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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [64, 0, -576, 0, -512, 0, 56, 0, 135, 0, 30, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 3663139112860606529536, 'disc_rad': 62, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[6, 2]]], [5, [[6, 2]]], [7, [[3, 4]]], [11, [[6, 2]]], [13, [[6, 2]]], [17, [[3, 4]]], [19, [[6, 2]]], [23, [[2, 4], [1, 4]]], [29, [[2, 6]]], [31, [0]], [37, [[6, 2]]], [41, [[3, 4]]], [43, [[6, 2]]], [47, [[2, 2], [1, 8]]], [53, [[6, 2]]], [59, [[6, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [324, 64], 'galois_label': '12T58', 'galt': 58, 'grd': 102.38052790852275, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 17, 'label': '12.4.3663139112860606529536.17', 'local_algs': ['2.4.11.15', '2.4.11.4', '2.4.10.3', '31.3.2.1', '31.3.2.1', '31.3.2.1', '31.3.2.1'], 'minimal_sibling': [242, 352, -552, -712, 0, -48, 20, 0, 1], 'monogenic': -1, 'num_ram': 2, 'r2': 4, 'ramps': [2, 31], 'rd': 62.6596239759, 'regulator': {'__RealLiteral__': 0, 'data': '8325812.53378', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-2.0.1', '8.-10.-1.1', '-92.-112.92.44.-25.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{5}{1796} a^{10} + \\frac{219}{3592} a^{8} - \\frac{207}{898} a^{6} - \\frac{3599}{3592} a^{4} + \\frac{721}{898} a^{2} + \\frac{154}{449} \\)', '\\( \\frac{463}{7184} a^{10} + \\frac{3287}{1796} a^{8} + \\frac{40957}{7184} a^{6} - \\frac{25553}{3592} a^{4} - \\frac{18039}{898} a^{2} + \\frac{916}{449} \\)', '\\( \\frac{439}{3592} a^{10} + \\frac{12353}{3592} a^{8} + \\frac{36299}{3592} a^{6} - \\frac{42199}{3592} a^{4} - \\frac{18096}{449} a^{2} + \\frac{1642}{449} \\)', '\\( \\frac{61}{1796} a^{10} + \\frac{435}{449} a^{8} + \\frac{5815}{1796} a^{6} - \\frac{403}{898} a^{4} - \\frac{3190}{449} a^{2} - \\frac{905}{449} \\)', '\\( \\frac{21}{449} a^{10} + \\frac{2109}{1796} a^{8} + \\frac{147}{449} a^{6} - \\frac{8949}{1796} a^{4} + \\frac{349}{898} a^{2} - \\frac{17}{449} \\)', '\\( \\frac{10956205}{14368} a^{11} + \\frac{437369}{1796} a^{10} + \\frac{164901987}{7184} a^{9} + \\frac{26331423}{3592} a^{8} + \\frac{1512735523}{14368} a^{7} + \\frac{15097139}{449} a^{6} + \\frac{95982649}{1796} a^{5} + \\frac{61309453}{3592} a^{4} - \\frac{691412709}{1796} a^{3} - \\frac{55202213}{449} a^{2} - \\frac{214844732}{449} a - \\frac{68613778}{449} \\)', '\\( \\frac{67121797}{7184} a^{11} + \\frac{92167585}{7184} a^{10} + \\frac{535054519}{1796} a^{9} + \\frac{183676684}{449} a^{8} + \\frac{13097031087}{7184} a^{7} + \\frac{17984340795}{7184} a^{6} + \\frac{14227469033}{3592} a^{5} + \\frac{19537184427}{3592} a^{4} + \\frac{2411370681}{898} a^{3} + \\frac{3311632745}{898} a^{2} - \\frac{142547893}{449} a - \\frac{195561170}{449} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6 - 1/2*a^2', '1/4*a^7 - 1/2*a^5 - 1/4*a^3', '1/16*a^8 - 1/8*a^6 - 1/16*a^4 - 1/2*a^2 - 1/2', '1/16*a^9 - 1/8*a^7 - 1/16*a^5 - 1/2*a^3 - 1/2*a', '1/14368*a^10 + 213/7184*a^8 + 7/14368*a^6 - 1089/3592*a^4 - 615/1796*a^2 + 161/449', '1/28736*a^11 + 213/14368*a^9 + 7/28736*a^7 - 1089/7184*a^5 - 615/3592*a^3 + 161/898*a']}
Number field data - 12.4.3663139112860606529536.17