-
nf_fields • Show schema
{'cm': False, 'coeffs': [-5, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 39, 'dirichlet_group': [], 'disc_abs': 40961876024838127401621530331262000449545568958365685141156708328663776670554879764461327, 'disc_rad': 40961876024838127401621530331262000449545568958365685141156708328663776670554879764461327, 'disc_sign': -1, 'frobs': [[2, [[12, 3], [2, 1], [1, 1]]], [3, [[27, 1], [10, 1], [2, 1]]], [5, [[18, 2], [2, 1], [1, 1]]], [7, [[19, 1], [13, 1], [5, 1], [1, 2]]], [11, [[12, 1], [9, 1], [8, 1], [7, 1], [3, 1]]], [13, [[25, 1], [10, 1], [3, 1], [1, 1]]], [17, [[9, 2], [8, 1], [6, 1], [4, 1], [3, 1]]], [19, [[22, 1], [14, 1], [2, 1], [1, 1]]], [23, [[24, 1], [6, 1], [5, 1], [4, 1]]], [29, [[37, 1], [2, 1]]], [31, [[35, 1], [3, 1], [1, 1]]], [37, [[18, 1], [11, 1], [7, 1], [3, 1]]], [41, [[19, 1], [10, 2]]], [43, [[21, 1], [14, 1], [2, 1], [1, 2]]], [47, [[38, 1], [1, 1]]], [53, [[30, 1], [6, 1], [2, 1], [1, 1]]], [59, [[21, 1], [7, 1], [6, 1], [4, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [10198941040598721679320140869951448678400000000, 10198941040598721679320140869951448678400000000, 10198941040598721679320140869951448678400000000, 10198941040598721679320140869951448678400000000, 10198941040598721679320140869951448678400000000, 10198941040598721679320140869951448678400000000, 10198941040598721679320140869951448678400000000, 10198941040598721679320140869951448678400000000], 'galois_label': '39T306', 'galt': 306, 'grd': 2.0239040497226673e+44, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '39.1.40961876024838127401621530331262000449545568958365685141156708328663776670554879764461327.1', 'local_algs': ['m229.2.1.1', 'm229.1.10.0', 'm229.1.11.0', 'm229.1.16.0', 'm1987.1.1.0', 'm1987.1.1.0', 'm1987.2.1.1', 'm1987.1.3.0', 'm1987.1.4.0', 'm1987.1.8.0', 'm1987.1.20.0', 'm142963.1.1.0', 'm142963.1.1.0', 'm142963.1.2.0', 'm142963.2.1.1', 'm142963.1.33.0', 'm1366812637.1.1.0', 'm1366812637.1.1.0', 'm1366812637.2.1.1', 'm1366812637.1.6.0', 'm1366812637.1.12.0', 'm1366812637.1.17.0', 'm810114948493.1.1.0', 'm810114948493.1.1.0', 'm810114948493.2.1.1', 'm810114948493.1.35.0', 'm156226602792479.1.2.0', 'm156226602792479.2.1.1', 'm156226602792479.1.3.0', 'm156226602792479.1.5.0', 'm156226602792479.1.7.0', 'm156226602792479.1.20.0', 'm2528280980108249089.2.1.1', 'm2528280980108249089.1.3.0', 'm2528280980108249089.1.3.0', 'm2528280980108249089.1.31.0', 'm1439749307724964790152813.1.1.0', 'm1439749307724964790152813.1.1.0', 'm1439749307724964790152813.1.2.0', 'm1439749307724964790152813.2.1.1', 'm1439749307724964790152813.1.8.0', 'm1439749307724964790152813.1.12.0', 'm1439749307724964790152813.1.13.0'], 'monogenic': 1, 'num_ram': 8, 'r2': 19, 'ramps': [229, 1987, 142963, 1366812637, 810114948493, 156226602792479, 2528280980108249089, 1439749307724964790152813], 'rd': 187.116593981, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, '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', 'a^23', 'a^24', 'a^25', 'a^26', 'a^27', 'a^28', 'a^29', 'a^30', 'a^31', 'a^32', 'a^33', 'a^34', 'a^35', 'a^36', 'a^37', 'a^38']}
Number field data - 39.1.40961876024838127401621530331262000449545568958365685141156708328663776670554879764461327.1