} + \\frac{154535}{10399} a^{3} + \\frac{328488}{10399} a^{2} + \\frac{2230846}{10399} a + \\frac{931587}{10399} \\)', '\\( \\frac{917}{155985} a^{9} - \\frac{4307}{155985} a^{8} + \\frac{10643}{155985} a^{7} - \\frac{2445}{10399} a^{6} - \\frac{1151}{31197} a^{5} + \\frac{12970}{31197} a^{4} - \\frac{16104}{10399} a^{3} + \\frac{39179}{10399} a^{2} + \\frac{7856}{10399} a - \\frac{4023}{10399} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/5*a^5', '1/15*a^6 + 1/3*a^4', '1/15*a^7 - 1/15*a^5', '1/155985*a^8 + 658/155985*a^6 - 7792/31197*a^4 - 1832/10399*a^2 + 3456/10399', '1/155985*a^9 + 658/155985*a^7 - 7763/155985*a^5 - 1832/10399*a^3 + 3456/10399*a']} -
nf_fields_extra • Show schema
{'dirichlet_group': [], 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[8, 1], [2, 1]]], [11, [[4, 1], [2, 2], [1, 2]]], [13, [[4, 2], [2, 1]]], [17, [[4, 2], [1, 2]]], [19, [[4, 2], [2, 1]]], [23, [[4, 2], [1, 2]]], [29, [[10, 1]]], [31, [[5, 2]]], [37, [[4, 2], [2, 1]]], [41, [[2, 4], [1, 2]]], [43, [[4, 2], [2, 1]]], [47, [[8, 1], [2, 1]]], [53, [[4, 2], [2, 1]]], [59, [[10, 1]]]], 'label': '10.6.2332800000000000000.12', 'res': {}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{21}{51995} a^{8} - \\frac{142}{155985} a^{6} - \\frac{2143}{31197} a^{4} - \\frac{1027}{10399} a^{2} - \\frac{651}{10399} \\)', '\\( \\frac{100}{31197} a^{8} - \\frac{1256}{51995} a^{6} - \\frac{17173}{31197} a^{4} - \\frac{888}{10399} a^{2} + \\frac{53761}{10399} \\)', '\\( \\frac{233}{155985} a^{8} - \\frac{2671}{155985} a^{6} - \\frac{6110}{31197} a^{4} + \\frac{9902}{10399} a^{2} + \\frac{46121}{10399} \\)', '\\( \\frac{3916}{155985} a^{8} - \\frac{8764}{31197} a^{6} - \\frac{96397}{31197} a^{4} + \\frac{84390}{10399} a^{2} - \\frac{16201}{10399} \\)', '\\( \\frac{1117}{10399} a^{9} - \\frac{490}{10399} a^{8} - \\frac{164534}{155985} a^{7} + \\frac{72028}{155985} a^{6} - \\frac{2546128}{155985} a^{5} + \\frac{222286}{31197} a^{4} + \\frac{304259}{10399} a^{3} - \\frac{136692}{10399} a^{2} + \\frac{2582600}{10399} a - \\frac{1140733}{10399} \\)', '\\( \\frac{5862}{51995} a^{9} - \\frac{196}{51995} a^{8} - \\frac{52828}{51995} a^{7} - \\frac{22939}{155985} a^{6} - \\frac{915794}{51995} a^{5} + \\frac{47732}{31197} a^{4} + \\frac{154535}{10399} a^{3} + \\frac{328488}{10399} a^{2} + \\frac{2230846}{10399} a + \\frac{931587}{10399} \\)', '\\( \\frac{917}{155985} a^{9} - \\frac{4307}{155985} a^{8} + \\frac{10643}{155985} a^{7} - \\frac{2445}{10399} a^{6} - \\frac{1151}{31197} a^{5} + \\frac{12970}{31197} a^{4} - \\frac{16104}{10399} a^{3} + \\frac{39179}{10399} a^{2} + \\frac{7856}{10399} a - \\frac{4023}{10399} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/5*a^5', '1/15*a^6 + 1/3*a^4', '1/15*a^7 - 1/15*a^5', '1/155985*a^8 + 658/155985*a^6 - 7792/31197*a^4 - 1832/10399*a^2 + 3456/10399', '1/155985*a^9 + 658/155985*a^7 - 7763/155985*a^5 - 1832/10399*a^3 + 3456/10399*a']}
Number field data - 10.6.2332800000000000000.12