Formats: - HTML - YAML - JSON - 2026-07-22T07:25:45.863474
  • nf_fields • Show schema
    {'class_group': [5], 'class_number': 5, 'cm': False, 'coeffs': [1771561, 0, 0, 0, 0, -47916, 0, 0, 0, 0, 2486, 0, 0, 0, 0, -36, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 20, 'disc_abs': 23383113568432629108428955078125, 'disc_rad': 55, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [143, 80], 'galois_label': '20T26', 'galt': 26, 'grd': 68.02072465087673, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '20.0.23383113568432629108428955078125.1', 'local_algs': ['5.1.20.27a1.4', '11.1.5.4a1.4', '11.1.5.4a1.3', '11.1.5.4a1.2', '11.5.1.0a1.1'], 'maximal_cm_subfield': [1, -1, 1, -1, 1], 'maxp': 11, 'monogenic': -1, 'narrow_class_group': [5], 'narrow_class_number': 5, 'num_ram': 2, 'r2': 10, 'ramps': [5, 11], 'rd': 37.020741826, 'regulator': {'__RealLiteral__': 0, 'data': '45537996.331', 'prec': 40}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '1.-1.1.-1.1'], 'torsion_order': 10, 'unit_signature_rank': 0, 'used_grh': True}
  • nf_fields_extra • Show schema
    {'dirichlet_group': [], 'frobs': [[2, [[4, 5]]], [3, [[4, 5]]], [5, [0]], [7, [[4, 5]]], [11, [0]], [13, [[4, 5]]], [17, [[4, 5]]], [19, [[10, 2]]], [23, [[4, 5]]], [29, [[10, 2]]], [31, [[5, 3], [1, 5]]], [37, [[4, 5]]], [41, [[5, 3], [1, 5]]], [43, [[4, 5]]], [47, [[4, 5]]], [53, [[4, 5]]], [59, [[10, 2]]]], 'label': '20.0.23383113568432629108428955078125.1', 'res': {}, 'torsion_gen': '\\( \\frac{7}{798600} a^{15} - \\frac{1099}{798600} a^{10} + \\frac{1571}{72600} a^{5} - \\frac{623}{600} \\)', 'units': ['\\( \\frac{1}{26620} a^{15} - \\frac{9}{6655} a^{10} + \\frac{21}{484} a^{5} - \\frac{2}{5} \\)', '\\( \\frac{161}{96630600} a^{19} - \\frac{1}{732050} a^{18} - \\frac{8}{1098075} a^{17} - \\frac{1}{199650} a^{16} - \\frac{1}{72600} a^{15} + \\frac{859}{96630600} a^{14} + \\frac{193}{1464100} a^{13} + \\frac{96}{366025} a^{12} - \\frac{49}{399300} a^{11} + \\frac{1}{24200} a^{10} - \\frac{7}{1756920} a^{9} - \\frac{212}{33275} a^{8} - \\frac{457}{39930} a^{7} + \\frac{107}{9075} a^{6} - \\frac{41}{6600} a^{5} + \\frac{8207}{72600} a^{4} + \\frac{67}{1100} a^{3} - \\frac{39}{550} a^{2} - \\frac{19}{60} a - \\frac{17}{40} \\)', '\\( \\frac{9}{8052550} a^{19} - \\frac{3}{585640} a^{18} + \\frac{8}{1098075} a^{17} - \\frac{1}{72600} a^{16} + \\frac{7}{798600} a^{15} - \\frac{2303}{24157650} a^{14} + \\frac{1741}{8784600} a^{13} - \\frac{96}{366025} a^{12} + \\frac{1}{24200} a^{11} - \\frac{41}{53240} a^{10} + \\frac{1743}{366025} a^{9} - \\frac{2191}{266200} a^{8} + \\frac{457}{39930} a^{7} - \\frac{41}{6600} a^{6} + \\frac{1439}{72600} a^{5} - \\frac{761}{9075} a^{4} + \\frac{581}{6600} a^{3} + \\frac{39}{550} a^{2} - \\frac{17}{40} a - \\frac{93}{200} \\)', '\\( \\frac{71}{48315300} a^{19} + \\frac{13}{2196150} a^{18} - \\frac{3}{292820} a^{17} + \\frac{1}{159720} a^{16} - \\frac{1}{14520} a^{15} - \\frac{213}{4026275} a^{14} - \\frac{191}{1464100} a^{13} + \\frac{2951}{4392300} a^{12} + \\frac{61}{266200} a^{11} + \\frac{49}{24200} a^{10} + \\frac{281}{878460} a^{9} + \\frac{1013}{199650} a^{8} - \\frac{3511}{133100} a^{7} - \\frac{179}{72600} a^{6} - \\frac{241}{6600} a^{5} - \\frac{63}{6050} a^{4} + \\frac{29}{220} a^{3} + \\frac{1411}{3300} a^{2} + \\frac{21}{200} a - \\frac{81}{200} \\)', '\\( \\frac{83}{48315300} a^{19} + \\frac{1}{732050} a^{18} - \\frac{17}{1756920} a^{17} - \\frac{7}{798600} a^{16} + \\frac{7}{798600} a^{15} - \\frac{4319}{48315300} a^{14} - \\frac{193}{1464100} a^{13} + \\frac{1729}{8784600} a^{12} + \\frac{41}{53240} a^{11} - \\frac{41}{53240} a^{10} + \\frac{8473}{4392300} a^{9} + \\frac{212}{33275} a^{8} - \\frac{5537}{798600} a^{7} - \\frac{1439}{72600} a^{6} + \\frac{1439}{72600} a^{5} + \\frac{91}{7260} a^{4} - \\frac{67}{1100} a^{3} - \\frac{691}{6600} a^{2} + \\frac{93}{200} a - \\frac{93}{200} \\)', '\\( \\frac{629}{96630600} a^{19} - \\frac{101}{8784600} a^{18} + \\frac{29}{1756920} a^{17} + \\frac{1}{798600} a^{16} - \\frac{1}{19965} a^{15} - \\frac{8003}{96630600} a^{14} + \\frac{127}{8784600} a^{13} + \\frac{287}{1756920} a^{12} - \\frac{1367}{798600} a^{11} + \\frac{53}{15972} a^{10} + \\frac{79597}{8784600} a^{9} - \\frac{12673}{798600} a^{8} + \\frac{3529}{159720} a^{7} + \\frac{1073}{72600} a^{6} - \\frac{83}{1815} a^{5} - \\frac{8971}{72600} a^{4} + \\frac{899}{6600} a^{3} + \\frac{331}{1320} a^{2} - \\frac{1159}{600} a + \\frac{269}{60} \\)', '\\( \\frac{169}{32210200} a^{19} + \\frac{101}{8784600} a^{18} + \\frac{1}{585640} a^{17} - \\frac{17}{798600} a^{16} - \\frac{19}{266200} a^{15} - \\frac{4753}{32210200} a^{14} - \\frac{127}{8784600} a^{13} + \\frac{1223}{1756920} a^{12} + \\frac{83}{266200} a^{11} - \\frac{731}{798600} a^{10} + \\frac{19197}{2928200} a^{9} + \\frac{12673}{798600} a^{8} + \\frac{21}{10648} a^{7} - \\frac{1081}{72600} a^{6} - \\frac{2347}{24200} a^{5} - \\frac{6381}{24200} a^{4} - \\frac{899}{6600} a^{3} + \\frac{227}{264} a^{2} + \\frac{251}{200} a - \\frac{667}{600} \\)', '\\( \\frac{79}{96630600} a^{19} - \\frac{1}{8784600} a^{18} + \\frac{37}{2928200} a^{17} + \\frac{13}{266200} a^{16} + \\frac{1}{133100} a^{15} + \\frac{3811}{96630600} a^{14} + \\frac{1101}{2928200} a^{13} - \\frac{1}{2928200} a^{12} - \\frac{557}{798600} a^{11} + \\frac{94}{99825} a^{10} + \\frac{2143}{1756920} a^{9} - \\frac{1601}{798600} a^{8} + \\frac{5337}{266200} a^{7} + \\frac{1893}{24200} a^{6} + \\frac{61}{12100} a^{5} - \\frac{457}{72600} a^{4} + \\frac{19}{40} a^{3} + \\frac{79}{440} a^{2} - \\frac{137}{120} a - \\frac{8}{15} \\)', '\\( \\frac{29}{8052550} a^{19} - \\frac{1}{2196150} a^{18} - \\frac{43}{1756920} a^{17} - \\frac{1}{399300} a^{16} + \\frac{13}{798600} a^{15} - \\frac{757}{16105100} a^{14} + \\frac{677}{4392300} a^{13} + \\frac{6409}{8784600} a^{12} - \\frac{17}{79860} a^{11} - \\frac{519}{266200} a^{10} + \\frac{2188}{366025} a^{9} + \\frac{23}{39930} a^{8} - \\frac{21607}{798600} a^{7} - \\frac{677}{36300} a^{6} - \\frac{1363}{72600} a^{5} + \\frac{277}{12100} a^{4} + \\frac{421}{3300} a^{3} + \\frac{3329}{6600} a^{2} + \\frac{127}{300} a - \\frac{311}{200} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/2*a^5 - 1/2', '1/2*a^6 - 1/2*a', '1/10*a^7 + 1/5*a^6 + 1/10*a^5 + 1/10*a^2 + 1/5*a + 1/10', '1/10*a^8 + 1/5*a^6 - 1/5*a^5 + 1/10*a^3 + 1/5*a - 1/5', '1/10*a^9 - 1/10*a^6 - 1/5*a^5 + 1/10*a^4 - 1/10*a - 1/5', '1/660*a^10 + 27/110*a^5 + 11/60', '1/660*a^11 + 27/110*a^6 + 11/60*a', '1/660*a^12 + 1/22*a^7 + 1/10*a^6 - 1/5*a^5 - 1/60*a^2 + 1/10*a - 1/5', '1/7260*a^13 - 3/605*a^8 - 1/10*a^6 + 1/10*a^5 - 247/660*a^3 - 1/10*a + 1/10', '1/36300*a^14 - 1/36300*a^13 + 1/3300*a^12 - 1/3300*a^11 + 1/3300*a^10 - 124/3025*a^9 + 124/3025*a^8 + 27/550*a^7 - 27/550*a^6 + 27/550*a^5 + 1601/3300*a^4 - 1601/3300*a^3 - 49/300*a^2 + 49/300*a - 49/300', '1/798600*a^15 - 157/798600*a^10 - 10147/72600*a^5 - 89/600', '1/798600*a^16 - 157/798600*a^11 - 10147/72600*a^6 - 89/600*a', '1/8784600*a^17 - 1367/8784600*a^12 - 20707/798600*a^7 + 1/5*a^6 + 1/10*a^5 - 1939/6600*a^2 + 1/5*a + 1/10', '1/8784600*a^18 - 157/8784600*a^13 - 24667/798600*a^8 + 1/10*a^6 - 1/10*a^5 + 2191/6600*a^3 + 1/10*a - 1/10', '1/96630600*a^19 + 259/19326120*a^14 - 1/36300*a^13 + 1/3300*a^12 - 1/3300*a^11 + 1/3300*a^10 + 98357/8784600*a^9 + 124/3025*a^8 + 27/550*a^7 - 137/550*a^6 + 41/275*a^5 + 30643/72600*a^4 - 1601/3300*a^3 - 49/300*a^2 - 11/300*a - 19/300']}