-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-5202, 0, -3150, 0, 1860, 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, [[4, 2], [1, 2]]], [11, [[4, 2], [2, 1]]], [13, [[8, 1], [1, 2]]], [17, [[8, 1], [2, 1]]], [19, [[4, 1], [2, 2], [1, 2]]], [23, [[8, 1], [2, 1]]], [29, [[10, 1]]], [31, [[5, 2]]], [37, [[4, 2], [2, 1]]], [41, [[4, 1], [2, 3]]], [43, [[8, 1], [1, 2]]], [47, [[4, 2], [1, 2]]], [53, [[8, 1], [1, 2]]], [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': 16, 'label': '10.6.2332800000000000000.16', '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': '1584413.70604', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['-56.80.0.-20.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{877}{394707} a^{8} - \\frac{2298}{131569} a^{6} - \\frac{159949}{394707} a^{4} + \\frac{419539}{131569} a^{2} + \\frac{410603}{131569} \\)', '\\( \\frac{1484}{394707} a^{8} - \\frac{288}{131569} a^{6} - \\frac{216197}{394707} a^{4} + \\frac{187240}{131569} a^{2} + \\frac{254481}{131569} \\)', '\\( \\frac{73}{394707} a^{8} + \\frac{1759}{131569} a^{6} - \\frac{262}{394707} a^{4} - \\frac{226266}{131569} a^{2} - \\frac{165951}{131569} \\)', '\\( \\frac{25876}{6710019} a^{9} + \\frac{2972}{394707} a^{8} - \\frac{41549}{2236673} a^{7} - \\frac{19462}{394707} a^{6} - \\frac{4634704}{6710019} a^{5} - \\frac{533338}{394707} a^{4} + \\frac{8457737}{2236673} a^{3} + \\frac{1203763}{131569} a^{2} + \\frac{22921856}{2236673} a + \\frac{1828175}{131569} \\)', '\\( \\frac{1013}{131569} a^{8} + \\frac{12416}{394707} a^{6} - \\frac{382184}{394707} a^{4} - \\frac{69074}{131569} a^{2} + \\frac{12327}{131569} \\)', '\\( \\frac{544436}{6710019} a^{9} + \\frac{31358}{131569} a^{8} + \\frac{271006}{6710019} a^{7} + \\frac{42740}{131569} a^{6} - \\frac{25666266}{2236673} a^{5} - \\frac{4304730}{131569} a^{4} + \\frac{71013576}{2236673} a^{3} + \\frac{8979290}{131569} a^{2} + \\frac{98882890}{2236673} a + \\frac{13321459}{131569} \\)', '\\( \\frac{252082}{6710019} a^{9} - \\frac{602}{394707} a^{8} + \\frac{73108}{6710019} a^{7} + \\frac{12529}{131569} a^{6} - \\frac{37019522}{6710019} a^{5} + \\frac{456344}{394707} a^{4} + \\frac{29659931}{2236673} a^{3} - \\frac{671740}{131569} a^{2} + \\frac{37890406}{2236673} a - \\frac{990703}{131569} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/3*a^6 - 1/3*a^4', '1/3*a^7 - 1/3*a^5', '1/394707*a^8 + 61351/394707*a^6 + 106333/394707*a^4 - 22925/131569*a^2 + 33773/131569', '1/6710019*a^9 - 286544/2236673*a^7 - 156805/6710019*a^5 - 22925/2236673*a^3 - 492503/2236673*a']} -
nf_fields_extra • Show schema
{'dirichlet_group': [], 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[4, 2], [1, 2]]], [11, [[4, 2], [2, 1]]], [13, [[8, 1], [1, 2]]], [17, [[8, 1], [2, 1]]], [19, [[4, 1], [2, 2], [1, 2]]], [23, [[8, 1], [2, 1]]], [29, [[10, 1]]], [31, [[5, 2]]], [37, [[4, 2], [2, 1]]], [41, [[4, 1], [2, 3]]], [43, [[8, 1], [1, 2]]], [47, [[4, 2], [1, 2]]], [53, [[8, 1], [1, 2]]], [59, [[10, 1]]]], 'label': '10.6.2332800000000000000.16', 'res': {}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{877}{394707} a^{8} - \\frac{2298}{131569} a^{6} - \\frac{159949}{394707} a^{4} + \\frac{419539}{131569} a^{2} + \\frac{410603}{131569} \\)', '\\( \\frac{1484}{394707} a^{8} - \\frac{288}{131569} a^{6} - \\frac{216197}{394707} a^{4} + \\frac{187240}{131569} a^{2} + \\frac{254481}{131569} \\)', '\\( \\frac{73}{394707} a^{8} + \\frac{1759}{131569} a^{6} - \\frac{262}{394707} a^{4} - \\frac{226266}{131569} a^{2} - \\frac{165951}{131569} \\)', '\\( \\frac{25876}{6710019} a^{9} + \\frac{2972}{394707} a^{8} - \\frac{41549}{2236673} a^{7} - \\frac{19462}{394707} a^{6} - \\frac{4634704}{6710019} a^{5} - \\frac{533338}{394707} a^{4} + \\frac{8457737}{2236673} a^{3} + \\frac{1203763}{131569} a^{2} + \\frac{22921856}{2236673} a + \\frac{1828175}{131569} \\)', '\\( \\frac{1013}{131569} a^{8} + \\frac{12416}{394707} a^{6} - \\frac{382184}{394707} a^{4} - \\frac{69074}{131569} a^{2} + \\frac{12327}{131569} \\)', '\\( \\frac{544436}{6710019} a^{9} + \\frac{31358}{131569} a^{8} + \\frac{271006}{6710019} a^{7} + \\frac{42740}{131569} a^{6} - \\frac{25666266}{2236673} a^{5} - \\frac{4304730}{131569} a^{4} + \\frac{71013576}{2236673} a^{3} + \\frac{8979290}{131569} a^{2} + \\frac{98882890}{2236673} a + \\frac{13321459}{131569} \\)', '\\( \\frac{252082}{6710019} a^{9} - \\frac{602}{394707} a^{8} + \\frac{73108}{6710019} a^{7} + \\frac{12529}{131569} a^{6} - \\frac{37019522}{6710019} a^{5} + \\frac{456344}{394707} a^{4} + \\frac{29659931}{2236673} a^{3} - \\frac{671740}{131569} a^{2} + \\frac{37890406}{2236673} a - \\frac{990703}{131569} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/3*a^6 - 1/3*a^4', '1/3*a^7 - 1/3*a^5', '1/394707*a^8 + 61351/394707*a^6 + 106333/394707*a^4 - 22925/131569*a^2 + 33773/131569', '1/6710019*a^9 - 286544/2236673*a^7 - 156805/6710019*a^5 - 22925/2236673*a^3 - 492503/2236673*a']}
Number field data - 10.6.2332800000000000000.16