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nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [1, -2, 6, 8, -1, 7, 6, -10, 11, 15, -1, 15, 11, -10, 6, 7, -1, 8, 6, -2, 1], 'conductor': 0, 'degree': 20, 'dirichlet_group': [], 'disc_abs': 39479125871598264344535849, 'disc_rad': 1203, 'disc_sign': 1, 'frobs': [[2, [[10, 2]]], [3, [0]], [5, [[10, 2]]], [7, [[5, 4]]], [11, [[10, 2]]], [13, [[4, 2], [2, 6]]], [17, [[4, 4], [2, 2]]], [19, [[4, 4], [1, 4]]], [23, [[2, 10]]], [29, [[10, 2]]], [31, [[4, 2], [2, 6]]], [37, [[4, 2], [2, 6]]], [41, [[10, 2]]], [43, [[5, 4]]], [47, [[10, 2]]], [53, [[2, 10]]], [59, [[4, 2], [2, 6]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [160, 160], 'galois_label': '20T73', 'galt': 73, 'grd': 34.68429039204925, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '20.0.39479125871598264344535849.1', 'local_algs': ['3.2.1.2', '3.2.1.2', '3.8.4.1', '3.8.4.1', 'm401.1.2.0', 'm401.1.2.0', 'm401.2.2.2', 'm401.2.2.2', 'm401.2.2.2', 'm401.2.2.2'], 'minimal_sibling': [1, -1, 0, 0, -2, 1, -2, 0, 0, -1, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 10, 'ramps': [3, 401], 'rd': 19.046640137, 'regulator': {'__RealLiteral__': 0, 'data': '74630.3756382', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1, 1, 1], 'subfields': ['1.-1.1', '-1.3.4.-5.-1.1', '-1.10.-23.-3.44.-13.-18.9.-2.-1.1', '1.-3.13.2.30.-15.26.-3.6.-1.1', '1.-2.-2.-2.1.-1.1.-2.-2.-2.1'], 'torsion_gen': '\\( -\\frac{22}{27} a^{19} + \\frac{7}{27} a^{18} - \\frac{95}{27} a^{17} - \\frac{364}{27} a^{16} - \\frac{148}{9} a^{15} - \\frac{616}{27} a^{14} - \\frac{799}{27} a^{13} - \\frac{181}{9} a^{12} - \\frac{485}{27} a^{11} - \\frac{617}{27} a^{10} - \\frac{475}{27} a^{9} - \\frac{631}{27} a^{8} - 30 a^{7} - \\frac{614}{27} a^{6} - \\frac{521}{27} a^{5} - \\frac{143}{9} a^{4} - \\frac{182}{27} a^{3} - \\frac{109}{27} a^{2} - \\frac{64}{27} a + \\frac{10}{27} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{37}{27} a^{19} - \\frac{37}{27} a^{18} + \\frac{188}{27} a^{17} + \\frac{466}{27} a^{16} + \\frac{154}{9} a^{15} + \\frac{667}{27} a^{14} + \\frac{763}{27} a^{13} + 9 a^{12} + \\frac{287}{27} a^{11} + \\frac{497}{27} a^{10} + \\frac{301}{27} a^{9} + \\frac{568}{27} a^{8} + \\frac{278}{9} a^{7} + \\frac{389}{27} a^{6} + \\frac{275}{27} a^{5} + \\frac{68}{9} a^{4} - \\frac{67}{27} a^{3} - \\frac{68}{27} a^{2} + \\frac{61}{27} a - \\frac{22}{27} \\)', '\\( \\frac{25}{27} a^{19} - \\frac{7}{9} a^{18} + \\frac{122}{27} a^{17} + \\frac{115}{9} a^{16} + \\frac{115}{9} a^{15} + \\frac{550}{27} a^{14} + \\frac{650}{27} a^{13} + \\frac{362}{27} a^{12} + \\frac{478}{27} a^{11} + 22 a^{10} + \\frac{337}{27} a^{9} + \\frac{620}{27} a^{8} + \\frac{716}{27} a^{7} + \\frac{376}{27} a^{6} + 17 a^{5} + \\frac{44}{3} a^{4} + \\frac{107}{27} a^{3} + \\frac{46}{9} a^{2} + \\frac{100}{27} a - \\frac{10}{9} \\)', '\\( \\frac{10}{27} a^{19} + \\frac{4}{27} a^{18} + \\frac{11}{27} a^{17} + \\frac{212}{27} a^{16} + \\frac{58}{9} a^{15} - \\frac{11}{27} a^{14} - \\frac{4}{3} a^{13} - \\frac{320}{27} a^{12} - \\frac{55}{3} a^{11} - \\frac{170}{27} a^{10} - \\frac{98}{27} a^{9} - \\frac{8}{3} a^{8} + \\frac{58}{27} a^{7} - 8 a^{6} - \\frac{461}{27} a^{5} - \\frac{122}{9} a^{4} - \\frac{346}{27} a^{3} - \\frac{187}{27} a^{2} - \\frac{32}{27} a - \\frac{8}{27} \\)', '\\( \\frac{10}{27} a^{19} + \\frac{2}{3} a^{18} + \\frac{23}{27} a^{17} + \\frac{29}{3} a^{16} + \\frac{164}{9} a^{15} + \\frac{466}{27} a^{14} + \\frac{707}{27} a^{13} + \\frac{479}{27} a^{12} + \\frac{64}{27} a^{11} + \\frac{29}{3} a^{10} + \\frac{271}{27} a^{9} + \\frac{236}{27} a^{8} + \\frac{707}{27} a^{7} + \\frac{556}{27} a^{6} + 7 a^{5} + \\frac{58}{9} a^{4} - \\frac{82}{27} a^{3} - \\frac{65}{9} a^{2} - \\frac{14}{27} a - \\frac{11}{9} \\)', '\\( \\frac{1}{3} a^{19} - \\frac{7}{9} a^{18} + \\frac{23}{9} a^{17} + \\frac{10}{9} a^{16} + \\frac{10}{9} a^{15} + \\frac{34}{9} a^{14} - \\frac{4}{3} a^{13} - \\frac{29}{9} a^{12} + 2 a^{11} - \\frac{23}{9} a^{10} + \\frac{1}{9} a^{9} + \\frac{17}{3} a^{8} - \\frac{2}{9} a^{7} - 2 a^{6} + \\frac{10}{9} a^{5} - \\frac{35}{9} a^{4} - \\frac{14}{9} a^{3} + \\frac{2}{9} a^{2} - \\frac{1}{9} a - \\frac{1}{3} \\)', '\\( \\frac{13}{27} a^{19} + \\frac{1}{9} a^{18} + \\frac{74}{27} a^{17} + \\frac{68}{9} a^{16} + \\frac{166}{9} a^{15} + \\frac{646}{27} a^{14} + \\frac{641}{27} a^{13} + \\frac{524}{27} a^{12} + \\frac{304}{27} a^{11} + \\frac{56}{9} a^{10} + \\frac{316}{27} a^{9} + \\frac{494}{27} a^{8} + \\frac{617}{27} a^{7} + \\frac{616}{27} a^{6} + \\frac{137}{9} a^{5} + 4 a^{4} - \\frac{25}{27} a^{3} - \\frac{31}{9} a^{2} - \\frac{23}{27} a - \\frac{5}{9} \\)', '\\( \\frac{28}{27} a^{19} - \\frac{16}{27} a^{18} + \\frac{131}{27} a^{17} + \\frac{409}{27} a^{16} + \\frac{58}{3} a^{15} + \\frac{628}{27} a^{14} + \\frac{826}{27} a^{13} + \\frac{61}{3} a^{12} + \\frac{392}{27} a^{11} + \\frac{593}{27} a^{10} + \\frac{523}{27} a^{9} + \\frac{568}{27} a^{8} + \\frac{284}{9} a^{7} + \\frac{611}{27} a^{6} + \\frac{452}{27} a^{5} + \\frac{124}{9} a^{4} + \\frac{119}{27} a^{3} + \\frac{43}{27} a^{2} + \\frac{52}{27} a - \\frac{40}{27} \\)', '\\( \\frac{5}{27} a^{19} - \\frac{2}{9} a^{18} + \\frac{28}{27} a^{17} + \\frac{14}{9} a^{16} + \\frac{10}{3} a^{15} - \\frac{4}{27} a^{14} + \\frac{25}{27} a^{13} + \\frac{34}{27} a^{12} - \\frac{130}{27} a^{11} - \\frac{10}{9} a^{10} + \\frac{92}{27} a^{9} - \\frac{116}{27} a^{8} + \\frac{40}{27} a^{7} + \\frac{62}{27} a^{6} - \\frac{46}{9} a^{5} - \\frac{20}{9} a^{4} + \\frac{10}{27} a^{3} - \\frac{16}{3} a^{2} - \\frac{13}{27} a - \\frac{1}{9} \\)', '\\( \\frac{32}{27} a^{19} - \\frac{14}{9} a^{18} + \\frac{172}{27} a^{17} + 13 a^{16} + \\frac{92}{9} a^{15} + \\frac{434}{27} a^{14} + \\frac{463}{27} a^{13} + \\frac{22}{27} a^{12} + \\frac{212}{27} a^{11} + \\frac{113}{9} a^{10} + \\frac{107}{27} a^{9} + \\frac{430}{27} a^{8} + \\frac{532}{27} a^{7} + \\frac{71}{27} a^{6} + \\frac{53}{9} a^{5} + \\frac{11}{3} a^{4} - \\frac{137}{27} a^{3} - \\frac{7}{9} a^{2} + \\frac{56}{27} a - \\frac{8}{3} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', '1/3*a^12 - 1/3*a^11 + 1/3*a^10 + 1/3*a^7 - 1/3*a^6 + 1/3*a^5 + 1/3*a^2 - 1/3*a + 1/3', '1/3*a^13 + 1/3*a^10 + 1/3*a^8 + 1/3*a^5 + 1/3*a^3 + 1/3', '1/3*a^14 + 1/3*a^11 + 1/3*a^9 + 1/3*a^6 + 1/3*a^4 + 1/3*a', '1/9*a^15 + 1/9*a^14 + 1/9*a^13 + 1/9*a^12 + 1/9*a^11 - 4/9*a^10 + 4/9*a^9 + 1/9*a^8 + 1/9*a^7 - 2/9*a^6 - 4/9*a^5 - 2/9*a^4 + 1/9*a^3 + 1/9*a^2 + 4/9*a + 4/9', '1/9*a^16 + 4/9*a^11 - 1/9*a^10 - 1/3*a^9 - 1/3*a^7 - 2/9*a^6 + 2/9*a^5 + 1/3*a^4 + 1/3*a^2 - 4/9', '1/9*a^17 + 1/9*a^12 + 2/9*a^11 + 1/3*a^10 - 1/3*a^8 + 4/9*a^7 - 4/9*a^6 + 1/3*a^3 - 1/3*a^2 - 1/9*a - 1/3', '1/27*a^18 - 1/27*a^16 + 1/9*a^14 + 4/27*a^13 + 2/27*a^12 + 11/27*a^11 + 4/27*a^10 + 4/9*a^9 - 11/27*a^8 + 8/27*a^7 + 5/27*a^6 + 1/27*a^5 + 4/9*a^4 - 4/27*a^2 + 7/27', '1/27*a^19 - 1/27*a^17 + 1/27*a^14 - 1/27*a^13 - 1/27*a^12 + 10/27*a^11 - 4/9*a^10 + 4/27*a^9 + 5/27*a^8 - 7/27*a^7 - 11/27*a^6 - 4/9*a^5 + 2/9*a^4 - 7/27*a^3 - 4/9*a^2 + 4/27*a + 2/9']}
Number field data - 20.0.39479125871598264344535849.1