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nf_fields • Show schema
{'cm': False, 'coeffs': [-5, -5, 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, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 47, 'dirichlet_group': [], 'disc_abs': 58809609539096281933776108952608119538900395786445119029601887271096760564217760247629485093057155609130859375, 'disc_rad': 2069179184422487361951858898842293758555224471177117584023284627285928121752435, 'disc_sign': -1, 'frobs': [[2, [[42, 1], [3, 1], [2, 1]]], [3, [[42, 1], [3, 1], [2, 1]]], [5, [0]], [7, [[21, 1], [19, 1], [5, 1], [2, 1]]], [11, [[21, 1], [13, 1], [10, 1], [2, 1], [1, 1]]], [13, [[35, 1], [12, 1]]], [17, [[29, 1], [11, 1], [5, 1], [2, 1]]], [19, [[25, 1], [16, 1], [3, 1], [1, 3]]], [23, [[45, 1], [2, 1]]], [29, [[24, 1], [18, 1], [3, 1], [2, 1]]], [31, [[31, 1], [15, 1], [1, 1]]], [37, [[27, 1], [20, 1]]], [41, [[42, 1], [2, 1], [1, 3]]], [43, [[46, 1], [1, 1]]], [47, [[46, 1], [1, 1]]], [53, [[21, 1], [16, 1], [4, 2], [1, 2]]], [59, [[38, 1], [3, 1], [2, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [253120619351356091693114049724811725076235980636160000000000, 129311620755584090321482177576805989984598816194560000000000, 129311620755584090321482177576805989984598816194560000000000], 'galois_label': '47T6', 'galt': 6, 'grd': 3.1082242924364957e+39, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '47.1.58809609539096281933776108952608119538900395786445119029601887271096760564217760247629485093057155609130859375.1', 'local_algs': ['m5.47.1.46', '101.1.0.1', '101.1.0.1', '101.1.0.1', '101.1.0.1', '101.2.1.2', 'm101.1.41.0', 'm4097384523608885865251205740281769818921236576588351651531256687694907171787.1.1.0', 'm4097384523608885865251205740281769818921236576588351651531256687694907171787.2.1.1', 'm4097384523608885865251205740281769818921236576588351651531256687694907171787.1.4.0', 'm4097384523608885865251205740281769818921236576588351651531256687694907171787.1.9.0', 'm4097384523608885865251205740281769818921236576588351651531256687694907171787.1.31.0'], 'monogenic': 0, 'num_ram': 3, 'r2': 23, 'ramps': [5, 101, 4097384523608885865251205740281769818921236576588351651531256687694907171787], 'rd': 216.531047325, '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', 'a^39', 'a^40', 'a^41', 'a^42', 'a^43', 'a^44', 'a^45', '1/3*a^46 + 1/3*a^45 + 1/3*a^44 + 1/3*a^43 + 1/3*a^42 + 1/3*a^41 + 1/3*a^40 + 1/3*a^39 + 1/3*a^38 + 1/3*a^37 + 1/3*a^36 + 1/3*a^35 + 1/3*a^34 + 1/3*a^33 + 1/3*a^32 + 1/3*a^31 + 1/3*a^30 + 1/3*a^29 + 1/3*a^28 + 1/3*a^27 + 1/3*a^26 + 1/3*a^25 + 1/3*a^24 + 1/3*a^23 + 1/3*a^22 + 1/3*a^21 + 1/3*a^20 + 1/3*a^19 + 1/3*a^18 + 1/3*a^17 + 1/3*a^16 + 1/3*a^15 + 1/3*a^14 + 1/3*a^13 + 1/3*a^12 + 1/3*a^11 + 1/3*a^10 + 1/3*a^9 + 1/3*a^8 + 1/3*a^7 + 1/3*a^6 + 1/3*a^5 + 1/3*a^4 + 1/3*a^3 + 1/3*a^2 + 1/3*a - 1/3']}
Number field data - 47.1.58809609539096281933776108952608119538900395786445119029601887271096760564217760247629485093057155609130859375.1