Formats: - HTML - YAML - JSON - 2026-09-12T12:18:16.873972
  • nf_fields • Show schema
    {'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [7168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 20, 'disc_abs': 2988151979474457198592000000000000, 'disc_rad': 70, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [320, 120, 152], 'galois_label': '20T42', 'galt': 42, 'grd': 84.94359407115167, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '20.0.2988151979474457198592000000000000.1', 'local_algs': ['2.1.2.3a1.2', '2.1.2.3a1.4', '2.4.2.12a1.9', '2.4.2.12a1.1', '5.4.1.0a1.1', '5.4.4.12a1.4', '7.1.20.19a1.1'], 'maximal_cm_subfield': [2, -1, 1], 'maxp': 7, 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 3, 'r2': 10, 'ramps': [2, 5, 7], 'rd': 47.18132511247428, 'regulator': {'__RealLiteral__': 0, 'data': '738827162.6953382', 'prec': 54}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['2.-1.1', '28.0.0.0.1', '-7.0.0.0.0.1', '7.0.0.0.0.0.0.0.0.0.1'], 'torsion_order': 2, 'unit_signature_rank': 0, 'used_grh': True}
  • nf_fields_extra • Show schema
    {'dirichlet_group': [], 'frobs': [[2, [0]], [3, [[4, 4], [2, 2]]], [5, [0]], [7, [0]], [11, [[10, 1], [5, 2]]], [13, [[4, 5]]], [17, [[4, 5]]], [19, [[2, 10]]], [23, [[4, 4], [2, 1], [1, 2]]], [29, [[2, 8], [1, 4]]], [31, [[10, 2]]], [37, [[4, 4], [1, 4]]], [41, [[20, 1]]], [43, [[4, 4], [2, 1], [1, 2]]], [47, [[4, 4], [2, 2]]], [53, [[4, 4], [2, 2]]], [59, [[2, 10]]]], 'label': '20.0.2988151979474457198592000000000000.1', 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{1}{1280} a^{16} + \\frac{1}{640} a^{12} + \\frac{1}{64} a^{10} - \\frac{1}{80} a^{8} + \\frac{1}{10} a^{4} - \\frac{1}{4} a^{2} - \\frac{3}{10} \\)', '\\( -\\frac{1}{5120} a^{18} - \\frac{1}{2560} a^{16} + \\frac{1}{640} a^{14} + \\frac{1}{320} a^{12} - \\frac{1}{80} a^{10} + \\frac{1}{160} a^{8} + \\frac{3}{80} a^{6} - \\frac{1}{20} a^{4} - \\frac{3}{10} a^{2} + \\frac{2}{5} \\)', '\\( -\\frac{1}{5120} a^{18} + \\frac{1}{2560} a^{16} + \\frac{1}{640} a^{14} - \\frac{1}{320} a^{12} - \\frac{1}{80} a^{10} - \\frac{1}{160} a^{8} + \\frac{3}{80} a^{6} + \\frac{1}{20} a^{4} - \\frac{3}{10} a^{2} - \\frac{2}{5} \\)', '\\( -\\frac{1}{5120} a^{18} - \\frac{1}{2560} a^{16} + \\frac{1}{640} a^{14} - \\frac{3}{640} a^{12} + \\frac{1}{320} a^{10} + \\frac{1}{160} a^{8} - \\frac{7}{80} a^{6} - \\frac{1}{20} a^{4} - \\frac{1}{20} a^{2} - \\frac{11}{10} \\)', '\\( -\\frac{1}{5120} a^{19} + \\frac{1}{5120} a^{18