Formats: - HTML - YAML - JSON - 2026-07-22T09:12:34.284636
  • nf_fields • Show schema
    {'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 0, 0, 0, 0, 22, 0, 0, 0, 0, -6, 0, 0, 0, 0, -22, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 20, 'disc_abs': 7812500000000000000000000, 'disc_rad': 10, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [40, 54], 'galois_label': '20T6', 'galt': 6, 'grd': 17.564650049460273, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '20.4.7812500000000000000000000.1', 'local_algs': ['2.2.2.4a1.2', '2.4.2.8a1.1', '2.4.2.8a1.1', '5.1.20.27a1.1'], 'maxp': 5, 'minimal_sibling': [1, 5, 5, -5, 0, 11, 45, -170, 220, -85, -194, 350, -205, -140, 420, -464, 325, -155, 50, -10, 1], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 8, 'ramps': [2, 5], 'rd': 17.5646500495, 'regulator': {'__RealLiteral__': 0, 'data': '44054.0373872', 'prec': 44}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-1.-1.1', '5.0.-5.0.1', '-4.10.0.-5.0.1', '1.-5.10.-5.-15.32.-15.-5.10.-5.1'], 'torsion_order': 2, 'unit_signature_rank': 3, 'used_grh': False}
  • nf_fields_extra • Show schema
    {'dirichlet_group': [], 'frobs': [[2, [0]], [3, [[20, 1]]], [5, [0]], [7, [[20, 1]]], [11, [[2, 10]]], [13, [[4, 5]]], [17, [[4, 5]]], [19, [[2, 8], [1, 4]]], [23, [[20, 1]]], [29, [[10, 2]]], [31, [[2, 10]]], [37, [[4, 5]]], [41, [[5, 4]]], [43, [[20, 1]]], [47, [[20, 1]]], [53, [[4, 5]]], [59, [[2, 8], [1, 4]]]], 'label': '20.4.7812500000000000000000000.1', 'res': {'gal': ['1,0,0,0,0,26,0,0,0,0,338,0,0,0,0,840,0,0,0,0,1091,0,0,0,0,620,0,0,0,0,162,0,0,0,0,-18,0,0,0,0,1'], 'sib': ['1,5,5,-5,0,11,45,-170,220,-85,-194,350,-205,-140,420,-464,325,-155,50,-10,1']}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( a \\)', '\\( \\frac{9}{50} a^{17} - \\frac{201}{50} a^{12} + \\frac{13}{50} a^{7} + \\frac{177}{50} a^{2} \\)', '\\( \\frac{1}{10} a^{15} - \\frac{11}{5} a^{10} - \\frac{1}{2} a^{5} + \\frac{3}{5} \\)', '\\( \\frac{4}{25} a^{17} + \\frac{1}{50} a^{16} + \\frac{1}{50} a^{15} - \\frac{177}{50} a^{12} - \\frac{12}{25} a^{11} - \\frac{12}{25} a^{10} - \\frac{12}{25} a^{7} + \\frac{37}{50} a^{6} + \\frac{37}{50} a^{5} + \\frac{149}{50} a^{2} + \\frac{14}{25} a + \\frac{14}{25} \\)', '\\( \\frac{1}{10} a^{19} - \\frac{3}{25} a^{18} - \\frac{1}{25} a^{17} - \\frac{1}{25} a^{16} + \\frac{1}{25} a^{15} - \\frac{111}{50} a^{14} + \\frac{131}{50} a^{13} + \\frac{22}{25} a^{12} + \\frac{23}{25} a^{11} - \\frac{22}{25} a^{10} - \\frac{9}{50} a^{9} + \\frac{28}{25} a^{8} + \\frac{1}{5} a^{7} - \\frac{16}{25} a^{6} - \\frac{1}{5} a^{5} + \\frac{141}{50} a^{4} - \\frac{17}{10} a^{3} - \\frac{11}{25} a^{2} - \\frac{32}{25} a + \\frac{11}{25} \\)', '\\( \\frac{14}{25} a^{19} - \\frac{4}{25} a^{17} + \\frac{1}{25} a^{15} - \\frac{617}{50} a^{14} + \\frac{177}{50} a^{12} - \\frac{43}{50} a^{10} - \\frac{72}{25} a^{9} + \\frac{12}{25} a^{7} - \\frac{18}{25} a^{5} + \\frac{579}{50} a^{4} - \\frac{149}{50} a^{2} + \\frac{41}{50} \\)', '\\( \\frac{11}{25} a^{19} - \\frac{6}{25} a^{18} - \\frac{3}{50} a^{17} + \\frac{3}{50} a^{16} + \\frac{1}{50} a^{15} - \\frac{243}{25} a^{14} + \\frac{132}{25} a^{13} + \\frac{13}{10} a^{12} - \\frac{63}{50} a^{11} - \\frac{11}{25} a^{10} - \\frac{44}{25} a^{9} + \\frac{7}{5} a^{8} + \\frac{41}{50} a^{7} - \\frac{83}{50} a^{6} - \\frac{1}{10} a^{5} + \\frac{247}{25} a^{4} - \\frac{106}{25} a^{3} - \\frac{77}{50} a^{2} + \\frac{7}{10} a - \\frac{7}{25} \\)', '\\( \\frac{11}{50} a^{19} + \\frac{2}{25} a^{18} + \\frac{3}{25} a^{17} - \\frac{1}{10} a^{16} - \\frac{3}{50} a^{15} - \\frac{121}{25} a^{14} - \\frac{17}{10} a^{13} - \\frac{131}{50} a^{12} + \\frac{109}{50} a^{11} + \\frac{32}{25} a^{10} - \\frac{13}{10} a^{9} - \\frac{44}{25} a^{8} - \\frac{28}{25} a^{7} + \\frac{51}{50} a^{6} + \\frac{57}{50} a^{5} + \\frac{113}{25} a^{4} + \\frac{21}{50} a^{3} + \\frac{17}{10} a^{2} - \\frac{49}{50} a - \\frac{8}{25} \\)', '\\( \\frac{11}{25} a^{19} - \\frac{1}{10} a^{18} + \\frac{7}{50} a^{17} - \\frac{2}{25} a^{16} + \\frac{1}{50} a^{15} - \\frac{243}{25} a^{14} + \\frac{111}{50} a^{13} - \\frac{31}{10} a^{12} + \\frac{9}{5} a^{11} - \\frac{11}{25} a^{10} - \\frac{44}{25} a^{9} + \\frac{9}{50} a^{8} - \\frac{19}{50} a^{7} - \\frac{11}{25} a^{6} - \\frac{1}{10} a^{5} + \\frac{247}{25} a^{4} - \\frac{141}{50} a^{3} + \\frac{163}{50} a^{2} - \\frac{43}{25} a + \\frac{18}{25} \\)', '\\( \\frac{9}{50} a^{19} - \\frac{1}{10} a^{18} + \\frac{4}{25} a^{17} + \\frac{1}{25} a^{16} + \\frac{1}{50} a^{15} - \\frac{199}{50} a^{14} + \\frac{111}{50} a^{13} - \\frac{87}{25} a^{12} - \\frac{22}{25} a^{11} - \\frac{11}{25} a^{10} - \\frac{29}{50} a^{9} + \\frac{9}{50} a^{8} - \\frac{46}{25} a^{7} - \\frac{1}{5} a^{6} - \\frac{1}{10} a^{5} + \\frac{27}{10} a^{4} - \\frac{141}{50} a^{3} + \\frac{88}{25} a^{2} + \\frac{11}{25} a - \\frac{7}{25} \\)', '\\( \\frac{11}{25} a^{19} - \\frac{1}{10} a^{18} - \\frac{1}{25} a^{17} + \\frac{1}{10} a^{16} + \\frac{1}{50} a^{15} - \\frac{243}{25} a^{14} + \\frac{111}{50} a^{13} + \\frac{23}{25} a^{12} - \\frac{111}{50} a^{11} - \\frac{11}{25} a^{10} - \\frac{44}{25} a^{9} + \\frac{9}{50} a^{8} - \\frac{16}{25} a^{7} - \\frac{9}{50} a^{6} - \\frac{1}{10} a^{5} + \\frac{247}{25} a^{4} - \\frac{141}{50} a^{3} - \\frac{32}{25} a^{2} + \\frac{141}{50} a + \\frac{18}{25} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', '1/5*a^7 - 1/5*a^6 - 1/5*a^5 + 2/5*a^2 - 2/5*a - 2/5', '1/5*a^8 - 2/5*a^6 - 1/5*a^5 + 2/5*a^3 + 1/5*a - 2/5', '1/5*a^9 + 2/5*a^6 - 2/5*a^5 + 2/5*a^4 - 1/5*a + 1/5', '1/10*a^10 + 2/5*a^5 - 1/10', '1/10*a^11 + 2/5*a^6 - 1/10*a', '1/10*a^12 + 2/5*a^6 + 2/5*a^5 + 1/10*a^2 - 1/5*a - 1/5', '1/10*a^13 - 1/5*a^6 + 2/5*a^5 + 1/10*a^3 - 2/5*a - 1/5', '1/50*a^14 - 1/25*a^13 - 1/50*a^12 + 1/25*a^11 + 1/50*a^10 + 2/25*a^9 + 1/25*a^8 - 2/25*a^7 - 6/25*a^6 - 3/25*a^5 - 21/50*a^4 + 6/25*a^3 + 21/50*a^2 + 9/25*a + 9/50', '1/50*a^15 + 1/50*a^10 + 17/50*a^5 + 13/50', '1/50*a^16 + 1/50*a^11 + 17/50*a^6 + 13/50*a', '1/50*a^17 + 1/50*a^12 - 3/50*a^7 + 2/5*a^6 + 2/5*a^5 + 23/50*a^2 - 1/5*a - 1/5', '1/50*a^18 + 1/50*a^13 - 3/50*a^8 - 1/5*a^6 + 2/5*a^5 + 23/50*a^3 - 2/5*a - 1/5', '1/50*a^19 + 1/25*a^13 + 1/50*a^12 - 1/25*a^11 - 1/50*a^10 + 3/50*a^9 - 1/25*a^8 + 2/25*a^7 - 4/25*a^6 - 12/25*a^5 + 7/25*a^4 - 6/25*a^3 - 21/50*a^2 - 4/25*a - 19/50']}