-
nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [625, 0, 0, 0, 250, 0, 500, 0, 375, 0, 100, 0, 10, 0, 0, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 479785216000000000000, 'disc_rad': 370, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[12, 1], [4, 1]]], [5, [0]], [7, [[12, 1], [4, 1]]], [11, [[6, 2], [2, 2]]], [13, [[4, 4]]], [17, [[4, 4]]], [19, [[4, 4]]], [23, [[4, 4]]], [29, [[4, 4]]], [31, [[4, 4]]], [37, [0]], [41, [[3, 4], [1, 4]]], [43, [[4, 4]]], [47, [[12, 1], [4, 1]]], [53, [[12, 1], [4, 1]]], [59, [[2, 4], [1, 8]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [128, 72, 48], 'galois_label': '16T181', 'galt': 181, 'grd': 51.250923193822786, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '16.0.479785216000000000000.1', 'local_algs': ['2.2.2.4a1.2', '2.2.6.16a1.6', '5.4.4.12a1.4', '37.4.1.0a1.1', '37.4.1.0a1.1', '37.4.2.4a1.2'], 'minimal_sibling': [125, 0, -750, 0, -1825, 0, -700, 0, -45, 0, 10, 0, 1], 'monogenic': -1, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 3, 'r2': 8, 'ramps': [2, 5, 37], 'rd': 19.6139664839, 'regulator': {'__RealLiteral__': 0, 'data': '2615.56096385', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-1.-1.1', '5.0.-5.0.1', '4.-3.5.-1.1', '1.1.1.0.0.0.1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{13}{5500} a^{14} - \\frac{63}{5500} a^{12} + \\frac{1}{22} a^{10} + \\frac{23}{220} a^{8} - \\frac{9}{110} a^{6} - \\frac{37}{44} a^{4} + \\frac{9}{44} a^{2} + \\frac{15}{22} \\)', '\\( \\frac{1}{550} a^{14} + \\frac{3}{1100} a^{12} - \\frac{3}{1100} a^{10} + \\frac{3}{11} a^{8} + \\frac{141}{220} a^{6} + \\frac{6}{11} a^{4} - \\frac{21}{44} a^{2} + \\frac{117}{44} \\)', '\\( \\frac{41}{5500} a^{14} - \\frac{43}{5500} a^{12} + \\frac{17}{275} a^{10} + \\frac{823}{1100} a^{8} + \\frac{92}{55} a^{6} + \\frac{151}{220} a^{4} - \\frac{41}{44} a^{2} + \\frac{49}{22} \\)', '\\( \\frac{1}{2750} a^{15} + \\frac{13}{2750} a^{14} - \\frac{2}{1375} a^{13} - \\frac{27}{5500} a^{12} + \\frac{3}{550} a^{11} + \\frac{9}{220} a^{10} + \\frac{4}{275} a^{9} + \\frac{129}{275} a^{8} + \\frac{1}{55} a^{7} + \\frac{239}{220} a^{6} - \\frac{16}{55} a^{5} + \\frac{57}{110} a^{4} - \\frac{6}{11} a^{3} - \\frac{15}{44} a^{2} - \\frac{29}{22} a + \\frac{71}{44} \\)', '\\( \\frac{2}{1375} a^{15} + \\frac{1}{1375} a^{14} - \\frac{8}{1375} a^{13} + \\frac{39}{5500} a^{12} + \\frac{6}{275} a^{11} - \\frac{21}{1100} a^{10} + \\frac{27}{275} a^{9} + \\frac{52}{275} a^{8} - \\frac{3}{110} a^{7} + \\frac{151}{220} a^{6} - \\frac{51}{110} a^{5} + \\frac{79}{110} a^{4} + \\frac{7}{22} a^{3} - \\frac{59}{44} a^{2} + \\frac{19}{11} a - \\frac{17}{44} \\)', '\\( \\frac{1}{5500} a^{15} + \\frac{1}{550} a^{14} + \\frac{29}{5500} a^{13} + \\frac{3}{1100} a^{12} - \\frac{2}{275} a^{11} - \\frac{3}{1100} a^{10} + \\frac{17}{220} a^{9} + \\frac{3}{11} a^{8} + \\frac{28}{55} a^{7} + \\frac{141}{220} a^{6} + \\frac{53}{44} a^{5} + \\frac{6}{11} a^{4} - \\frac{1}{44} a^{3} - \\frac{21}{44} a^{2} - \\frac{10}{11} a + \\frac{117}{44} \\)', '\\( \\frac{13}{5500} a^{15} - \\frac{1}{550} a^{14} - \\frac{63}{5500} a^{13} - \\frac{3}{1100} a^{12} + \\frac{1}{22} a^{11} + \\frac{3}{1100} a^{10} + \\frac{23}{220} a^{9} - \\frac{3}{11} a^{8} - \\frac{9}{110} a^{7} - \\frac{141}{220} a^{6} - \\frac{37}{44} a^{5} - \\frac{6}{11} a^{4} + \\frac{9}{44} a^{3} + \\frac{21}{44} a^{2} + \\frac{15}{22} a - \\frac{73}{44} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', '1/5*a^4', '1/5*a^5', '1/10*a^6 - 1/10*a^5 - 1/2*a^3 - 1/2*a - 1/2', '1/10*a^7 - 1/10*a^5 - 1/10*a^4 - 1/2*a^3 - 1/2*a^2 - 1/2', '1/50*a^8 - 1/10*a^4 - 1/2', '1/50*a^9 - 1/10*a^5 - 1/2*a', '1/50*a^10 - 1/10*a^5 - 1/2*a^3 - 1/2*a^2 - 1/2*a - 1/2', '1/50*a^11 - 1/10*a^5 - 1/10*a^4 - 1/2*a^2 - 1/2', '1/500*a^12 - 1/100*a^10 - 1/20*a^6 - 1/4*a^2 - 1/4', '1/500*a^13 - 1/100*a^11 - 1/20*a^7 - 1/4*a^3 - 1/4*a', '1/5500*a^14 - 1/1375*a^12 + 3/1100*a^10 - 3/1100*a^8 - 9/220*a^6 + 1/220*a^4 + 5/22*a^2 - 7/44', '1/5500*a^15 - 1/1375*a^13 + 3/1100*a^11 - 3/1100*a^9 - 9/220*a^7 + 1/220*a^5 + 5/22*a^3 - 7/44*a']}
Number field data - 16.0.479785216000000000000.1