} - \\frac{1}{1280} a^{17} + \\frac{3}{2560} a^{16} - \\frac{3}{1280} a^{15} + \\frac{1}{160} a^{14} - \\frac{3}{320} a^{13} + \\frac{9}{640} a^{12} - \\frac{9}{320} a^{11} + \\frac{9}{320} a^{10} - \\frac{3}{160} a^{9} + \\frac{7}{160} a^{8} - \\frac{1}{40} a^{7} - \\frac{3}{80} a^{6} + \\frac{1}{40} a^{5} - \\frac{1}{10} a^{4} + \\frac{1}{5} a^{3} + \\frac{1}{20} a^{2} + \\frac{3}{10} a - \\frac{17}{10} \\)', '\\( -\\frac{1}{5120} a^{19} + \\frac{1}{512} a^{18} - \\frac{3}{2560} a^{17} + \\frac{1}{1280} a^{16} + \\frac{7}{1280} a^{15} - \\frac{1}{128} a^{14} - \\frac{1}{160} a^{13} + \\frac{11}{640} a^{12} - \\frac{9}{320} a^{11} - \\frac{1}{64} a^{10} + \\frac{23}{160} a^{9} - \\frac{1}{80} a^{8} - \\frac{7}{80} a^{7} + \\frac{1}{4} a^{6} - \\frac{11}{40} a^{5} - \\frac{13}{20} a^{4} + \\frac{6}{5} a^{3} - \\frac{1}{4} a^{2} - \\frac{13}{10} a + \\frac{67}{10} \\)', '\\( \\frac{1}{128} a^{15} + \\frac{1}{32} a^{10} - \\frac{1}{4} a^{5} - 6 \\)', '\\( -\\frac{1}{5120} a^{19} - \\frac{1}{1280} a^{18} - \\frac{3}{512} a^{17} - \\frac{1}{320} a^{16} + \\frac{7}{1280} a^{15} + \\frac{1}{160} a^{14} - \\frac{1}{64} a^{13} + \\frac{21}{640} a^{12} + \\frac{31}{320} a^{11} + \\frac{9}{320} a^{10} + \\frac{3}{32} a^{9} + \\frac{17}{40} a^{8} + \\frac{53}{80} a^{7} + \\frac{11}{40} a^{6} + \\frac{9}{8} a^{5} + \\frac{31}{10} a^{4} + \\frac{27}{10} a^{3} + \\frac{41}{20} a^{2} + \\frac{15}{2} a + \\frac{157}{10} \\)', '\\( \\frac{173}{2560} a^{19} + \\frac{131}{1280} a^{18} + \\frac{147}{2560} a^{17} - \\frac{319}{2560} a^{16} - \\frac{133}{320} a^{15} - \\frac{3}{5} a^{14} - \\frac{189}{640} a^{13} + \\frac{503}{640} a^{12} + \\frac{387}{160} a^{11} + \\frac{269}{80} a^{10} + \\frac{129}{80} a^{9} - \\frac{179}{40} a^{8} - \\frac{1093}{80} a^{7} - \\frac{1547}{80} a^{6} - \\frac{52}{5} a^{5} + \\frac{481}{20} a^{4} + \\frac{1581}{20} a^{3} + \\frac{2379}{20} a^{2} + \\frac{351}{5} a - \\frac{702}{5} \\)'], 'zk': ['1', 'a', '1/2*a^2', '1/2*a^3', '1/4*a^4', '1/4*a^5', '1/8*a^6', '1/8*a^7', '1/16*a^8', '1/16*a^9', '1/64*a^10 - 1/2', '1/64*a^11 - 1/2*a', '1/128*a^12 - 1/4*a^2', '1/128*a^13 - 1/4*a^3', '1/256*a^14 - 1/8*a^4', '1/256*a^15 - 1/8*a^5', '1/2560*a^16 - 1/320*a^12 + 1/40*a^8 - 1/16*a^6 + 1/20*a^4 - 2/5', '1/2560*a^17 - 1/320*a^13 + 1/40*a^9 - 1/16*a^7 + 1/20*a^5 - 2/5*a', '1/5120*a^18 - 1/640*a^14 - 1/320*a^10 - 1/32*a^8 + 1/40*a^6 - 1/5*a^2 - 1/2', '1/5120*a^19 - 1/640*a^15 - 1/320*a^11 - 1/32*a^9 + 1/40*a^7 - 1/5*a^3 - 1/2*a']}